Benjamin Tee https://benjamintee.github.io/projects/ Urban data science projects and visualisation. quarto-1.7.32 Sun, 27 Sep 2026 00:00:00 GMT Analysis of Singapore’s MRT/LRT passenger flows Benjamin Tee https://benjamintee.github.io/projects/Singapore-Rail-Network-Analysis/

1. Introduction

With the completion of the Circle Line (CCL) loop on 12 July 2026, Singapore’s MRT/LRT network currently spans just under 280km and will be progressively expanded to about 360km by the early 2030s. When completed, Singapore’s total rail length will exceed that of major cities such as Tokyo or Hong Kong today and will be comparable to that of London and New York1.

On an average weekday, this network successfully carries more than 3.6 million passenger journeys2. Demand is largely bimodal with the morning peak from 7am to 9am, and a broader evening peak between 5pm to 8pm.

Network science provides us with a useful set of tools to study this complex system and understand the patterns behind these flows. The graph model was built earlier conceptualising stations as nodes, tracks as edges, weighted by distance, journey time, and observed passenger flows from LTA’s tap-in/tap-out records in Aug 2026.

This article seeks to address three main questions: (a) where do passengers come from and where are they going, (b) which parts of the network carry this movement, and (c) which segments are most important in the network?

2. Where do passengers come from, and where are they going?

2.1 The daily rhythm

Daily passenger journeys have bimodal peaks. The morning peak (7-9 AM) is more compressed, likely a consequence of fixed school and office start times. The evening peak (5-8 PM) is heavier, and lasts longer over three hours instead of two. Between them sits a midday trough at roughly a third of peak volume. This pattern is broadly consistent across all MRT lines.

Figure 1: Average weekday journeys by hour of day. Use the dropdown to toggle journeys for each line.

2.2 Where do journeys begin and end?

Parsing the origin-destination data from LTA allows us to count the total entries and exits at each station during the AM and PM peak windows.

Stations with the most tap-ins and tap-outs, average weekday AM peak (07:00–08:59)
Busiest origins Busiest destinations
Station Lines Tap-ins Station Lines Tap-outs
1 Yishun NS 15,226 Raffles Place EW NS 29,811
2 Admiralty NS 14,156 Tanjong Pagar EW 17,109
3 Woodlands NS TE 14,152 Jurong East EW NS 16,794
4 Bukit Panjang BP DT 14,031 Novena NS 13,573
5 Sengkang NE SK 13,982 Outram Park EW NE TE 12,620
6 Tampines DT EW 13,963 Downtown DT 12,435
7 Serangoon CC NE 13,893 Kent Ridge CC 11,446
8 Sembawang NS 13,642 Orchard NS TE 11,175
9 Lakeside EW 12,499 Newton DT NS 10,820
10 Khatib NS 12,255 Bugis DT EW 10,591
Stations with the most tap-ins and tap-outs, average weekday PM peak (17:00–19:59)
Busiest origins Busiest destinations
Station Lines Tap-ins Station Lines Tap-outs
1 Raffles Place EW NS 36,838 Woodlands NS TE 24,102
2 Jurong East EW NS 28,141 Yishun NS 22,201
3 Tanjong Pagar EW 21,311 Serangoon CC NE 21,964
4 Orchard NS TE 19,071 Tampines DT EW 21,702
5 Bugis DT EW 18,379 Boon Lay EW 19,413
6 HarbourFront CC NE 17,557 Sengkang NE SK 18,834
7 Novena NS 16,849 Jurong East EW NS 18,595
8 Newton DT NS 16,124 Newton DT NS 16,100
9 Outram Park EW NE TE 15,991 Sembawang NS 16,078
10 City Hall EW NS 15,620 Bukit Panjang BP DT 15,853

Unsurprisingly, the busiest AM Peak journeys begin from residential towns such as Yishun, Admiralty, Woodlands and Sembawang along the North-South Line, with Sengkang, Tampines, Bukit Panjang and Lakeside following closely. Most AM Peak journeys end in the central business district and surrounding areas.

Passengers originate relatively evenly from residential areas, but flow is concentrated toward a handful of city centre destinations. Yishun, the top origin station, sends 15.2k passengers, only 24% more than tenth-placed Khatib (12.3k). In contrast, Raffles Place receives 29.8k passengers, 1.7 times the next highest destination station (Tanjong Pagar, 17.1k). Two destinations (Jurong East and Kent Ridge) are outside the centre but draw heavy AM Peak arrivals as a second commercial hub and a university-and-science-park cluster, consistent with decentralisation counter-flows.

By evening the pattern reverses. Eight of the ten busiest AM Peak destinations become the busiest PM Peak origins, with residential towns the top destinations. Jurong East and Newton are among the top 10 PM Peak origins and destinations, presenting themselves as two-way hubs rather than pure workplaces or residential areas.

2.3 How might we characterise stations?

Plotting tap-ins / tap-outs illustrates (a) how busy a station is (total flows) and (b) whether the station sends or receives more people during AM and PM peak hours.

The spatial distribution of origin (sending) and destination (receiving) stations is visible in Figure 2. During AM Peak, the direction of travel is mainly toward the central areas, with some stations like Newton and Clementi having large but balanced bidirectional flows. During PM Peak, the pattern flips, as evidenced by the color swaps with passengers mainly moving out of the central areas toward residential towns. Newton, Paya Lebar and Clementi have large but balanced bidirectional flows.

Figure 2: MRT stations by total flows (bubble area: tap-ins plus tap-outs) and direction (colour), average weekday AM peak. Net origins send at least 30% more passengers than they receive; net destinations receive at least 30% more than they send; balanced stations fall in between. The three busiest stations of each category are labelled.
Figure 3: The same stations in the evening peak, on the same scale and with the same thresholds.

3. Which stations and segments are the busiest?

3.1 Assigning flows and calculating throughput

Origin–destination records tell us where each journey starts and ends, but not the route taken in between. To fill this gap, we assume every passenger takes the fastest way — working it out using Dijkstra’s algorithm. Each journey is credited to every segment along its route, and to the station where it changes lines. Add these journeys up gives us the number of people along each segment.

To assess the ‘busyness’ of a station, we measure overall throughput — tap-ins, tap-outs and transfers, which reflects the number of people passing through. This has implications on platform crowding, safety and station design.

3.2 Busiest stations during AM / PM Peak

Looking at the data, interchange stations are the busiest, with transfers accounting for a large share of total passenger flows. The busiest interchanges have intersecting major lines (i.e. North-South (NS) and East-West (EW) lines).

Jurong East stands out with the largest total station throughput, reflecting its critical role in distributing passengers in Western Singapore.

Circle line (CCL) interchange stations also features prominently, reflecting the line’s orbital role in connecting passengers between lines.

  • AM Peak: Bishan, Serangoon, Paya Lebar and Buona Vista
  • PM Peak: Serangoon, Dhoby Ghaut and Paya Lebar

Thomson-East Coast (TEL) line interchange stations (e.g. Orchard, Woodlands) see relatively less transfers, but could grow in importance with emerging residential areas or as passengers become more familiar with transferring via these stations.

Busiest MRT stations by throughput, average weekday AM peak (07:00–08:59). Tap-ins and tap-outs come from the fare records; transfers are inferred from fastest-path routing and are an upper bound.
Station Lines Tap-ins Tap-outs Transfers Total % Trf
1 Jurong East EW NS 6,263 16,794 52,603 75,660 70%
2 Outram Park EW NE TE 3,035 12,620 50,209 65,865 76%
3 Raffles Place EW NS 775 29,811 17,847 48,432 37%
4 Bishan CC NS 10,538 3,483 30,198 44,219 68%
5 Serangoon CC NE 13,893 4,902 25,273 44,068 57%
6 Paya Lebar CC EW 5,046 8,898 20,994 34,937 60%
7 Buona Vista CC EW 2,833 10,128 20,796 33,757 62%
8 Bukit Panjang BP DT 14,031 5,658 12,903 32,593 40%
9 Dhoby Ghaut CC NE NS 1,940 5,408 24,252 31,600 77%
10 Woodlands NS TE 14,152 7,506 9,564 31,222 31%
The same measure in the evening peak (17:00–19:59).
Station Lines Tap-ins Tap-outs Transfers Total % Trf
1 Jurong East EW NS 28,141 18,595 68,645 115,381 59%
2 Outram Park EW NE TE 15,991 4,713 76,001 96,705 79%
3 City Hall EW NS 15,620 10,516 46,213 72,349 64%
4 Serangoon CC NE 11,284 21,964 32,324 65,572 49%
5 Dhoby Ghaut CC NE NS 10,833 7,777 41,764 60,373 69%
6 Paya Lebar CC EW 15,502 13,507 31,312 60,322 52%
7 Orchard NS TE 19,071 13,211 26,640 58,921 45%
8 Raffles Place EW NS 36,838 5,669 9,500 52,007 18%
9 Bishan CC NS 7,229 7,562 34,387 49,178 70%
10 Woodlands NS TE 11,565 24,102 12,815 48,482 26%

3.3 Busiest line segments

Segments along the North-East line consistently feature the most passengers.

During AM Peak, flows between Hougang to Kovan and Kovan to Serangoon are the highest before some passengers exit at Serangoon to switch to other lines. Nonetheless, overall load remains heavy through toward the city (i.e Woodleigh –> Potong Pasir –> Boon Keng –> Farrer Park –> Little India) before dissipating. More than 60,000 passengers travel through the busiest segment (Kovan to Serangoon), roughly equivalent to the capacity of 440 double decker buses!

The picture is consistent during PM peak, with heavy passenger flows away from the city on the North-East line. The Buona Vista–Dover–Clementi stretch also carries heavy evening flows westward, swelling at Buona Vista as passengers transfer from the Circle Line.

Figure 4: Track segments by peak-direction load, average weekday AM peak. Line width shows busier direction’s volume.
Busiest track segments by peak-direction load, average weekday AM peak (07:00–08:59). Direction shown is the busier of the two; peak share is that direction’s load as a fraction of the two-way total.
From To Line Peak direction Reverse Peak share
1 Kovan Serangoon NE 60,141 8,007 88%
2 Hougang Kovan NE 56,837 7,121 89%
3 Farrer Park Little India NE 56,159 7,359 88%
4 Boon Keng Farrer Park NE 55,144 6,848 89%
5 Woodleigh Potong Pasir NE 54,987 7,163 88%
6 Potong Pasir Boon Keng NE 54,809 7,005 89%
7 Serangoon Woodleigh NE 54,439 7,386 88%
8 Clementi Dover EW 53,265 17,860 75%
9 Ang Mo Kio Bishan NS 53,180 10,658 83%
10 Little India Dhoby Ghaut NE 52,880 7,187 88%
Figure 5: The same measure in the evening peak (17:00–19:59), on the same scale.
The same measure in the evening peak (17:00–19:59).
From To Line Peak direction Reverse Peak share
1 Little India Farrer Park NE 67,925 18,099 79%
2 Serangoon Kovan NE 67,100 17,355 79%
3 Dhoby Ghaut Little India NE 66,691 18,764 78%
4 Boon Keng Potong Pasir NE 64,474 16,591 80%
5 Potong Pasir Woodleigh NE 64,247 16,757 79%
6 Farrer Park Boon Keng NE 64,041 17,452 79%
7 Dover Clementi EW 63,624 32,243 66%
8 Buona Vista Dover EW 63,223 33,067 66%
9 Woodleigh Serangoon NE 63,042 17,130 79%
10 Kovan Hougang NE 62,328 15,866 80%

4. Which parts of the network are most important?

While Sections 2 and 3 show which stations and segments have the highest volume, passenger traffic alone does not define system criticality. A low-volume station may serve as a single point of failure between two major hubs, while a high-traffic station might have close substitutes. Network science provides several measures to evaluate topological importance and identify components that maintain system connectivity.

4.1 An overview of centrality measures

Betweenness centrality counts how often a station lies on the path between two others. A station with high betweenness is a broker: passengers pass through it on their way somewhere else, and if it closed, their journeys would have to be rerouted. Interchanges tend to score highly, but so do stations at structural pinch points, where a single stretch of track is the only connection between two parts of the network.

Closeness centrality measures how near a station is to everywhere else, on average. A station with high closeness is well placed — journeys from it reach the rest of the network quickly.

Both measures are built on shortest paths, so the results depend on how “shortest” is defined and which journeys are counted. We compute each three ways:

  1. Topological structure. Every stretch of track is equal, and the measures reflect the shape of the network.
  2. Weighted by travel time. The shortest path is the quickest one. Transfer penalties at interchanges are taken into account.
  3. Weighted by passenger demand. For betweenness, each pair of stations is counted by the number of journeys actually made between them, so a station scores highly when it lies on routes many people travel. Closeness has no meaningful demand-weighted form and hence we do not report the computations.

4.2 What the rankings show

Topological network. On the unweighted network, eight of the ten stations with the highest betweenness centrality are Circle Line interchanges (Buona Vista, Botanic Gardens, Bishan, Serangoon, MacPherson, Caldecott, Paya Lebar and Marina Bay). The Circle Line is orbital, crossing every radial line. In a network where every stop counts equally it offers the shortest way between any two lines without passing through the city centre. Outram Park tops the list as the meeting point of three lines on the edge of the central business district. Closeness tells a different story where the best-placed stations (Little India, Newton, Dhoby Ghaut, Rochor and Bugis) sit around the geographic centre of the network, a similar number of stops from everywhere.

Travel time weighted. Once paths are measured in minutes, stations near the city centre rise in ranking. Several Circle Line interchanges fall away from the top of the betweenness ranking. Serangoon and Bishan fall in rank, as routes that save a stop but cost a transfer lose their advantage. Chinatown climbs thirteen places. The closeness ranking shifts more significantly, the geographic centre gives way to the southern CBD, and three Thomson–East Coast Line stations with no interchange (Havelock, Maxwell and Great World) climb twenty or more places. On the newest line, running directly through the heart of the city, a station can reach much of the network quickly without changing trains. Dhoby Ghaut, despite serving three lines, slips five places. An interchange gives options, but come with a cost in transfer time. As such, a station near several interchanges, on a direct line, can outperform one that is itself an interchange.

Passenger demand weighted. Counting the journeys people actually make, Outram Park remains first, and Serangoon, Bishan and Buona Vista stay near the top. However, the rest of the list now features stations along corridors identified in Section 3. Dhoby Ghaut rises eleven places, City Hall twelve, and two ordinary stops with no interchange at all, Dover and Clementi, climb ten places each. They have no structural reason to rank highly, but sit on the single East-West Line corridor carrying the west’s AM Peak commute into the city, so a large share of all journeys pass through them. Closeness is not computed for this layer.

Top MRT stations by betweenness and closeness on the unweighted network, where every stretch of track counts as one step.
Betweenness Closeness
Station Lines Station Lines
1 Outram Park EW NE TE Little India DT NE
2 Buona Vista CC EW Newton DT NS
3 Botanic Gardens CC DT Dhoby Ghaut CC NE NS
4 Bishan CC NS Rochor DT
5 Serangoon CC NE Bugis DT EW
6 MacPherson CC DT Stevens DT TE
7 Caldecott CC TE City Hall EW NS
8 Paya Lebar CC EW Botanic Gardens CC DT
9 Marina Bay CC NS TE Clarke Quay NE
10 Little India DT NE Caldecott CC TE
The same measures with paths weighted by journey time, including interchange walking time and wait penalty. Change is the movement in rank from the structural layer.
Betweenness Closeness
Station Lines Change Station Lines Change
1 Outram Park EW NE TE – Outram Park EW NE TE ▲ 10
2 Buona Vista CC EW – Havelock TE ▲ 20
3 MacPherson CC DT ▲ 3 Chinatown DT NE ▲ 9
4 Chinatown DT NE ▲ 13 Maxwell TE ▲ 28
5 Paya Lebar CC EW ▲ 3 Great World TE ▲ 25
6 Bishan CC NS ▼ 2 City Hall EW NS ▲ 1
7 Marina Bay CC NS TE ▲ 2 Tanjong Pagar EW ▲ 12
8 Jurong East EW NS ▲ 6 Dhoby Ghaut CC NE NS ▼ 5
9 Serangoon CC NE ▼ 4 Orchard NS TE ▲ 5
10 Stevens DT TE ▲ 2 Raffles Place EW NS ▲ 3
Betweenness with each station pair weighted by its journeys, average weekday AM peak. Closeness is not shown as it has no meaningful demand-weighted form. Change is the movement in rank from the travel-time layer.
Betweenness
Station Lines Change
1 Outram Park EW NE TE –
2 Serangoon CC NE ▲ 7
3 Buona Vista CC EW ▼ 1
4 Dhoby Ghaut CC NE NS ▲ 11
5 Bishan CC NS ▲ 1
6 Jurong East EW NS ▲ 2
7 Little India DT NE ▲ 7
8 Dover EW ▲ 10
9 City Hall EW NS ▲ 12
10 Clementi EW ▲ 10

4.3 Three kinds of importance

The three layers broadly separate stations into three groups.

  • Important on every measure. Outram Park, Buona Vista, Bishan and Serangoon rank highly whether the network is judged by its shape, its speed or its usage. These are the stations where structural position and actual demand coincide, and where any disruption would be felt most widely.
  • Important by position, less intensely used. Botanic Gardens, Caldecott, MacPherson, Paya Lebar and Marina Bay, which are all Circle Line interchanges, matter in the structure of the network but drop out once demand is counted. They represent orbital connections the network has but does not yet fully rely on during the AM peak, routes that could absorb passengers diverted from a disrupted radial line.
  • Important by use, not position. Dover and Clementi rank lower on structure but high on demand. Their importance comes from the volume funnelled through them rather than from any unique place in the network. A corridor that carries heavy demand with few nearby alternatives is where a disruption would cause the most difficulty.

The contrast between the first and last groups is notable. While topology alone places emphasis on interchanges, actual demand shows that some of the stations the network relies on most are ordinary stops on busy single-line corridors.

MRT stations ranking in the top 10 on at least 3 of the five centrality measures. Btw = betweenness, Cls = closeness. Closeness has no demand-weighted form, so the maximum possible total is five.
Structure Travel time Demand
Station Lines Btw Cls Btw Cls Btw Total
Outram Park EW NE TE ✓ ✓ ✓ ✓ 4
Serangoon CC NE ✓ ✓ ✓ 3
Buona Vista CC EW ✓ ✓ ✓ 3
Dhoby Ghaut CC NE NS ✓ ✓ ✓ 3
Bishan CC NS ✓ ✓ ✓ 3
Little India DT NE ✓ ✓ ✓ 3
City Hall EW NS ✓ ✓ ✓ 3

5. Conclusion

My overall take is that the numbers mostly confirm what anyone who rides the MRT already feels. Each morning, passengers pour out of residential towns and converge on a handful of stations in the city centre, and each evening the whole pattern runs in reverse. The North East Line carries the heaviest of that tide, with trains far fuller in one direction than the other.

What surprised me most was how differently each station looks depending on how you measure its network importance. Measured by topology alone, the Circle Line interchanges stand out as the stations that knit everything together. Measured by how people actually travel, the spotlight moves to the busy radial corridors, including stations like Dover and Clementi that matter simply because so many journeys pass through them. Outram Park ranks near the top on almost every measure, with Buona Vista, Bishan and Serangoon close behind as the network’s most consistent brokers. These stations merit close attention from a resilience and reliability perspective.

There are limits to all this. The model assumes everyone takes the fastest route and is based on monthly aggregated data. But it does raise a question worth exploring next - what happens to these journeys when one of these key stations is disrupted? With the Circle Line loop now complete, it would also be interesting to see whether those orbital connections start carrying more of the load in the months ahead.

This article was written in tandem with coursework for the CASA0002 Urban Simulation module.

References

Barabási, A.-L. (2025) Network Science by Albert-László Barabási. Available at: http://networksciencebook.com/ (Accessed: September 10, 2026).
CNA (2026) “Blending form and function: A first look at 3 new MRT stations that will close the Circle Line loop - CNA,” Channel News Asia. Available at: https://www.channelnewsasia.com/singapore/circle-line-cantonment-price-edward-road-keppel-mrt-stations-first-look-6172836 (Accessed: September 10, 2026).
GeekforGeeks (2026) “Find Shortest Paths from Source to all Vertices using Dijkstra’s Algorithm,” GeeksforGeeks. Available at: https://www.geeksforgeeks.org/dsa/dijkstras-shortest-path-algorithm-greedy-algo-7/ (Accessed: September 10, 2026).
LTA (2015) “Train Station Chinese Names LTA data.gov.sg.” Available at: https://data.gov.sg/datasets/d_d312a5b127e1ae74299b8ae664cedd4e/view (Accessed: September 10, 2026).
LTA (2026) “LTA Dynamic Datasets.” Available at: https://datamall.lta.gov.sg/content/datamall/en/dynamic-data.html#Public%20Transport (Accessed: September 10, 2026).
NetworkX (2025) “NetworkX — NetworkX documentation.” Available at: https://networkx.org/en/ (Accessed: September 10, 2026).
OSM (2026) “Singapore/Rail Transport - OpenStreetMap Wiki.” Available at: https://wiki.openstreetmap.org/wiki/Singapore/Rail_Transport (Accessed: September 10, 2026).
URA (2026) “Master Plan 2025 Planning Area Boundary (No Sea) URA.” Available at: https://data.gov.sg/datasets/d_2cc750190544007400b2cfd5d7f53209/view (Accessed: September 10, 2026).

Footnotes

  1. Growing Singapore’s land transport network (LTA, 2026)↩︎

  2. More train rides taken in first half-year, but overall public transport use stays below 2019 levels, (ST, 2025)↩︎

]]> Networks Urban Simulation Resilience Complexity https://benjamintee.github.io/projects/Singapore-Rail-Network-Analysis/ Sun, 27 Sep 2026 00:00:00 GMT Network Models: Evaluating the resilience of the London Underground Network Benjamin Tee https://benjamintee.github.io/projects/Network-Models/

1. Objective

This analysis applies concepts in network science to evaluate the resilience of the London Underground. We examine the differences when we look at the network topologically and when weighted by observed passenger flows. The study then rounds off by simulating station closures, to identify which stations have the most significant impact on the network.

2. Background

Network science began with a puzzle about a city. In 1736, Leonhard Euler was asked whether one could cross all seven bridges of the Königsberg exactly once. His answer, that this depended not on the bridges’ lengths or the city’s layout, but on how the landmasses connected, established a founding insight of graph theory: structure alone determines what a system permits (Barnett, 2009).

The method is surprisingly simple. Represent a system as nodes joined by edges, and much of its behaviour becomes calculable. For a transit network, the translation is natural: stations are nodes, track between them edges. This gives a topological network, a map of connectivity, indifferent to distance or demand, which isolates what the system’s shape alone implies about where it is fragile.

But structure is only half the story. A station may sit at a critical junction and carry almost nobody while another may lie on an unremarkable stretch of line and move tens of thousands each morning. Attaching passenger volumes to edges produces a weighted network, shifting the question from how a system is built to how it is actually used.

Resilience can be further understood through the concept of centrality which asks the question “which nodes matter most”. Depending on the objective, a station might be important because many lines meet there, because a disproportionate share of journeys must route through it, or because it sits close to everywhere else.

3. Network Centrality Measures

Centrality measures (Newman, 2010) can be computed for the underground network as follows:

  1. Degree Centrality counts the number of direct connections a node has, reflecting its immediate prominence in the network. For a node v in graph G with N nodes, it can be represented as:

    where is the number of edges that are incident to and the denominator normalises by the maximum possible degree. Degree centrality identifies underground stations with the most number of direct line connections such as interchanges (e.g. King’s Cross St. Pancras station with six lines). High degree nodes are critical because they are the primary points of passenger transfer between lines. When a high-degree station fails, passengers lose multiple routing options.

  2. Betweenness Centrality measures how frequently a node lies on the shortest path between other node pairs. It can be represented as

    where is the total number of shortest paths between nodes and , is the number of those paths passing through node , and the condition indicates that is an intermediate node rather than an endpoint. Betweenness centrality identifies stations that act as ‘bridges’ or ‘brokers’ in the underground network where a disproportionate share of journeys must pass through to find the shortest route. They sit at structurally pivotal positions in the network geography and bridge between two otherwise weakly connected clusters. High betweenness centrality nodes are critical because their removal would force many passengers onto less efficient alternative routes or eliminate viable routes altogether.

  3. Closeness Centrality measures how close a node is to all other nodes in the network, based on the sum of shortest path distances. It can be represented as:

    where us the length of a geodesic path from to and is the mean geodesic distance from to , averaged over all vertices in the network. Closeness centrality identifies underground stations from which the entire network is most efficiently reachable which minimise expected travel time or transfers to any destination. From a resilience perspective, high closeness stations are crucial because their failure degrades network-wide accessibility most severely. When a high-closeness station closes, average journey lengths across the entire network increase substantially.

A quick visual of centrality measures

Figure 1: A quick visual of centrality measures

4.1 Topological Network

The topological measure of the network reflects the infrastructural view of the network with stations as nodes and connecting lines as unweighted edges. While this allows us to identify structurally important stations based on network position, it may abstracts away information (e.g. distance, passenger flows) that could matter more.

Table 1: Top 10 stations by degree, betweenness, and closeness centrality (topological network)
Degree Centrality Betweenness Centrality Closeness Centrality
1 Stratford 1 Stratford 1 Green Park
2 Bank and Monument 2 Bank and Monument 2 Bank and Monument
3 King’s Cross St. Pancras 3 Liverpool Street 3 King’s Cross St. Pancras
4 Baker Street 4 King’s Cross St. Pancras 4 Westminster
5 Green Park 5 Waterloo 5 Waterloo
6 Liverpool Street 6 Green Park 6 Oxford Circus
7 Oxford Circus 7 Euston 7 Bond Street
8 Waterloo 8 Westminster 8 Angel
9 West Ham 9 Baker Street 9 Farringdon
10 Earl’s Court 10 Finchley Road 10 Moorgate

4.2 Scenario Analysis - Topological node removal

To investigate the resilience of the topological network, we sequentially remove the highest ranked node (by each centrality measure) and evaluate the impact on the (a) number of connected components, (b) largest connected component, (c) diameter of the largest connected component.

Table 2: Structural metrics used to assess network degradation under sequential node removal
Metric What it measures What a change signals
Number of connected components How many separate sub-networks the system has fractured into. A value of 1 means every station remains reachable from every other. An increase means the network has broken apart: some stations can no longer be reached from others by tube at all.
Size of the largest connected component (LCC) The number of stations in the biggest remaining intact sub-network. A sharp fall means the removal has severed a substantial portion of the network, not merely trimmed its edges.
Diameter of the largest connected component The longest shortest path within that sub-network — the number of stops between its two most distant stations. An increase means journeys have become less direct: the network still holds together, but passengers must travel further to cross it.
Table 3: Sequential node removal ranked by degree centrality
Iteration Node Removed LCC Size No. of Components Diameter of LCC
0 — 401 1 36
1 Stratford 379 3 49
2 Bank and Monument 378 3 49
3 King’s Cross St. Pancras 377 3 49
4 Baker Street 374 4 49
5 Canning Town 360 6 50
6 Green Park 359 6 51
7 Earl’s Court 358 6 51
8 Waterloo 357 6 51
9 Turnham Green 356 6 53
10 Willesden Junction 337 8 59
Table 4: Sequential node removal ranked by betweenness centrality
Iteration Node Removed LCC Size No. of Components Diameter of LCC
0 — 401 1 36
1 Stratford 379 3 49
2 King’s Cross St. Pancras 378 3 49
3 Waterloo 377 3 49
4 Bank and Monument 376 3 49
5 Canada Water 375 3 55
6 West Hampstead 227 4 38
7 Earl’s Court 226 4 39
8 Shepherd’s Bush 196 5 37
9 Euston 173 6 38
10 Baker Street 170 7 48
Table 5: Sequential node removal ranked by closeness centrality
Iteration Node Removed LCC Size No. of Components Diameter of LCC
0 — 401 1 36
1 Green Park 400 1 36
2 King’s Cross St. Pancras 399 1 38
3 Waterloo 398 1 40
4 Bank and Monument 397 1 42
5 West Hampstead 396 1 50
6 Canada Water 226 2 38
7 Stratford 226 4 38
8 Earl’s Court 225 4 39
9 Shepherd’s Bush 195 5 40
10 Oxford Circus 194 5 40
Figure 1: Network degradation under sequential node removal, by centrality measure. Each removal targets the highest-ranked remaining node, with centrality recomputed after every step.

The results reveal differences in how each measure identifies vulnerable stations and the severity of degradation following removal.

Degree centrality targets the most connected interchange stations. Its effect on the largest component is gradual (337 stations retained after 10 removals), but it fragments the network more than either alternative, producing 8 separate components and stretching the surviving diameter furthest, from 36 to 59 stops. Removing well-connected hubs shears off peripheral branches without severing the core.

Betweenness centrality identifies broker stations lying on the greatest number of shortest paths. Early removals produce similar degradation to degree, but removing West Hampstead at iteration 6 cuts the LCC from 375 to 227 stations in a single step. The accompanying fall in diameter, from 55 to 38, is not an improvement: the network has shed its longest branches into separate fragments rather than becoming more compact. Broker stations are distinctive because they act as sole connectors between otherwise separate segments, so their failure causes disproportionate connectivity loss.

Closeness centrality targets stations that anchor overall network efficiency. Its first five removals leave the network entirely intact, with the diameter expanding steadily from 36 to 50 stops. Removing Canada Water at iteration 6 then collapses the LCC from 396 to 226 stations, showing that a network can absorb sustained degradation before failing abruptly.

These distinctions carry direct policy implications. High-betweenness stations (King’s Cross, West Hampstead, Euston) represent structural failure risks requiring contingency planning and route redundancy. High-closeness stations (Green Park, Waterloo, Bank and Monument) anchor system-wide efficiency, and their disruption warrants demand-management strategies even where connectivity remains intact. Betweenness centrality is the most operationally useful single measure for identifying catastrophic failure points, but it should be monitored alongside closeness centrality, which captures the slower degradation in journey times that fragmentation metrics miss entirely.

5.1 Weighted Network (Flows)

Table 6: Top 10 stations by weighted degree, betweenness, and closeness centrality (flow-weighted network). Betweenness and closeness use inverse flows as edge weights, so heavily used corridors are treated as shorter paths.
Weighted Degree Weighted Betweenness Weighted Closeness
1 Bank and Monument 1 Green Park 1 Green Park
2 Green Park 2 Bank and Monument 2 Westminster
3 Waterloo 3 Waterloo 3 Waterloo
4 King’s Cross St. Pancras 4 Westminster 4 Bank and Monument
5 Westminster 5 Liverpool Street 5 Oxford Circus
6 Liverpool Street 6 Stratford 6 Victoria
7 Euston 7 Euston 7 Bond Street
8 Stratford 8 Victoria 8 Liverpool Street
9 Victoria 9 Oxford Circus 9 Warren Street
10 Baker Street 10 Bond Street 10 Stratford

Attaching flows changes the picture substantially. Under weighted degree centrality, Bank & Monument (646,117) has the largest connection strength in passenger terms — a station’s importance now reflects how many people pass through it rather than how many lines meet there.

The shift is sharper for weighted betweenness, where Green Park (45,000) emerges as the most critical broker, followed by Bank and Monument (36,249) and Waterloo (31,444). Stratford, which topped the topological betweenness ranking, falls to sixth. Green Park’s rise makes operational sense: it sits at the intersection of the Jubilee, Victoria and Piccadilly lines, bridging three of the highest-flow corridors in central London. The weighted ranking concentrates almost entirely on Zone 1, reflecting that the most operationally significant brokers are those bridging the highest-demand corridors, not those that happen to lie on topological shortest paths.

Under weighted closeness, Green Park ranks first (95.98), with Westminster, Waterloo and Bank and Monument close behind. The scores are, however, tightly clustered. The top ten span less than 0.1%, which suggests both a well-connected Zone 1 core and that inverse-flow weighting compresses the distance scale enough to limit the measure’s discriminating power.

5.2 Scenario Analysis - Closure of Origin Station

Station-pair with largest Origin-Destination (OD) Flow

The largest single origin–destination flow runs from Waterloo to Bank and Monument, carrying 15,946 passengers during the AM peak. This reflects the intense commuter demand between the South Bank and the City of London during morning rush hour.

Closing Waterloo would affect
- 90,722 passengers in total
- 67,314 departing and
- 23,408 arriving.

These figures reflect AM Peak demand only (NUMBAT timeband 3), and are most applicable to peak commuter conditions. Waterloo’s role as a major South Bank terminus means its AM Peak outflows are particularly high relative to other periods. It should be noted that the OD flows represent direct station-to-station demand from the NUMBAT dataset (TfL, 2025a), distinct from the edge-level flow weights used in the weighted centrality analysis in Section 2.1, which were derived by assigning all OD demand onto shortest paths through the network.

Table 7: Top 10 origin–destination pairs by passenger flow (AM peak, Monday–Thursday)
Rank Origin Destination Passengers
1 Waterloo Bank and Monument 15,946
2 Waterloo Canary Wharf 8,085
3 Stratford Liverpool Street 6,946
4 London Bridge Canary Wharf 6,165
5 Victoria Oxford Circus 5,181
6 Canada Water Canary Wharf 4,030
7 Stratford Canary Wharf 3,875
8 Liverpool Street Farringdon 3,755
9 Finsbury Park Highbury & Islington 3,659
10 Canada Water London Bridge 3,202

Routing options for closure of origin station

If the origin station were closed, which station should passengers go to instead, and how long would it take them to walk there? These are questions network analysis can answer directly.

Candidate stations were first identified within 1,500 m Euclidean distance of the affected station.

Table 8: Stations within 1,500 m straight-line distance of Waterloo
Rank Station Straight-line distance (m)
1 Lambeth North 486
2 Southwark 649
3 Embankment 721
4 Westminster 841
5 Temple 891
6 Charing Cross 1,021
7 Blackfriars 1,244
8 Elephant & Castle 1,284
9 Covent Garden 1,306
10 Leicester Square 1,337
11 St. James’s Park 1,386
12 Borough 1,471

For each candidate, walking distance from Waterloo was computed as the shortest path on the OSMnx pedestrian road network. Assuming a walking speed of 1.3 m/s (“The Planning for Walking Toolkit,” 2020), this yields a walking time. Tube travel time was then added, based on the shortest path through the Underground network to the destination station. Two rankings follow: the closest station on foot, and the fastest overall journey.

Table 9: Alternative stations ranked by shortest total travel time
Rank Alternative station Walking time (min) Walking dist (m) Tube time (min) Total travel time (min)
1 Southwark 11.2 873 3.3 14.5
2 Embankment 12.4 965 4.6 17.0
3 Lambeth North 11.9 931 5.2 17.1
4 Temple 17.8 1,390 3.3 21.1
5 Westminster 16.0 1,251 5.7 21.7
6 Blackfriars 19.8 1,544 2.1 21.9
7 Charing Cross 16.8 1,314 5.2 22.0
8 Elephant & Castle 19.0 1,483 3.7 22.7
9 Borough 22.4 1,746 2.3 24.7
10 Covent Garden 20.7 1,613 5.2 25.9
11 Leicester Square 21.7 1,695 5.8 27.5
12 St. James’s Park 25.3 1,975 6.6 31.9

The fastest alternative journey runs through Southwark at 14.5 minutes.

Walking times across all candidates range from 11.2 to 25.3 minutes, so the burden of disruption falls unevenly depending on where within the station’s catchment a passenger begins.

Figure 2: Alternative boarding stations following Waterloo closure. Candidates lie within 1,800 m straight-line distance of the closed station, with walking routes computed on the OSMnx pedestrian network and journey times to Bank and Monument. The three fastest options by total travel time are highlighted; the second and third are effectively tied given the model’s flat tube-speed assumption.

6. Reflections and Limitations

Representing stations as nodes and the links between adjacent stations as edges is a simple but powerful concept. This enables the computation of network centrality measures that assess whuch stations carry most structural weight. The sequential removal of nodes reveals how much the network can lose before it fractures. Shortest-path algorithms show which viable alternatives are most efficient when a station closes.

Findings depend on whether a topological or weighted network view is adoppted. Stratford leads the topological rankings but falls to sixth once passenger flows are attached, while Green Park rises to first. Neither is wrong, they just describe different kinds of importance. A station can be structurally pivotal while carrying modest demand, or the reverse. For planning, that means taking into account both views when deploying resilience enhancement measures.

Some simplifications are worth noting. This model treats travel time as proportional to distance, setting aside dwell time at stations, service frequency and the cost of changing lines — which matters most where alternatives are separated by a minute or two. The removal experiment also assumes displaced passengers disappear, when in practice they redistribute onto neighbouring stations. Coupling the network structure to a demand-assignment model would capture that cascade, and would be a natural next step for further analysis.

This article was partially drawn from my coursework for the CASA0002 Urban Simulation assignment.
Source code and data can be found here.

References

Barnett, J. H. (2009) “Early Writings on Graph Theory: Euler Circuits and The Königsberg Bridge Problem,” in Hopkins, B. (ed.) Resources for Teaching Discrete Mathematics. 1st ed. Mathematical Association of America, pp. 197–208. doi: 10.5948/UPO9780883859742.026.
Newman, M. E. J. (2010) “Measures and metrics: An introduction to some standard measures and metrics for quantifying network structure, many of which were introduced first in the study of social networks, although they are now in wide use in many other areas,” in Newman, M. (ed.) Networks: An Introduction. Oxford University Press, p. 0. doi: 10.1093/acprof:oso/9780199206650.003.0007.
TfL (2025a) “Crowding.data.tfl.gov.uk.” TfL. Available at: https://crowding.data.tfl.gov.uk/ (Accessed: April 20, 2026).
TfL (2025b) “FOI Reply - FOI-0318-2526,” Transport for London. Available at: https://www.tfl.gov.uk/corporate/transparency/freedom-of-information/foi-request-detail (Accessed: April 20, 2026).
“The Planning for Walking Toolkit” (2020).
Vries, J. de (2004) “Exponential or Power Distance-Decay for Commuting? An Alternative Specification.” doi: 10.1068/a39369.
Wilson, A. (1971) “A Family of Spatial Interaction Models, and Associated Developments,” 3, pp. 1–32. doi: 10.1068/a030001.
]]> Networks Urban Simulation Resilience Complexity https://benjamintee.github.io/projects/Network-Models/ Sun, 26 Apr 2026 00:00:00 GMT Investigating how transport connectivity shapes secondary school choice and access to opportunities across London Benjamin Tee Tabata Paredes Yujing (Olivia) Xing https://benjamintee.github.io/projects/Pathways-to-Progress/

Overview

This project examines how transport accessibility shapes access to high-performing secondary schools across London, and whether spatial disadvantage in school access reinforces broader patterns of socio-economic inequality. The analysis is presented as an interactive scrollytelling webpage — Pathways to Progress — combining travel time modelling, deprivation analysis and spatial clustering, visualised through Mapbox GL JS and Chart.js.

Live site can be found here!↗
Explore it below.

Research Questions

Main RQ: How does accessibility to high-performing secondary schools vary across London’s neighbourhoods, and to what extent does this reflect patterns of socio-economic disadvantage?

Sub-RQ 1 — Spatial Variation in Access: How does travel time to high-performing secondary schools vary across London by public transit, walking, and cycling — and where are the greatest disparities concentrated?

Sub-RQ 2 — Deprivation and Vulnerability: Is poor accessibility to high-performing schools systematically associated with neighbourhood deprivation, and where do pockets of compounded geographic and socio-economic disadvantage exist?

Datasets

Dataset Source Resolution Use
Secondary school register DfE Get Information About Schools School School locations, admissions policy, capacity
Ofsted inspection ratings Ofsted School School quality classification
Key Stage 4 results DfE National Statistics School Progress 8 and Attainment 8 scores
LSOA 2021 boundaries ONS Open Geography Portal LSOA Geographic unit for travel time analysis
GTFS transit feeds TfL, National Rail, DfT Route/stop Bus and rail schedules for transit routing
Index of Multiple Deprivation 2019 MHCLG LSOA IDACI and overall deprivation scores
Median household income (AHC) MHCLG / CACI MSOA Income estimates per neighbourhood cluster
National Travel Survey 2017–2024 DfT National/regional Mode share patterns for school travel
School capacity data (SCAP 2024) DfE School/borough Capacity utilisation by borough
OS Meridian 2 Ordnance Survey National Urban area masking for map layers
ONS Population Estimates ONS LA Secondary-age population by borough

Methodology

1. School Database (“build_schools_database.py”)

A comprehensive database of London secondary schools was compiled from the DfE’s Get Information About Schools register, supplemented with Ofsted inspection records and KS4 performance data. Schools were classified by admissions policy (selective vs. non-selective), Ofsted rating (Outstanding, Good, Requires Improvement, Inadequate), and performance quartile based on Progress 8 and Attainment 8 scores relative to all London schools. Top 25% thresholds were computed from this London-wide distribution to ensure comparability across boroughs.

2. Travel Context

Desktop research was conducted on school travel patterns for London children, drawing on DfT’s National Travel Survey (2017–2024) and published TfL school travel analyses. This established baseline mode shares — walking/cycling (~54%), transit (~24%), car (~19%) — and contextualised the policy landscape around school choice, travel barriers, and the geography of oversubscription.

3. Travel Time Matrix (“traveltimematrix.py”)

Transit feeds across London’s bus and rail network were compiled into an integrated GTFS feed. Using R5PY (a Python interface to the R5 routing engine), a travel time matrix was computed from each LSOA 2021 population-weighted centroid to all destination schools, segmented by school quality threshold (all schools, Ofsted Outstanding, Top 25% P8, Top 25% Att8) and travel mode (walk, transit, car). A Tuesday morning peak departure window (08:00–09:00) was used to reflect realistic school commute conditions.

4. Isochrones (“isochrones.py”)

Comparative isochrones were generated in R5PY for two contrasting locations — Clapham North (Lambeth) and Harold Hill (Havering) — to illustrate the stark difference in catchment accessibility between a well-connected inner London neighbourhood and a peripheral outer London estate. Isochrones were computed at 15, 30, and 45-minute thresholds by transit.

5. Spatial Layers and Processing

The travel time matrix was joined to the LSOA 2021 boundary layer. To focus the analysis on human settlements, layers were masked using OS Meridian 2 built-up area data, following O’Brien & Cheshire (2016). Boundaries were simplified using a 100-metre tolerance to balance visual continuity with file efficiency. Final layers were reprojected to WGS84 (EPSG:4326) and converted to .mbtiles using Tippecanoe, ensuring full geometric fidelity across all zoom levels for Mapbox integration.

6. Visualisation Stack

Maps were built in Mapbox GL JS, with dark-themed basemap styling applied programmatically to improve luminosity and contrast of choropleth layers and cluster boundaries. Charts were built in Chart.js. A scrollytelling architecture using Intersection Observer APIs drives map transitions, layer visibility, and stat counter animations in response to the user’s scroll position.

7. Deprivation Data

The Income Deprivation Affecting Children Index (IDACI) and overall IMD scores were extracted from MHCLG’s Index of Multiple Deprivation (2019) and merged to the LSOA 2021 geographic layer. Median household income after housing costs (AHC) was sourced at MSOA level and matched to each LSOA as a supplementary socio-economic indicator.

8. Bivariate LISA Clustering (“clustering.ipynb”)

A bivariate Local Indicators of Spatial Association (LISA) analysis was conducted using esda.Moran_Local_BV from the PySAL ecosystem, with transit time to the nearest Top 25% P8 school as the focal variable (X) and IDACI score as the spatial lag variable (Y). A K-Nearest Neighbours weight matrix (k=8) was used in place of Queen contiguity to avoid connectivity gaps introduced by the River Thames. LSOAs without a reachable school within the routing window were assigned a penalty travel time of 120 minutes. Statistical significance was assessed at p < 0.05 using 999 permutations. Clusters were classified into four quadrants: High-High (high travel time, high deprivation — the primary vulnerability indicator), Low-High, High-Low, and Low-Low.

9. Income by Cluster

Median household income after housing costs was matched from MSOA to LSOA level and aggregated by LISA cluster to produce a comparative income profile, contextualising the economic resources available to families in each cluster type.

10. Narrative and Interactivity

Analysis outputs were compiled into five webpage sections following a scroll-driven narrative structure. Interactive features — including cluster selection buttons, map highlight synchronisation, borough hover effects, and animated stat counters — were implemented using vanilla JavaScript Intersection Observer APIs to maintain a single-file architecture with no build step dependency.

Cartographic Design

Several cartographic principles guided the visual design of the webpage:

  1. Dark basemap: A custom dark Mapbox style reduces visual noise, allowing choropleth colours and cluster boundaries to dominate. Land, roads, and water were programmatically darkened to near-black to maximise luminance contrast with data layers.
  2. Colour semantics: Cluster colours follow an intuitive red-blue diverging scheme — red tones for high deprivation and high travel time (vulnerability), blue tones for low deprivation and low travel time (relative advantage), consistent with established cartographic conventions for disadvantage mapping.
  3. Opacity as emphasis: Layer opacity is used dynamically to direct attention: non-selected clusters dim to near-invisible when a cluster is chosen, focusing the reader’s eye on the highlighted group without removing spatial context entirely.
  4. Progressive disclosure: The scrollytelling format reveals complexity incrementally — beginning with city-wide patterns before zooming into specific clusters, boroughs, and household-level statistics — reducing cognitive load while building analytical depth.
  5. Luminosity and contrast: Off-white borough boundary outlines and bright cluster highlight borders provide high-contrast visual feedback on mouseover, supporting both aesthetic clarity and accessibility.

Webpage Architecture

The project is hosted as a static site on GitHub Pages. The entire application is contained within a single pathways_to_progress.html file, which embeds all CSS styling, JavaScript logic, chart data, and scroll behaviour inline. Map tile layers are hosted on Mapbox Studio as vector tilesets accessed via the Mapbox GL JS API at runtime.

This single-file architecture was a deliberate design choice. By embedding chart data, CSS tokens, and interactive logic directly in the HTML, the project eliminates module bundlers, and server-side dependencies allowing a fully portable, version-controllable page that renders identically in any modern browser without a development environment.

Map layers uploaded to Mapbox Studio include the LISA cluster fill layer, cluster outline layer for hover highlighting, and the LSOA travel time choropleth. Data for charts and summary statistics are embedded directly within the HTML to avoid additional HTTP requests and ensure the page loads as a single unit.

This approach achieves a practical balance between reliability — no external data endpoints to fail — and maintainability — all logic and content are co-located in one inspectable file, reducing risk of deployment errors.

This visualisation was submitted as part of a joint project for the CASA0029 Urban Data Visualisation module.
Source code and data can be found here.

References

  • Conway, M.W., Byrd, A. and van der Linden, M. (2017) “Evidence-Based Transit and Land Use Sketch Planning Using Interactive Accessibility Methods on Combined Schedule and Headway-Based Networks,” Transportation Research Record, 2653(1), pp. 45–53. Available at: https://doi.org/10.3141/2653-06.
  • Fink, C. et al. (2022) “r5py: Rapid Realistic Routing with R5 in Python.” Zenodo. Available at: https://doi.org/10.5281/zenodo.7060438.
  • O’Brien, O. and Cheshire, J. (2016) Full article: Interactive mapping for large, open demographic data sets using familiar geographical features. Journal of Maps. Available at: https://doi.org/doi:10.1080/17445647.2015.1060183.
  • Smith, D. (2023) “R5R Accessibility Workshop,” CityGeographics. Available at: https://citygeographics.org/r5r-workshop/
  • “tippecanoe: Builds vector tilesets from large (or small) collections of GeoJSON, FlatGeobuf, or CSV features” (no date). Available at: https://github.com/felt/tippecanoe

References

Newman, M. E. J. (2010) “Measures and metrics: An introduction to some standard measures and metrics for quantifying network structure, many of which were introduced first in the study of social networks, although they are now in wide use in many other areas,” in Newman, M. (ed.) Networks: An Introduction. Oxford University Press, p. 0. doi: 10.1093/acprof:oso/9780199206650.003.0007.
TfL (2025a) “Crowding.data.tfl.gov.uk.” TfL. Available at: https://crowding.data.tfl.gov.uk/ (Accessed: April 20, 2026).
TfL (2025b) “FOI Reply - FOI-0318-2526,” Transport for London. Available at: https://www.tfl.gov.uk/corporate/transparency/freedom-of-information/foi-request-detail (Accessed: April 20, 2026).
“The Planning for Walking Toolkit” (2020).
Vries, J. de (2004) “Exponential or Power Distance-Decay for Commuting? An Alternative Specification.” doi: 10.1068/a39369.
Wilson, A. (1971) “A Family of Spatial Interaction Models, and Associated Developments,” 3, pp. 1–32. doi: 10.1068/a030001.
]]> R5py Accessibility Inequality https://benjamintee.github.io/projects/Pathways-to-Progress/ Sun, 26 Apr 2026 00:00:00 GMT Constructing a Passenger-Flow Weighted Graph of the Singapore MRT/LRT Network Benjamin Tee https://benjamintee.github.io/projects/Singapore-Rail-Network/

1. Introduction

At its core, every rail network can be conceptualised as a graph — stations as nodes, tracks as edges. This simple conceptualisation yields significant analytical power through the mathematical and computational tools provided by the field of network science. It allows us to model how passengers navigate transit systems, spot hidden single points of failure, and stress-test disruptions before they occur in the real world.

The utility of this approach grows with what we embed in the graph. A purely topological graph captures basic connectivity and network structure. Incorporating distance between nodes introduces spatial routing. Adding travel times and transfer penalties captures frictions that shape passenger decisions. Finally, layering on actual passenger flows creates a realistic model of how the system is used day to day.

This technical annex builds that model layer by layer for Singapore’s rail system — mapping its topology, weighting it with travel times, and grounding it in observed passenger flows to produce a useful tool for investigation and analysis.

2. Data Ingredients

Here’s a quick overview of the data required to build this graph and why it is needed.

Source Dataset Role in the Graph
OpenStreetMap (Overpass API) Route relations, station sequences, track geometry Topological skeleton — nodes, edges, and physical edge lengths
Data.gov.sg Train station codes reference Ground truth for line codes; used to validate OSM topology & resolve interchanges
LTA DataMall GTFS Schedule (Train) feed Scheduled inter-station running times (stop_times, trips, calendar)
LTA DataMall Passenger Volume by Origin-Destination (PV/ODTrain) Hourly trip counts between station pairs by day type (demand matrix)
Reddit user u/catcourtesy Interchange transfer times dataset Platform-to-platform transfer times at all interchange stations
URA Master Plan 2025 Planning Area Boundary Geographic context for visualization only (not part of graph structure)

3. Building the Network Graph

Step 1: Constructing the topological skeleton from OpenStreetMap (OSM)

Each MRT/LRT line in OSM exists as a route relation, which is an ordered sequence of station stops with the way geometry connecting them. Specifically, we are interested in obtaining the coordinates of each station (nodes), the lines connecting each station (ways) and the order in which they are connected (relations). Parsing each route relation in order and stitching the resulting station sequence together produces the network’s raw topology, i.e. which station connects to which, and how far apart they are.

Understanding OSM data

OpenStreetMap models the physical world using three fundamental building blocks:

  • Node: A single point defined by latitude and longitude (e.g., a station entrance, signal light, or amenity).
  • Way: An ordered sequence of nodes that forms a line (e.g., a rail track segment) or a closed polygon (e.g., a station building).
  • Relation: A group that links nodes and ways to define complex systems (e.g., train route composed of multiple physical tracks and station stops).

To obtain the relevant data from OSM, the overpass API was queried for routes with the following tags (train, subway, light rail, monorail), within the Singapore area boundary. In total, after excluding the Jurong Regional Line, Sentosa Express and Airport Skytrain, 26 route relations covering the full MRT/LRT network were obtained.

Table 1: MRT and LRT route relations retained from OSM, by line and direction
System Line # Directions
MRT Circle Line 4 Anticlockwise Loop ↺ · Clockwise Loop ↻ · Dhoby Ghaut → Prince Edward Road · Prince Edward Road → Dhoby Ghaut
MRT Downtown Line 2 Bukit Panjang → Expo · Expo → Bukit Panjang
MRT East-West Line 4 Changi Airport → Tanah Merah · Pasir Ris → Tuas Link · Tanah Merah → Changi Airport · Tuas Link → Pasir Ris
MRT North East Line 2 Harbourfront → Punggol Coast · Punggol Coast → Harbourfront
MRT North-South Line 2 Jurong East → Marina South Pier · Marina South Pier → Jurong East
MRT Thomson–East Coast Line 2 Bayshore → Woodlands North · Woodlands North → Bayshore
LRT Bukit Panjang Line 2 Service A · Service B
LRT Punggol Line 4 East Loop ↺ · East Loop ↻ · West Loop ↺ · West Loop ↻
LRT Sengkang Line 4 East Loop ↺ · East Loop ↻ · West Loop ↺ · West Loop ↻
Total 26

Step 2: Validating sequences using LTA data on station locations

A map is only as good as it is accurate. Fortunately, OSM data in Singapore is pretty well-established, and the data accurately mirrors official sources, with the latest network improvements (e.g. closing of circle-line loop in Jul 2026). Station codes and sequences were checked against official data from LTA to derive the system map:

Comparing OSM station coordinates against official station centroids, the average difference of 30m across all stations is reasonably small, with the largest difference coming just under 200m. Pretty accurate! Now, we are ready to assemble the graph.

Table 2: Difference between LTA and OSM data for station centroids (Top 5)
Station Code Station Name Difference (m)
TE20 Marina Bay 196.1
DT32 Tampines 176.1
TE26 Marine Parade 138.7
DT19 Chinatown 124.2
TE2 Woodlands 122.4

Step 3: Assemble undirected graph with stations as nodes and tracks as edges

The graph is built with NetworkX, a Python library for creating and analysing networks. Each station code is stored as a node, placed at its OpenStreetMap coordinates. Stations that are consecutive stops on a route relation are joined by a track edge, which is weighted by the distance measured along the stitched line geometry, which gives the true track distance rather than a straight line. To account for interchanges,zero-length edges we addded between every set of nodes that share a station name. For example, each Dhoby Ghaut station on the Circle Line, North East Line and North South Line were retained, and connected to one another with zero-length edges to account for passenger transfers. These carry no distance, but are given a real travel time in Step 4.

The result is a single connected graph of 217 nodes and 249 edges covering the full MRT and LRT network. Plotting it allows us to check that everything is in order.

Figure 1: Singapore MRT/LRT network, stations coloured by line
Make this Notebook Trusted to load map: File -> Trust Notebook
Figure 2: Singapore MRT/LRT network, stations coloured by line

Step 4: Add on travel times using GTFS schedule for realistic routing

Travel times between stations

To accurately assign passenger flows, an objective measure of how passengers might likely travel, given an origin, and destination station is needed.

A suitable measure is the total travel duration of the trip. Passengers desire to minimise travel times to their destination, and naturally select the fastest route between origin and destination stations. Passengers intuitively refer to Google Maps or Citymapper to find the shortest time taken to get between A and B, and so this is a representative way to model passenger behaviour and choice. Other options include optimising for physical track distance or travel cost, but both feature less prominently in the decision-making process. Moreover, Singapore adopts a distance-based charging approach to ensure that passengers are charged based on their actual usage of the transport network, so the difference in prices between different routes to the same destination is minimal.

To obtain the travel times between adjacent stations in the network, we can tap on the unified GTFS schedule provided by LTA via DataMall. While this can simply be obtained through the station boards encountered at station platforms, the GTFS schedule provides travel durations specific to train schedules at different periods of the day, which enables more accurate modelling.

Travel time information commonly found on station boards. Source: SBS Transit
Understanding GTFS schedule data

GTFS (General Transit Feed Specification) is the standard format agencies publish timetables in. Two parts matter:

  • Routes and stops: A stop is a place passengers board, and a route is a named service (e.g. the East-West Line). A trip is one vehicle running that route once, and stop times record when it calls at each stop in order — so the station sequence comes from the timetable itself rather than from a map.
  • Schedules and frequencies: Departures are given either as explicit clock times for every trip, or as a headway — one trip every few minutes between set hours.

In Singapore, this data comes from LTA DataMall, which aggregates travel time information across the major operators SMRT and SBS Transit. The GTFS describes the planned timetable, not observed operation.

Time taken for interchange transfers

Another piece of information needed to construct an accurate network is the time taken for transfers at interchange stations. Singapore has approximately 30 train interchange stations. However, not all interchanges were built the same. Earlier ones like City Hall and Raffles Place were constructed with transfers in mind with platforms opposite each other or one short escalator ride away. Newer interchange stations like Bugis, Buona Vista and Woodlands require passengers to walk longer distances for connecting trains. Fortunately, we have this data courtesy of Reddit user u/catcourtesy, who measured each transfer timing between platforms of different lines by walking through the actual transfers. In reality, transfers also include the waiting time for the train on the next line. To account for this, 3 minutes were added on average for all transfers.

Shortest total travel duration

By combining travel time between stations and transfer times within interchange stations, a realistic graph network for the MRT/LRT system can be built. Dijkstra’s algorithm was applied to find the shortest path between two stations, which can then be used to derive the most rational route with transfers, and allocate passenger flows between origin and destination stations accordingly.

The table below shows an example of an optimal route taken between Tampines (DTL) and Bishan (CCL).

Shortest journey from Tampines (Downtown Line) to Bishan (Circle Line): 1 transfer, 11 stops, about 29.2 minutes.
Station Name Line Time (min)
DT32 Tampines Downtown Line 0.0
DT31 Tampines West Downtown Line 2.0
DT30 Bedok Reservoir Downtown Line 4.0
DT29 Bedok North Downtown Line 6.0
DT28 Kaki Bukit Downtown Line 8.0
DT27 Ubi Downtown Line 10.0
DT26 MacPherson Downtown Line 13.0
CC10 MacPherson Circle Line 17.2
CC11 Tai Seng Circle Line 19.2
CC12 Bartley Circle Line 21.2
CC13 Serangoon Circle Line 23.2
CC14 Lorong Chuan Circle Line 26.2
CC15 Bishan Circle Line 29.2
Table 3: Shortest journey from Tampines (Downtown Line) to Bishan (Circle Line): 1 transfer, 11 stops, about 29.2 minutes.

Step 5: Allocate Origin-Destination Passenger Flows

Next, we allocate the origin-destination (OD) passenger volume data. Data from LTA covers the number of trips between MRT stop pairs, where passengers tap in and out of the fare gantry. Trips are reported by hour and by day type — weekdays, and weekends/public holidays. Each OD pair’s trips are then assigned to the fastest path between its endpoints, and every edge along that path is credited with them.

For the purposes of this annex, Weekday AM peak (7–9am) flows were used from Aug 2026.

To visualise the flows, a graph of Singapore’s MRT and LRT system was plotted, with edge thickness corresponding to passenger flows during the weekday AM peak. Because the graph is undirected, each edge carries the combined load in both directions. On this measure, the heaviest loading sits on the East-West Line’s western approach, Jurong East to Clementi, Clementi to Dover and Dover to Buona Vista, followed closely by the North East Line through Hougang to Kovan and Kovan to Serangoon.

That ranking changes once direction is taken into account. The North East Line shows stronger tidal behaviour. Kovan to Hougang carries roughly nine times as much traffic inbound as outbound during the morning peak, against a little over three times on Dover to Buona Vista, possibly due to the counter-flows from Buona Vista’s employment cluster. Ranked by peak-direction load rather than two-way total, the North East Line segments move to the top.

Figure 3: Passenger link loads on an average weekday during the 7–9 AM peak. Line thickness is proportional to the number of trips whose fastest route traverses that segment; dotted lines are interchange transfers.
Table 4: Busiest track segments by combined two-way load, average weekday AM peak (07:00–08:59).
Busiest track segments by combined two-way load, average weekday AM peak (07:00–08:59).
From To Line Both ways Peak direction Peak share
Dover Buona Vista East-West Line 71,376 52,174 73%
Clementi Dover East-West Line 71,126 53,265 75%
Jurong East Clementi East-West Line 70,339 52,358 74%
Kovan Serangoon North East Line 68,148 60,141 88%
Hougang Kovan North East Line 63,957 56,837 89%
Ang Mo Kio Bishan North-South Line 63,838 53,180 83%
Farrer Park Little India North East Line 63,518 56,159 88%
Tiong Bahru Outram Park East-West Line 63,065 41,995 67%
Woodleigh Potong Pasir North East Line 62,150 54,987 88%
Boon Keng Farrer Park North East Line 61,993 55,144 89%
Table 5: Busiest track segments by peak-direction load, average weekday AM peak (07:00–08:59). Direction shown is the busier of the two.
Busiest track segments by peak-direction load, average weekday AM peak (07:00–08:59). Direction shown is the busier of the two.
From To Line Peak direction Reverse Peak share
Kovan Serangoon North East Line 60,141 8,007 88%
Hougang Kovan North East Line 56,837 7,121 89%
Farrer Park Little India North East Line 56,159 7,359 88%
Boon Keng Farrer Park North East Line 55,144 6,848 89%
Woodleigh Potong Pasir North East Line 54,987 7,163 88%
Potong Pasir Boon Keng North East Line 54,809 7,005 89%
Serangoon Woodleigh North East Line 54,439 7,386 88%
Clementi Dover East-West Line 53,265 17,860 75%
Ang Mo Kio Bishan North-South Line 53,180 10,658 83%
Little India Dhoby Ghaut North East Line 52,880 7,187 88%

Likewise, we can plot these flows corresponding to each hour of the day and see how the thickness of the edges vary. Notice how the flows change quite significantly with bimodal AM and PM peaks.

Figure 4: Weekday passenger link loads by hour of day.

This pattern illustrates the persistent challenge for infrastructure planners all around the world dealing with bimodal peaks. Capacity needs to be adequately provisioned for the heaviest direction in the heaviest hour, yet overall network usage remains noticeably lower for the rest of the day, often making it difficult to justify the disproportionate capital and operating expenditure needed to sustain a larger network. Addressing this challenge requires a concerted effort with a range of different measures such as staggered working hours, off-peak fare incentives, and careful land use planning that distributes trip origins and destinations more evenly across the network.

Now, we are ready to move on to deeper investigation and analysis.

This article was written in tandem with coursework for the CASA0002 Urban Simulation module.

References

Barabási, A.-L. (2025) Network Science by Albert-László Barabási. Available at: http://networksciencebook.com/ (Accessed: September 10, 2026).
CNA (2026) “Blending form and function: A first look at 3 new MRT stations that will close the Circle Line loop - CNA,” Channel News Asia. Available at: https://www.channelnewsasia.com/singapore/circle-line-cantonment-price-edward-road-keppel-mrt-stations-first-look-6172836 (Accessed: September 10, 2026).
GeekforGeeks (2026) “Find Shortest Paths from Source to all Vertices using Dijkstra’s Algorithm,” GeeksforGeeks. Available at: https://www.geeksforgeeks.org/dsa/dijkstras-shortest-path-algorithm-greedy-algo-7/ (Accessed: September 10, 2026).
LTA (2015) “Train Station Chinese Names LTA data.gov.sg.” Available at: https://data.gov.sg/datasets/d_d312a5b127e1ae74299b8ae664cedd4e/view (Accessed: September 10, 2026).
LTA (2026) “LTA Dynamic Datasets.” Available at: https://datamall.lta.gov.sg/content/datamall/en/dynamic-data.html#Public%20Transport (Accessed: September 10, 2026).
NetworkX (2025) “NetworkX — NetworkX documentation.” Available at: https://networkx.org/en/ (Accessed: September 10, 2026).
OSM (2026) “Singapore/Rail Transport - OpenStreetMap Wiki.” Available at: https://wiki.openstreetmap.org/wiki/Singapore/Rail_Transport (Accessed: September 10, 2026).
URA (2026) “Master Plan 2025 Planning Area Boundary (No Sea) URA.” Available at: https://data.gov.sg/datasets/d_2cc750190544007400b2cfd5d7f53209/view (Accessed: September 10, 2026).
]]> Networks Urban Simulation Resilience Complexity https://benjamintee.github.io/projects/Singapore-Rail-Network/ Sun, 26 Apr 2026 00:00:00 GMT Retail Location Optimisation via Spatial Interaction Modelling: A Case Study of the Borough of Havering Benjamin Tee https://benjamintee.github.io/projects/Spatial-Interaction-Models/

Objective

This study applies a production-constrained spatial interaction model to evaluate two candidate supermarket locations in the London Borough of Havering. A poisson log-linear GLM with exponential distance decay was calibrated using 80,604 customer trips across 775 local areas and 56 existing stores.

By comparing two potential sites, the model reveals that footfall was more sensitive to overall location and accessibility than store size, with Location A drawing 11% more predicted traffic than Location B due to its central reach, which widens if travel costs rise. However, Location B outperforms Location A in local walkability, with over 1,700 more residents living within a 15-minute walk. These results highlight the strategic tension in retail location analysis, forcing decision makers to weigh macro-level catchment against micro-level pedestrian accessibility.

2. Spatial Interaction Models

Spatial interaction models are used to predict flows (e.g. trips, trade, migration) between origins and destinations as a function of the characteristics at each location and the cost of travelling between them. The simplest gravity model, as formalised by Wilson (1971), assumes that interaction is proportional to the “mass” at each location and inversely proportional to the separation between them.

2.1 Introduction to Spatial Interaction Models

2.1.1 Unconstrained (gravity) model

The basic form is the unconstrained gravity model, where only total flows are conserved. This is commonly used in trade or migration modelling where neither origin nor destination totals are known in advance.

where is the predicted flow from origin to destination . and represent origin and destination parameters (e.g. population or jobs), and is distance or travel cost. is a deterrence or cost function that captures decay with either a power function or an exponential function , where is the distance decay parameter — a larger means people are much less willing to travel far. is a scaling constant, while and are elasticity parameters calibrated from data. governs how strongly origin size translates to flow generation, and models how strongly destination attractiveness influences flows. For example, a larger means larger stores draw disproportionately more people. When , the model reduces to the standard gravity form.

2.1.2 Production-constrained model

The production-constrained (origin-constrained) model imposes , ensuring total outflows from each origin match observed production through balancing factor . This specification is typically applied in retail location analysis and transport trip distribution, where the number of trips originating from each zone is known but destination choice is to be modelled.

2.1.3 Attraction-constrained model

The attraction-constrained (destination-constrained) model imposes , ensuring total inflows into each destination match observed flows through balancing factor . This specification is typically applied where destinations have fixed capacities, such as migration to cities with a fixed housing stock or hospital allocation with fixed bed counts.

2.1.4 Doubly-constrained model

Finally, the doubly-constrained model is used when both origin and destination totals are known. Both and must hold simultaneously, enforced by coupled balancing factors and . As both totals are fixed, the elasticities and are no longer free parameters and , enter linearly. Since and are mutually dependent, they are solved iteratively. This model is well-suited to commuting flows, where both residential population and workplace employment totals are known.

2.2 Fitting and Calibrating Spatial Interaction Models

The production-constrained model is adopted for this analysis, given that we know the residential population in each of the 775 Output Areas (OAs) in Havering, and wish to predict how these populations distribute their trips across 56 existing supermarkets (i.e. we don’t know destination totals). The attractiveness of each store can be measured by its floor area (m²), and the cost is the road network distance.

We test both a power and an exponential cost function to model deterrence.

Cost Function Formula Behaviour
Power (inverse) Slow initial decay, heavy tail. People occasionally travel far
Exponential Rapid decay. Interaction drops off sharply with distance

We specify the production-constrained model as a Poisson regression by taking logs of the right-hand side of Equation and assuming these are logarithmically linked to the Poisson-distributed mean () of the variable:

Here are origin fixed effects estimated for each OA, which absorb the balancing factor and directly enforce the production constraint for every origin exactly.

We obtain the regression outcomes in Table 1.

Table 1: Goodness-of-fit comparison: power vs exponential cost function.
Cost function γ (attractiveness) β (deterrence) β units R² RMSE
Power 0.114 0.076 dimensionless (elasticity) 0.1163 4.121
Exponential 0.116 0.000023 per metre 0.1168 4.120

Both models yield similar goodness-of-fit, with the exponential form marginally better. The low indicates that store size has only a modest effect on store choice. The low values indicate a relatively flat distance decay, meaning that people in Havering are more willing to travel, consistent with car-dependent suburban retail patterns. The of is modest but expected given the sparsity of the observed flow matrix.

Flow conservation is guaranteed structurally by the balancing factor , defined as:

which ensures that for all . This is confirmed empirically in Figure 1.

Figure 1: Flow conservation check - predicted total outflows per Output Area against observed totals. All 775 OAs lie on the 45° line, confirming the production constraint holds.

3. Scenario Analysis

3.1 Assessment of Two Candidate Supermarket Locations

Two candidate sites in the London Borough of Havering are evaluated. Location A (E00011326) is sited centrally, where population is more concentrated but competition is stricter. Location B (E00011710) sits at the Southern periphery with less surrounding competition (Figure 2). The site assessment is undertaken under two scenarios, each introducing a single new store into the destination set independently.

We undertake simulation for two store sizes () to evaluate the sensitivity of the results to store size.

The negative exponential cost function is adopted. Access to supermarkets is highly localized, as individuals exhibit strong sensitivity to distance when carrying purchases home, a pattern well-captured by the exponential form’s rapid spatial decay (devries2004?). Unlike the long-tailed power function, which overestimates the relevance of distant supermarkets, the exponential model better reflects routine suburban access constraints. This conceptual fit is confirmed empirically, yielding superior goodness-of-fit (, ) compared to the power model (, ).

The calibrated and are held fixed from the calibration stage; only is recomputed to accommodate the expanded destination set, with flow conservation verified after each run.

Summary of Results

Metric Small A Small B Large A Large B
Total flow (trips) 1,368 1,228 1,782 1,605
Mean weighted distance 4,397 m 8,819 m 4,391 m 8,743 m
Mean market share 1.72% 1.55% 2.25% 2.02%

Location A (E00011326) is the stronger investment in both scenarios. It attracts 11% more flow than Location B, as the exponential cost function penalises Location B’s peripheral position (mean customer distance ~4.4 km vs ~8.8 km for B). Location B (E00011710) sits on the southern periphery of the borough, where the surrounding population is sparse and most residents face longer distances to reach it.

We observe a modest size effect (). Scaling from to increases predicted flow by approximately 30%, consistent across both locations, as enters the model uniformly regardless of site.

One limitation is that only flows from within Havering are redistributed to the proposed supermarkets. In reality, Location B’s position on the southern boundary means that OAs outside Havering’s southern edge fall within its natural catchment but are excluded from the model, which may cause its predicted flows to be slightly underestimated relative to Location A.

Figure 2: Site assessment for both candidate stores. (a) Population density by Output Area with both candidate sites; (b) predicted flows from OA centroids to each proposed store; (c) trips diverted from existing stores, sized by store floor area. Panels b and c show each site introduced independently, not simultaneously.

3.2 Assessment of Sharp Increase in Transport Costs

Assuming a sharp increase in transport cost arising from a congestion and fuel surcharge, residents would be more reluctant to travel long distances. This could translate to a sharper distance decay function. We explore what happens when increases by 50% and 100%. The calibrated baseline per meter implies that a journey of 5 km is discounted by a factor of relative to a journey of zero distance. Doubling to increases this penalty to , meaning longer trips become meaningfully less attractive under the shock scenario.

The sensitivity analysis reveals an asymmetric response to transport cost increases. As increases by 50% and 100%, Location B’s predicted flows decline consistently across both size scenarios, while Location A’s flows increase marginally (Figure 3). This reflects the mechanics of the production-constrained model: as rises, the exponential decay penalises Location B’s peripheral position more severely, and the balancing factor redistributes those lost trips to closer alternatives. The mean weighted distance to Location A also falls slightly under higher (4,416 m → 4,379 m), confirming that its catchment becomes more localised and efficient under cost pressure.

Table 2: Predicted flows to the new store under increasing distance decay. Δ columns compare the 100% shock against baseline.
Scenario β (baseline) 1.5β 2β Δ vs baseline Δ %
Small A 1,382 1,389 1,395 +13 +0.9%
Small B 1,253 1,201 1,152 -101 -8.1%
Large A 1,796 1,805 1,813 +17 +0.9%
Large B 1,629 1,561 1,498 -131 -8.0%
Figure 3: Sensitivity of predicted flows to the new store under increasing distance decay. Colour and marker distinguish candidate site; opacity distinguishes store size. Gamma is held constant throughout.

Location A remains the recommended investment under the transport cost increase scenarios. Its relative advantage over Location B widens as costs increase. This finding is robust to the cost shock assumption.

3.3 Walkability Access within 15-min catchment

To determine walkability access to the proposed supermarket, we compute the number of residents whose Output Area centroid lies within a 15-minute walking catchment of each candidate location. We adopt TfL’s assumed walking speed of 1.3 m/s (TfL, 2025b), giving a maximum walking distance of:

We can use the road network distance from each OA centroid to the candidate store node, computed via OSMnx shortest path lengths, to determine which OAs fall within this threshold. Figure 4 illustrates the 15-minute walking catchment for each candidate site. The top row shows the accessible road network within 15 min for both locations and Output Areas that fall within. The bottom row shows the resident population as dot density within those same areas.

Figure 4: 15-minute walking catchment for each candidate site. An Output Area counts as reachable when its centroid lies within 1,170 m of the store along the pedestrian network. Top row: reachable streets and the qualifying Output Areas. Bottom row: resident population as dot density within those same areas.

Within a 15-minute walk, Location B serves a visibly larger accessible population (6,247 residents across 18 OAs) compared to Location A (4,517 residents across 13 OAs), as seen by the thicker dot density in Figure 4.

This reversal reflects an important distinction between local walking access and borough-wide trip attraction. Location B’s southern catchment, while peripheral in the context of Havering as a whole, sits within a relatively densely populated residential area at close road network distances. Location A, despite attracting significantly more predicted trips overall under the production-constrained model (1,368 vs 1,228 for the small scenario; 1,782 vs 1,605 for the large scenario), draws these trips from a wider, more dispersed catchment, reflected in its lower mean weighted distance of ~4,400 m, rather than a concentrated walkable neighbourhood.

The two metrics capture different accessibility dimensions. If the investment objective is to maximise immediate access for local residents, Location B has a marginal advantage. If the objective is to maximise total predicted footfall across Havering, Location A remains the stronger choice. Given that supermarket viability typically depends on total trip volume, Location A remains the recommended investment. Notwithstanding, Location B may better address a localised gap in pedestrian-accessible grocery provision in the southern part of the borough.

4. Reflections

Enabling data-driven decisions and judgment. Deciding where to locate a store often relies on experience and instinct. A spatial interaction model grounds that decision in evidence by evaluating population distribution, travel distance, and store attractiveness to project trip distribution. Rather than offering a qualitative preference, it produces a quantifiable benchmark—showing that Location A attracts roughly 11% more visits than Location B, and identifies the primary driver - customers traveling to Location B face double the average distance (8.8 km versus 4.4 km).

Three key findings emerged from the analysis:

  1. Floor space yields diminishing returns: A tenfold increase in store size yielded only a 30% increase in visits, demonstrating that prime location outweighs store size gains.

  2. Travel cost sensitivity: Higher travel costs widen Location A’s advantage, as rising transport friction forces shoppers to prioritize proximity over choice, disproportionately impacting the peripheral site.

  3. Walkability divergence: Location B reverses the overall ranking on foot, placing 6,247 residents within a 15-minute walk compared to Location A’s 4,517. Overall customer draw and pedestrian accessibility represent distinct policy goals.

Model limitations. The framework assumes a closed, fixed demand pool and cannot account for latent demand or trip frequency changes. Crucially, the borough boundary cutoff disadvantages Location B, which sits near the southern border and likely draws from neighboring catchments. Furthermore, using floor space as the sole proxy for store attractiveness overlooks brand equity, pricing, range, and parking, while assuming uniform distance decay across distinct transit modes.

Future directions. Refining the model could entail disaggregating travel modes, for example specifically separating motorists from pedestrians, to capture distinct spatial behaviors. Expanding the boundary beyond Havering would also eliminate edge-effect bias against Location B, while incorporating competitor density would contextualize Location A’s market environment. Finally, additional sensitivity incorporating a deterrance function using actual transport expenditure could also be studied.

This article was partially drawn from my coursework for the CASA0002 Urban Simulation assignment.
Source code and data can be found here.

References

Newman, M. E. J. (2010) “Measures and metrics: An introduction to some standard measures and metrics for quantifying network structure, many of which were introduced first in the study of social networks, although they are now in wide use in many other areas,” in Newman, M. (ed.) Networks: An Introduction. Oxford University Press, p. 0. doi: 10.1093/acprof:oso/9780199206650.003.0007.
TfL (2025a) “Crowding.data.tfl.gov.uk.” TfL. Available at: https://crowding.data.tfl.gov.uk/ (Accessed: April 20, 2026).
TfL (2025b) “FOI Reply - FOI-0318-2526,” Transport for London. Available at: https://www.tfl.gov.uk/corporate/transparency/freedom-of-information/foi-request-detail (Accessed: April 20, 2026).
“The Planning for Walking Toolkit” (2020).
Vries, J. de (2004) “Exponential or Power Distance-Decay for Commuting? An Alternative Specification.” doi: 10.1068/a39369.
Wilson, A. (1971) “A Family of Spatial Interaction Models, and Associated Developments,” 3, pp. 1–32. doi: 10.1068/a030001.
]]> Retail Optimisation Urban Simulation SIM https://benjamintee.github.io/projects/Spatial-Interaction-Models/ Sun, 26 Apr 2026 00:00:00 GMT Investigating The Holborn Escalator Paradox Benjamin Tee https://benjamintee.github.io/projects/Holborn-Escalator-Paradox/

Background

In 2016, Transport for London introduced a series of initiatives to reduce station crowding and improve safety on the Underground’s escalators. One of the more contentious was a trial at Holborn station. On selected escalators, walking was prohibited and passengers were asked to stand on both sides instead.

The reaction was not warm. The policy was described as “terrible”, “loopy”, “crap” and a “very bad idea”. Surely removing the option to walk would make things slower, not faster?

It didn’t. During rush hour, the trial found that 16,220 people could travel on Holborn’s 23.4m escalators under a standing-only regime, compared with 12,745 on escalators split between walkers and standers. Roughly a 30% improvement, achieved by asking people to do less.

The explanation lies in “escalator etiquette”, the deeply ingrained London convention of standing on the right and walking on the left. For the individual, this works well as those willing to walk move through the station faster than they otherwise would. But during peak periods the convention creates a structural imbalance. Queues build up at the foot of the escalator waiting to join the right-hand standing lane, while the left-hand walking lane runs well below capacity. The result is inefficient queueing, longer waits for the majority, and in some cases genuinely dangerous crowd dynamics in the concourse below.

So what actually drives this phenomenon, and why does encouraging standing yield higher throughput?

The Problem

Aggregate queueing models struggle with such questions, because the paradox is not a property of the escalator but a property of how individuals behave on it. The mechanism lives at the level of the person deciding which lane to join and how long to tolerate waiting before giving up on their preference.

Agent-based modelling is well-suited to study this. By treating individuals as autonomous “agents” following specific assigned rules, ABMs can be used to study bottom-up urban dynamics, pedestrian crowds, and the emergent patterns that arise from many simple interactions. Nobody in the system is behaving irrationally, yet the collective outcome is worse than it needs to be, a micro–macro disconnect of the kind Schelling (1971) made famous.

This project seeks to reproduce the empirical patterns observed in the Holborn escalator paradox and, in doing so, to better understand the reasons behind these crowd dynamics and provide insight into improved crowd management.

Model Description

The model is documented below following a partial ODD (Overview, Design concepts, Details) protocol, the standard reporting convention for agent-based models.

Purpose and Patterns

The model investigates the Holborn escalator paradox: the counterintuitive finding that prohibiting walking on escalators increases overall throughput during peak hour.

The primary research question is:

How does the proportion of walking versus standing commuters affect escalator throughput, and under what conditions does a standing-only policy outperform a mixed-behaviour regime?

Two subsidiary questions follow from it:

  1. How does the ratio of walking to standing commuters affect total throughput (passengers per minute)?
  2. How does lane-switching discipline affect performance during periods of congestion?

The model is evaluated on its ability to reproduce two empirical patterns. The first is throughput inversion, documented during TfL’s 2015–2016 standing trial at Holborn, where a standing-only policy on a long escalator increased capacity by approximately 30% during peak hours. The second is queue formation asymmetry, where queues form disproportionately in the waiting area because of limited lane availability, while the walking lane retains unused capacity.

Entities, State Variables, and Scales

Entities. Two entity types populate the model. Commuters (turtles) represent travellers arriving via the Underground. The environment (patches) mirrors station infrastructure, with patch types covering spawn (entrance), concourse (waiting area), marshalling area (where agents jostle to board), escalator steps, and an exit zone.

Agent state variables.

Variable Type/Range Description
walk-preference [0, 1] Base probability of preference to walk or stand on the escalator
is-walking? Boolean Current behaviour state: walking or standing
walk-speed [0, 1] Actualised probability of taking an extra step per tick. 0 for standers; inherits walk-probability for walkers
walk-probability [0, 100] Global parameter defining the “cadence” of walkers — the likelihood a walker moves an additional patch beyond the escalator’s mechanical movement in a single tick
preferred-lane-x Integer {0, 1} x-coordinate of the agent’s target lane. 0 for Left (Standing), 1 for Right (Walking)
blocked-ticks Integer ≥ 0 Consecutive ticks the agent has been unable to advance; triggers lane-switching via the lane-discipline threshold
arrival-tick Integer ≥ 0 Tick at which the agent joined the demand pool, used to calculate total station time
agent-state String “approaching” | “queueing” | “on-escalator”

Patch state variables.

Variable Type/Range Description
patch-type String “escalator-left” | “escalator-right” | “boundary-rails” | “concourse” | “marshalling” | “background” | “exit-zone” | “spawn”
is-step? Boolean True if the patch is part of the escalator belt; used to validate movement logic
step-number Integer ≥ 0 Vertical index (0–59) of the step relative to escalator-bottom-y
dist-to-escalator Integer ≥ 0 Dijkstra cost value calculated during setup; shortest path distance to the escalator entrance
path-selected? Boolean Temporary flag used during Dijkstra computation to track visited patches

Scales. Each patch represents ~0.4 metres, the depth of a standard escalator step, and each tick corresponds to 0.533 seconds. These are not arbitrary: they are chosen so that the escalator advances exactly 1 patch per tick, equivalent to 0.75 m/s — the standard operating speed for London Underground escalators.

Behavioural speed then emerges on top of this mechanical baseline. Walkers attempt one probabilistic extra step per tick, so an agent at 100% walk-probability moves 2 patches per tick (1.5 m/s), while one at 50% averages 1.5 patches per tick (1.13 m/s). This stochastic treatment allows small random variations in movement, better reflecting real variation in human movement than a fixed walking speed.

Process Overview and Scheduling

The simulation runs for 13,560 ticks - 120 minutes at 113 ticks/min. It comprises a 30-minute warm-up, a 60-minute rush hour (08:30–09:30), and a 30-minute cool-down. Five submodels execute sequentially each tick:

  1. Arrival (submodel-arrival). During rush hour, commuters arrive via train batch into a demand pool at fixed intervals, then drain into spawn patches at 30 pax/tick to model platform exit bottlenecks. Each agent is assigned a walker/stander type and preferred lane based on pct-walkers, and receives an arrival timestamp used to calculate end-to-end wait time. Off-peak, agents arrive at 20 per minute.
  2. Approach (submodel-approach). Agents follow a channel-based distance field toward the escalator. Directional penalty terms applied across two Euclidean cost surfaces create angled corridors, separating standers leftward and walkers rightward. Agents move on an 8-connected grid and transition to “queueing” on entering the marshalling zone.
  3. Boarding (submodel-boarding). Queued agents, sorted by proximity then FIFO, attempt to board their preferred lane. Boarding requires the bottom N steps to be empty, where N is step-gap-stand or step-gap-walk. Under mixed policy, lane discipline prevents switching until the patience threshold is exceeded; under standing-only, both lanes are used freely.
  4. Movement (submodel-movement). The escalator advances all agents 1 patch/tick, processed top-to-bottom. Walkers attempt one probabilistic extra step. Agents are blocked only by same-lane occupants ahead of them.
  5. Exit (submodel-exit). Agents reaching the top are counted, their journey time recorded, and are removed from the simulation.

The model then updates global counters, including per-minute throughput and mean travel times. All transitions are synchronous within each submodel.

Initialisation

On setup, two escalator lanes are created (x=0 for standing, x=1 for walking) spanning 60 steps vertically and flanked by boundary rails. A tapered marshalling zone of 4 rows funnels agents toward the entrance, while a 25-patch concourse and 10-row spawn zone represent the wider station. The channel-based distance field is computed once at setup rather than each tick, keeping runtime manageable across long simulations.

Default parameters are exposed as sliders:

Variable Default Range
pct-walkers 40% 0–100%
escalator-length 60 steps 20–60 steps
batch-size 220 persons 100–300 persons
train-interval 2.0 min 1.0–3.0 min
step-gap-stand 2 steps 1–4 steps
step-gap-walk 3 steps 1–4 steps
walk-probability 66% 0–100%
lane-discipline 120s 0–300s
off-peak-rate 20 persons/min 10–30 persons/min

Input Data

The model does not read external data files; instead, its parameters are calibrated directly against published specifications and TfL’s own trial figures.

Escalator geometry was derived from London Underground specifications — 0.4m step depth, 0.75 m/s speed, ~24m height — which together yield the 1 tick = 0.533s conversion. Throughput benchmarks draw from the Holborn pilot report, where counter data showed ~80 pax/min per escalator at peak, with standing-only carrying ~3,250 passengers against ~2,550 under mixed behaviour during 08:30–09:30. Train headway data, at 2–3 minute intervals across the Piccadilly and Central lines, informed the batch arrival parameterisation.

Submodels

Figure 1 sets out the five submodels and their decision logic in detail.

Flowchart showing the five submodels — arrival, approach, boarding, movement, exit — and the decision logic within each.

Figure 1: Summary of submodels and decision process flow

Calibration. The empirical paradox emerged under the following parameter set:

Component Parameter Value / Description
Demand calibration Batch size 200–240 passengers
Train interval 2 minutes
Demand condition Slightly exceeds escalator capacity to induce queue build-up
Escalator dynamics Step-gap (standing) 2 steps per person → ~56.5 pax/min/lane
Step-gap (walking) 3 steps per person → ~37.7 pax/min/lane
Lane discipline 120s, to mirror social norming and allow a denser standing lane relative to the walking lane

Note the demand condition in particular: demand is set to slightly exceed escalator capacity. This matters, because the paradox is a congestion phenomenon. Below capacity, lane allocation barely registers; it is only once queues begin to build that an under-used lane becomes an expensive one.

BehaviorSpace experiments were then run across 5 iterations with different random seeds, with a simple average taken for key output variables.

Results

The mixed regime performs worst, confirming the paradox.

Two line charts showing average peak throughput and average journey time against batch size, comparing standing-only, mixed, and all-walking regimes.

Figure 2: Escalator performance analysis — throughput vs journey time

Standing-only conditions (0% walkers) maximise throughput at ~110 pax/min, as both lanes are fully utilised. Under mixed conditions (40% walkers), lane discipline concentrates demand into a single standing lane while the walking lane is under-used, reducing throughput to ~95 pax/min — the lowest observed. At 100% walkers, both lanes are used again, but the larger step-gaps that walking requires cap throughput at ~104 pax/min.

The journey time panel is arguably the more striking of the two. Under the mixed regime, average journey time climbs steeply with demand, exceeding 1,750 seconds at the highest batch sizes tested, while the same demand under standing-only conditions is absorbed with far less delay.

Lane discipline is the mechanistic driver of the paradox.

Two line charts showing throughput and journey time against lane discipline threshold, with the mixed regime degrading sharply as discipline increases.

Figure 3: Average peak throughput and journey times at different lane discipline thresholds

Varying how long agents tolerate waiting before abandoning their preferred lane produces the clearest result in the study. At low thresholds (30s), standers switch lanes to redistribute demand, achieving throughput near standing-only levels (~104 pax/min). At high discipline (300s), agents refuse to switch despite visible congestion, and throughput falls 14% to ~93 pax/min while travel times exceed 16 minutes.

Critically, performance under standing-only and all-walking regimes remains essentially invariant to this parameter. Lane discipline only degrades the mixed regime — which is precisely what identifies the mechanism. The paradox arises from asymmetric lane utilisation dictated by social norms, not from walking itself.

Click to see how the models perform below.

Discussion

TfL’s standing-only trial succeeds not because it eliminates walking, but because it eliminates the norm that prevents standers from using both lanes.

This reframing opens up a wider set of interventions than a blanket ban. If the binding constraint is social norming rather than walking speed, then measures that interrupt the keep-right habit specifically during peak congestion such as signage, floor markings, platform announcements and staff direction, might capture a substantial share of the same benefit without removing walking as an option during quieter periods. The model suggests the gains are available wherever lane-switching becomes responsive to congestion.

Methodologically, the model situates itself at the intersection of pedestrian flow simulation and cellular automata approaches to collective behaviour. It builds on foundational CA pedestrian models by Blue & Adler (2001) and Burstedde et al. (2001), which demonstrate that simple rule-based movement on grids can reproduce realistic crowd dynamics, and adapts methods from evacuation studies by Galea et al. (2016) and Filippidis et al. (2026) to construct a two-lane escalator with unidirectional flow and mechanical movement.

Where conventional queueing models assume homogeneous agents and steady-state arrivals, this ABM introduces behavioural heterogeneity — varying walking speeds, lane discipline, and switching behaviour — to examine how individual behaviours shape aggregate outcomes. Throughput emergence arises from decentralised decision-making, including the observed inversion under mixed behaviour. Agents pursue individual-maximising objectives by seeking the shortest route to the escalator given their preferences. Environmental sensing occurs via lane-clear checks and the channel-based distance field, while adaptation operates through patience-driven lane switching, allowing the walk/stand composition to evolve endogenously. Stochasticity enters through batch arrivals, spawn location, agent types, and probabilistic walking.

Limitations. The model assumes a homogeneous population in terms of mobility, with no luggage, no accompanying children, and no accessibility needs, which would affect both boarding gaps and lane choice in practice. Lane discipline is treated as a single global patience threshold rather than a distribution across individuals, and agents do not learn across repeated journeys, though in reality commuters adapt their behaviour over weeks of experience. Finally, the model represents a single escalator in isolation, whereas the Holborn trial operated within a wider station system where displaced demand has somewhere else to go.

View the full model in netlogo here.

This article was submitted as part of my Master’s coursework for the CASA0011 Agent-Based Modelling for Spatial Systems module.

References

Blue, V.J. and Adler, J.L. (2001) “Cellular automata microsimulation for modeling bi-directional pedestrian walkways,” Transportation Research Part B: Methodological, 35(3), pp. 293–312. Available at: https://doi.org/10.1016/S0191-2615(99)00052-1.

Burstedde, C. et al. (2001) “Simulation of pedestrian dynamics using a 2-dimensional cellular automaton,” Physica A: Statistical Mechanics and its Applications, 295(3–4), pp. 507–525. Available at: https://doi.org/10.1016/S0378-4371(01)00141-8.

Filippidis, L. et al. (2026) “Assessing the impact of rider-only escalator etiquette using agent-based modelling,” Safety Science, 196, p. 107064. Available at: https://doi.org/10.1016/j.ssci.2025.107064.

Harrison, C. et al. (2016) “Report on Holborn Pilot for Standing on Both Sides of Escalators.”

Galea et al. (2016) Investigating the Representation of Merging Behavior at the Floor—Stair Interface in Computer Simulations of Multi-Floor Building Evacuations (2016). Available at: https://doi.org/10.1177/1042391508095092.

Schelling, T.C. (1971) “Dynamic models of segregation,” The Journal of Mathematical Sociology, 1(2), pp. 143–186. Available at: https://doi.org/10.1080/0022250X.1971.9989794.

]]> ABMs Transport NetLogo Urban Simulation https://benjamintee.github.io/projects/Holborn-Escalator-Paradox/ Wed, 01 Apr 2026 00:00:00 GMT Modelling Intergenerational Transfers and Wealth Inequality Benjamin Tee https://benjamintee.github.io/projects/Intergenerational-transfers-wealth-equality/

1. Background

Economic inequality remains a persistent structural challenge. Piketty and Goldhammer (2014) document rising wealth inequality across advanced economies, driven by returns to capital exceeding economic growth. Geography plays a foundational role in shaping these dynamics. Krugman (1991) shows how spatial clustering of economic activity creates self-reinforcing regional inequality while Chetty et al. (2014) demonstrate that a child’s place of birth remains one of the strongest predictors of economic mobility in the United States. These findings suggest that spatial resource distribution can imposes structural constraints that individual ability alone cannot overcome. Understanding why inequality emerges and what sustains it is relevant for policymakers designing redistributive interventions.

Intergenerational transfers compound these effects. Nekoei and Seim (2023) find that inheritances may initially reduce inequality but reverse over time as wealthier heirs accumulate more while poorer heirs deplete transfers.

Because such dynamics are difficult to isolate using traditional econometric methods, agent-based models provide a useful alternative for examining path dependence and emergent inequality (Farmer and Foley, 2009). SugarScape (Epstein and Axtell, 1996) which was originally designed to simulate how complex social phenomena emerge from simple interactions among heterogeneous individuals competing for limited resources, offers a useful framework for investigating how geography and inheritance jointly influence wealth stratification.

2. Aim

This study investigates how spatial resource distribution and intergenerational wealth transfers shape inequality. Two NetLogo SugarScape models were adapted to examine these mechanisms separately. SugarScape 2 evaluates how resource concentration (1 peak versus 4 peaks) affects survivability and inequality within a single generation. SugarScape 3 introduces wealth and location inheritance to understand how intergenerational transfers interact with geography to amplify or dampen inequality over time. Inequality is measured in both using the Gini coefficient1.

3. Methods

3.1 Model Modifications

SugarScape 2 (Constant Growback) and 3 (Wealth Distribution) from the NetLogo Models Library (Wilensky, 1999a, 1999b) were modified to share a common 50×50 landscape and agent trait ranges.

Resource maps were generated programmatically with 1–4 symmetric hills, using concentric sugar rings (1-4) scaled to maintain approximately constant total sugar (~3,700). Agents were assigned random vision (1-3), metabolism (1–3) and initial endowment (10–25).

SugarScape 3 further introduces:

  1. Wealth Inheritance: An inheritance-rate (0–1) transfers a fraction of a dying agent’s sugar to offspring. Only agents above median wealth pass on sugar, simulating capital preservation opportunities available only to wealthier populations.

  2. Location Inheritance: An inherit-location? toggle allows offspring to spawn near the parent (within 3 patches) rather than at a random location.

Additional reporters were added to track inequality (Gini), wealth, survival, and mortality.

3.2 Key Assumptions

SugarScape 2 models within-generation competition without replacement. Agents compete for resources and die permanently when sugar reaches zero. With no replacement, the population declines.

SugarScape 3 introduces finite lifespans with max-age (60-80) and one-to-one replacement, maintaining a constant population. With inheritance-rate set to zero, each generation begins without accumulated advantage. Increasing inheritance-rate introduces compounding effects.

All experiments used 400 initial agents and 10 repetitions per parameter combination and 1,000 ticks. Both models assumed constant growback (1 sugar per tick up to patch maximum), without trade, and movement toward the highest visible sugar patch.

3.3 Experimental Design

Experiment 1 (S2): num-hills was varied from 1 to 4 (Figure 1) to examine spatial concentration effects.

Number of Hills (from 1 to 4) with total sugar held approximately constant

Experiment 2 (S3): inheritance-rate was varied at intervals of 0.25 between 0.00 and 1.00, with inherit-location? toggled on and off, holding geography constant with num-hills = 2. inheritance-rate was subsequently varied at intervals of 0.05 to explore tipping points.

4. Results

4.1 Experiment 1: Resource Concentration and Inequality (S2)

Figure 2 shows how Gini changes over time for each hill configuration. All configurations begin with Gini around 0.122 and rise sharply in the first 100 ticks as agents compete for resources and weaker agents die off. The trajectories then plateau. The 1-hill configuration reaches the highest final Gini (0.448), while the 4-hill configuration reaches the lowest (0.354), with 2-hill and 3-hill configurations falling in between.

Gini Over Time by Resource Concentration

With total sugar held constant, survival rates were similar across configurations, suggesting that resource geography affects wealth distribution rather than carrying capacity. Mean wealth increased from 959 in the 1-hill setup to 1,117 in the 4-hill setup.

Table1

4.2 Experiment 2: Inheritance and Inequality (S3)

The introduction of wealth and location inheritance reveals a complex, non-linear relationship between intergenerational transfers and wealth stratification.

4.2.1 Wealth Inheritance only

Figure 3 plots Gini trajectories under varying inheritance-rate (0.00-1.00) without location inheritance. At moderate inheritance-rate (0.25-0.50), the Gini is lower than the no-inheritance baseline, falling from 0.458 to 0.431 at inheritance-rate = 0.50. However, at higher inheritance-rate (0.75-1.00), the Gini rises sharply above the baseline reaching up to 0.551 at full inheritance-rate (1.00).

Gini Over Time by Inheritance Rate

This U-shaped pattern reflects two competing dynamics. Moderate inheritance acts as insurance where offspring of above-median agents receive a buffer that reduces the impact of unfavourable random traits, compressing wealth distribution. At higher inheritance-rates, larger transfers create persistent wealth differences where wealth compounds across generations faster than it dissipates. Mean wealth rises significantly from 35 at baseline to 183 at full inheritance-rate (Table 2). Death rate decreases monotonically from 9.6 to 7.5, with fewer starvation deaths as inheritance-rate increases.

Table2

4.2.2 Wealth and Location Inheritance

(Figure 4) shows that the U-shaped Gini pattern persists when location inheritance is added.

However, enabling location inheritance reduces inequality compared to wealth inheritance alone. At inheritance-rate = 0, simply allowing offspring to start near their parent’s location reduces the Gini from 0.458 to 0.396. Offspring of successful agents are born close to productive resource hills, reducing search cost and early starvation risk. Over successive generations, agents gradually optimise their positions, compressing the gini distribution from below.

Figure 5 traces this mechanism. Location inheritance primarily operates through improved mortality. Starvation deaths fall from 5,265 to 4,028 at inheritance-rate = 0 when location inheritance is added, allowing more agents to survive to old age rather than dying in resource-scarce areas.

At inheritance-rate = 1, the effect on mean wealth becomes dramatic, rising from 183 without location inheritance to 342 with it, indicating that inherited proximity to resource hills enables compounding that wealth transfers alone cannot achieve (Figure 6). However, this advantage narrows the gap at high inheritance rates as both conditions converge to similarly elevated Gini values (0.551 vs. 0.541 at full inheritance), as capital accumulation increasingly dominates spatial effects (Figure 7).

Gini Over Time by Inheritance Rate

Table3

Effect of Location Inheritance Across Metrics

Mean Wealth by Inheritance Rate

Gini by Inheritance Rate

4.2.3 Comparison between experiments

The experiments reveal that geography establishes a structural baseline range of inequality generated through spatial competition, within which intergenerational mechanisms operate.

At low to moderate inheritance rates (0.25–0.50), inequality falls below the spatial-only baseline as modest transfers buffer stochastic disadvantage and compress dispersion, even while mean wealth rises. Once inheritance rates exceeds a threshold (≥ 0.75), accumulation dominates and wealth compounds across generations faster than it dissipates. Inequality then surpasses the spatial baseline, reaching 0.551 at full inheritance without location persistence and 0.541 with location persistence.

While the Gini coefficient provides a consistent basis for comparison, it captures different structural forms of inequality. In SugarScape 2, inequality reflects competitive selection within a single generation, driven by spatial concentration and trait variation. In SugarScape 3a, the Gini captures the net effect of capital persistence and competitive selection. In SugarScape 3b, inequality becomes spatially embedded, reflecting intergenerational transmission of both capital and locational advantage. Thus, similar Gini values across experiments may reflect fundamentally different generative mechanisms.

5. Discussion

5.1 Wealth inheritance dynamics (Insurance vs Accumulation)

The results highlight the interesting dual-nature of wealth inheritance. At low levels, it functions as a social safety net, reducing the number of “stochastic deaths” caused by poor trait draws (e.g., high metabolism or poor location endowment). However, as inheritance-rate approaches 1.0, the system transitions into a dynastic regime. Wealth becomes less a signal of agent fitness (vision or metabolism) but of ancestral luck.

5.2 Location inheritance dynamics

Location inheritance amplifies these dynamics as a powerful wealth multiplier. At low levels, location inheritance reduces death rate with some improvement in mean wealth. But at higher levels, when agents inherit both sugar and proximity to resource hills, significant compounding sees mean wealth at full inheritance nearly double relative to the wealth-only condition. This mirrors structural advantages in real-world systems where the wealthy compound gains through passive proximity to opportunities over generations, while agents without such positional inheritance must perform with near-flawless efficiency to achieve comparable outcomes.

5.3 Limitations and Sensitivities

Several limitations constrain the generalisability of findings.

  • Constant Population: The model utilizes a one-to-one replacement system upon agent death (hatch 1). In real-world systems, birth rates often correlate inversely with wealth, which could create steeper inequality trajectories.

  • Static Resource Hills: In a more dynamic environment, resource depletion or shifting climates could force migration, potentially disrupting the “location inheritance” advantage.

  • Trait Sensitivity: The Gini trajectories are highly sensitive to the metabolism and vision ratio. If metabolism were increased relative to sugar grow-back rates, the “insurance effect” of moderate inheritance might disappear, as even a small inheritance would be insufficient to prevent risk of starvation.

  • Limitations of the Gini coefficient: While the Gini coefficient provides a consistent basis for comparing inequality across spatial and inheritance regimes, it captures only the dispersion of wealth at a given moment, and does not distinguish between inequality arising from competitive selection and that arising from dynastic persistence. In high-inheritance scenarios, measured inequality may resemble or even fall below spatial-only baselines, yet wealth becomes increasingly decoupled from agent traits and more dependent on inherited position. The Gini therefore detects distributional change but not the underlying mechanism generating it. Future extensions could incorporate mobility (e.g. Rank-Rank slope (Venator, 2015; Van Der Erve et al., 2024)) or lineage-based measures to better capture structural persistence.

6. Conclusion

This study shows that spatial resource distribution establishes a structural baseline for inequality, but intergenerational transmission shapes how that inequality evolves. In the absence of inheritance, inequality reflects spatial competition and trait-based selection. Introducing wealth transfers produces a non-linear effect where moderate inheritance reduces inequality by buffering agents against stochastic disadvantage, while high inheritance generates compounding effects that exceeds the inequality produced by geography alone. Location inheritance reinforces these dynamics by lowering survival risk near productive resource clusters and accelerating wealth accumulation.

These findings suggest that inequality is shaped not only by unequal access to space, but by mechanisms that allow advantage to persist and accumulate across generations. Policies aimed at reducing inequality must therefore address both spatial disparities in opportunity and the channels through which unfair wealth and locational advantages are transmitted.

Additional Diagrams

Screenshot of Netlogo Interface under Experiment 1 (S2)

Netlogo Interface under Experiment 1 (S2)

Screenshot of Netlogo Interface under Experiment 2 (S3)

Netlogo Interface under Experiment 2 (S3)

This article was submitted as part of my coursework for the CASA0011 Agent-Based Modelling for Spatial Systems module.
Source code can be found here (https://github.com/benjamintee/CASA_ABM_Assessment)
Netlogo models can be found here (https://github.com/benjamintee/CASA_ABM_Assessment/nlogo)

References

Chetty, R. et al. (2014) “Where is the land of Opportunity? The Geography of Intergenerational Mobility in the United States *,” The Quarterly Journal of Economics, 129(4), pp. 1553–1623. doi: 10.1093/qje/qju022.
Epstein, J. M. and Axtell, R. L. (1996) Growing Artificial Societies: Social Science from the Bottom Up. The MIT Press. doi: 10.7551/mitpress/3374.001.0001.
Farmer, J. D. and Foley, D. (2009) “The economy needs agent-based modelling,” Nature, 460(7256), pp. 685–686. doi: 10.1038/460685a.
Hasell, J. (2023) “Measuring inequality: What is the Gini coefficient?” Our World in Data. Available at: https://ourworldindata.org/what-is-the-gini-coefficient (Accessed: February 24, 2026).
Krugman, P. (1991) “Increasing Returns and Economic Geography.”
Nekoei, A. and Seim, D. (2023) “How Do Inheritances Shape Wealth Inequality? Theory and Evidence from Sweden,” The Review of Economic Studies, 90(1), pp. 463–498. doi: 10.1093/restud/rdac016.
Piketty, T. and Goldhammer, A. (2014) “The Metamorphoses of Capital,” in Capital in the Twenty-First Century. Harvard University Press, pp. 113–139. Available at: https://www.jstor.org/stable/j.ctt6wpqbc.7.
Van Der Erve, L. et al. (2024) “Intergenerational mobility in the UK,” Oxford Open Economics, 3(Supplement_1), pp. i684–i708. doi: 10.1093/ooec/odad064.
Venator, J. (2015) “Measuring relative mobility, part 1,” Brookings. Available at: https://www.brookings.edu/articles/measuring-relative-mobility-part-1/ (Accessed: February 24, 2026).
Wilensky, U. (1999a) “NetLogo Models Library: Sugarscape 2 Constant Growback.” Evanston, IL: Center for Connected Learning; Computer-Based Modeling, Northwestern University. Available at: https://ccl.northwestern.edu/netlogo/models/Sugarscape2ConstantGrowback.
Wilensky, U. (1999b) “NetLogo Models Library: Sugarscape 3 Wealth Distribution.” Evanston, IL: Center for Connected Learning; Computer-Based Modeling, Northwestern University. Available at: https://ccl.northwestern.edu/netlogo/models/Sugarscape3WealthDistribution.

Footnotes

  1. The Gini coefficient measures the inequality of a frequency distribution such as income or wealth levels (Hasell, 2023). A Gini coefficient of 0 reflects perfect equality, where all income or wealth values are the same. In contrast, a Gini coefficient of 1 reflects maximal inequality among values, where a single individual has all the income or wealth while all others have none.↩︎

]]> ABMS Intergenerational Transfers Inequality https://benjamintee.github.io/projects/Intergenerational-transfers-wealth-equality/ Sun, 01 Mar 2026 00:00:00 GMT Visualising Household Energy Costs in England Benjamin Tee https://benjamintee.github.io/projects/Visualising-household-energy-costs/

Overview

This visualization provides an interactive map on the spatial distribution of domestic energy consumption across England and Wales (2015–2024). By integrating average gas and electricity consumption data from the Department for Energy Security and Net Zero (DESNZ) with Energy Performance Certificate (EPC) distributions, this visualisation provides insight into possible consumption hotspots and energy efficiency standards in urban settlements. This adds to the discourse in urban science on local progress toward national net-zero targets and highlights areas where poor housing quality may correlate with a higher energy burden (e.g. peri-urban areas).

Open full screen ↗

The map has been clipped to urban areas to show how energy consumption relates to urban geography and settlement size and calibrated to provide a national overview and distribution and at a more local scale to understand specific trends. Interactive features such as a (a) toggle between electricity and gas consumption, (b) slider to show temporal changes, and (c) point-and-click function to illustrate trends and localised energy performance, provide the user opportunities to further investigate specific data aspects.

Point-and-click function with Chart.js provides opportunities for investigation

Figure 2: Point-and-click function with Chart.js provides opportunities for investigation

Technical Aspects

Data preparation

Mean energy consumption data at Middle Layer Super Output Area (MSOA) and Local Authority (LA) level from 2015 to 2024 were cleaned and joined to the latest available Census geographies for England and Wales (2021) using pandas and geopandas in Python. This timeframe was selected to provide sufficient temporal coverage for trend analysis whilst minimising data processing assumptions required to harmonise historical consumption data (pre-2015) with updated MSOA and LA boundary definitions. Similarly, data on EPC certificates from 2018-2025 were summarised for their respective MSOA and LA boundaries.

Data scales

To optimize for web performance, the following steps were undertaken in QGIS: - Spatial Filtering: Polygons were clipped to urban boundaries using OS Meridian 2 data, focusing analysis on human settlements and settlement size (O’Brien & Cheshire, 2016). Polygon areas smaller than 1.2km2 at LA level and 0.2km2 at MSOA level were removed to focus attention while providing recognisable features. - Generalization: Boundaries were simplified using an 80-meter tolerance to balance visual continuity with file size efficiency. - Performance: Final layers were reprojected to WGS84 (EPSG:4326) and converted to GeoJSON for Mapbox integration.

Cartographic Aspects

The map was created using Mapbox GL JS, with a dark-mode basemap. High luminosity data layers were used to improve contrast and retain visual hierarchy. A diverging colour scheme (tested for colour-blind accessibility) distinguishes between high and low consumption tiers, providing an intuitive sense of “energy intensity.”

Interactivity was used to improve user experience and provide insights: - Landing page: Introduces objectives and functions. - Exploration: Users toggle between fuel types and years via UI widgets, triggering real-time filter updates. - Feedback: High-contrast off-white highlight layer provides visual feedback on mouseover. Sidebar widget provides information on the average consumption values for the selected fuel type and year. - Deep Dive: The point-and-click function triggers popups containing dual charts. A line chart visualizes the 10-year consumption trend, while a horizontal bar chart compares localized EPC groupings against national averages, offering a benchmark of domestic energy efficiency.

Landing page to provide guiding instructions to user

Figure 3: Landing page to provide guiding instructions to user

Dropdown function to toggle fuel consumption type

Figure 4: Dropdown function to toggle fuel consumption type

Limitations and Future Improvements

Given limitations in functionality with the customisation of place-label colour in Mapbox Studio Standard basemap to improve contrast, an alternative basemap (Mapbox Dark v11) was chosen which allowed place labels to be brightened to improve legibility in higher-density areas. Future iterations could incorporate Ofgem price data and household income estimates to map “energy burden”, the percentage of household income spent on total energy cost, providing a more direct metric for urban social justice and policy intervention.

This article was submitted as part of my coursework for the CASA0029 Urban Data Visualisation module.
Source code: github.com/benjamintee/CASA_UDV_Assessment
The full visualisation can be found here

References

O’Brien O, Cheshire J, 2016, “Interactive mapping for large, open demographic data sets using familiar geographical features” Journal of Maps 12(4) 676–683

DLUHC (2025) Energy Performance of Buildings Data England and Wales. Available at: https://epc.opendatacommunities.org/.

Department for Energy Security and Net Zero (2025a) Electricity and gas consumption estimates at MSOA level. Available at: https://www.gov.uk/government/collections/sub-national-electricity-consumption-data.

]]> Energy Geospatial Visualisation https://benjamintee.github.io/projects/Visualising-household-energy-costs/ Thu, 05 Feb 2026 00:00:00 GMT Examining Differences in Household Energy Costs across England Benjamin Tee https://benjamintee.github.io/projects/Household-Energy-Costs/

Background

While headline energy prices have fallen since their 2022 peak, average household bills in England in 2025 remain roughly £600 above pre-crisis levels. What began as a short-lived shock has become a persistent strain on household budgets.

The persistent increase in energy prices reshapes what households can afford, and it does so unevenly. Because energy bills depend not only on regulated unit rates but on how much energy a home consumes and how efficiently it uses that energy, two households facing identical tariffs can end up with very different bills. Understanding who is most exposed, and why, is central to designing effective energy policy.

From shock to persistence

The sharp rise in energy cost in 2022 was driven by global wholesale gas prices and exacerbated by geopolitical shocks1. Since then, wholesale prices have moderated. The government’s Energy Price Guarantee (EPG) temporarily also capped household exposure at the height of the crisis2.

Yet, this has not returned household bills to pre-2021 norms. Latest estimates show that the energy price cap remains around £600 (45%) higher than before the crisis (Figure 1). Moreover, the cap is projected to rise again in the coming quarters3. While volatility has eased, prices have settled at historically high levels.

Energy Price Cap (Oct 21 - Apr 26)

This persistence places growing pressure on households. Average levels of energy debt and the number of households in arrears have risen sharply since 2021 (Figure 2), suggesting that many have been unable to absorb higher costs through behavioural adjustments or savings alone (Ofgem, 2025a).

Average debt levels and households in arrears have risen sharply

While the impact is most acute for lower-income households, higher energy costs are also squeezing the broad-middle. At least 15% of middle-income households now report struggling to heat their homes adequately (Tilly Cook, 2025). It is therefore unsurprising that energy costs remain at the top of public concerns. A March 2025 IPSOS UK survey4 found that close to nine in ten respondents (88%) were worried about the price households pay for energy — a figure unchanged since the height of the crisis (Figure 3).

Energy costs remain a major public concern in England

Exposure is uneven across England

Although household energy prices are nationally regulated, the costs households face are far from uniform. Average bills depend not only on prices, but on how much energy households consume and how efficiently their homes convert energy into power.

As a result, some households face persistently high energy costs because they live in larger, older or less efficient homes, rely on more expensive heating systems, or have limited scope to reduce consumption. These differences reflect structural characteristics of housing rather than short-term behavioural choices alone.

Figure 4 illustrates this uneven exposure by mapping average household energy costs across England. Higher costs are concentrated across much of the North and Midlands, and parts of the South Coast, while lower average costs are more common in parts of the Southwest and East. There is also substantial variation within regions and cities.

If tariff rates are broadly similar, why does its impact differ so sharply across households, and what does that imply for equitable energy policy?

Burden of energy costs across England

What drives differences in household energy costs?

To explore these drivers, we estimate a multivariate model that relates average household energy costs to building age and energy efficiency, dwelling characteristics, household composition and heating infrastructure, while controlling for regional differences. We aim to identify structural factors that are most strongly associated with high energy costs.

Results are summarised in Table 1. Three findings stand out.

  1. Housing energy inefficiency is a central driver of high costs. Areas with a higher share of energy-inefficient homes (EPC bands D-G), face significantly higher annual energy costs, even after accounting for income and other housing characteristics. Poor insulation and inefficient heating systems amplify the associated increase of high prices, meaning that households in these areas face higher costs even where incomes are comparable to better-insulated areas elsewhere.
  2. Housing form and household composition matter. Older and larger dwellings, detached housing and areas with more large households all face higher energy costs, reflecting greater baseline energy needs. These factors help explain why some higher-income areas still experience high absolute cost: higher incomes often coincide with larger, more energy-intensive homes.
  3. Income shapes households’ capacity to absorb energy costs rather than costs alone. Higher incomes are associated with higher energy consumption and higher costs, but they also provide greater financial resilience. In contrast, areas characterised by lower incomes have far less scope to accommodate rising costs, particularly where poor housing efficiency or heating systems push cost upwards.
Summary of Key Regression Findings
Structural factor (MSOA-level) Modelled change in annual energy cost (per HH)
+10pp share of households with 4+ people ≈ +£170
+10% increase in median floor area of homes ≈ +£65-75
+10pp share of EPC D–G homes ≈ +£50–65
+10pp share of detached homes ≈+£50-60
+10% increase in household income ≈+£50-55
+10pp share of pre-1945 housing ≈+£15-20

Note: Effects are indicative averages and reflect associations rather than causal impact.

These findings explain why financial pressure may extend beyond the lowest-income groups. A substantial share of middle-income households report struggling with energy bills not solely because they consume unusually large amounts of energy, but because structural features expose them to persistently high costs. In equity terms, households with similar incomes can face different energy pressures depending on where and how they live.

Why place still matters

Even after accounting for income, housing characteristics and heating systems, some spatial variation in energy costs remains. This variation persists after controlling for regional differences, indicating finer localised differences such as housing stock composition, settlement patterns that shape how households experience energy prices.

Using a geographically weighted regression, Figure 5 shows how the influence of income and energy efficiency vary across England. In some areas, higher incomes are closely associated with higher energy costs, reflecting consumption linked to larger or more energy-intensive homes. In others, income plays a much weaker role. In contrast, the cost penalty associated with poor housing efficiency is uneven, with inefficient homes driving higher cost in some places but less so in others.

Spatial heterogeneity in mechanisms driving household energy costs

Towards equitable policy: From relief to resilience

These findings point to several policy considerations:

  • The limits of blunt instruments: Universal subsidies are politically expedient and provide immediate relief, but they respond to price rather than to the structural factors that shape consumption. These measures treat symptoms, often subsidizing consumption for those who need it less, while failing to provide deep support for those in the most inefficient homes.

  • Efficiency as Long-Term Protection: Sustained investment in housing energy efficiency, such as insulation and heating upgrades, remains the most effective long-term defense against structurally high prices. This is especially critical in areas where poor housing stock imposes “efficiency penalties” on residents regardless of their income.

  • Emphasis on Place-Based Targeting: The spatial heterogeneity identified in this study suggests that national income thresholds alone are insufficient. To ensure support reaches those most exposed, policy must become “place-sensitive,” accounting for local housing conditions and structural vulnerabilities that income data alone might overlook.

As energy prices settle at a higher level, the challenge for policymakers is to go beyond smoothing volatility, to designing interventions that shape a more equitable and efficient an energy system.

Technical Appendix

1. Study Objectives

This study examines the structural drivers of domestic energy costs (electricity and gas) at the Middle Layer Super Output Area (MSOA) level in England. First, it identifies how housing characteristics, household composition, and heating systems are associated with variation in average annual household energy costs. Second, it assesses whether these relationships exhibit spatial dependence, indicating that some areas are systematically exposed to higher energy costs even after observable characteristics are controlled for.

The analysis is descriptive and explanatory rather than causal. By focusing on small-area averages, it highlights how nationally regulated energy prices translate into uneven local cost pressures through differences in housing stock, energy efficiency and household structure. The emphasis is on identifying structural sources of exposure and inequity, rather than estimating behavioural responses or causal treatment effects.

2. Data & Assumptions

2.1 Spatial unit analysis and data sources

MSOAs offer a balance between spatial resolution and data stability, avoiding the volatility associated with smaller geographies while preserving meaningful spatial variation. The table below summarizes variables retained in the preferred specification.

Variable Source Methodology & assumptions
Annual electricity consumption (kWh) Department for Energy Security and Net Zero (2025a) MSOA mean domestic electricity consumption per meter
Annual gas consumption (kWh) Department for Energy Security and Net Zero (2025a) MSOA mean domestic gas consumption per meter
Electricity & gas prices Ofgem (2024) National average price cap values (incl. VAT), Jan–Mar 2024
Annual energy cost (dependent variable) Author Electricity + gas consumption × unit prices + standing charges
Share of pre-1945 housing Valuation Office Agency (2021) Proxy for legacy housing inefficiency
Share of EPC D–G dwellings EPC Register, DLUHC (2025) Proxy for poor energy efficiency (2019–2025)
Median floor area (log) EPC Register, DLUHC (2025) Logged to address skewness
Median household income (log) Office for National Statistics (2024) Logged median household income at MSOA-level
Share of detached dwellings Office for National Statistics (2022a) Captures structural heat loss
Share of households with 4+ occupants Office for National Statistics (2022b) Captures household size
Heating type shares Office for National Statistics (2022c) Electric-only, solid/liquid fuels, renewable networks
Urban–rural indicator Office for National Statistics (2022e) Binary classification
Region Office for National Statistics (2022d) Region fixed effects

We assume that energy prices are nationally regulated and spatially uniform, reflecting Ofgem price caps. Spatial variation in observed energy costs therefore arises from differences in consumption, housing efficiency and heating systems rather than local price-setting.

2.2 Exploratory analysis of data variables

Exploratory analysis (Figure A1) highlights substantial right-skewness in electricity costs and total energy costs, driven by a subset of MSOAs with high electricity reliance and larger dwellings. As household income is also right-skewed, log-transformation is applied. Heating system variables are unevenly distributed across space but are retained, as they represent structurally distinct energy systems with implications for electricity demand and exposure to high prices.

Distribution of variables of interest

Exploratory plots of the dependent variable against key predictors (Figure A2) inform variable selection and specification.

Bivariate relationship between energy cost and key predictors

3. Methodology and Model Specification

3.1 Construction of energy costs

Annual household energy costs are constructed by combining MSOA-level average electricity and gas consumption with national unit prices and standing charges. Electricity and gas costs are calculated separately and summed to obtain total average annual energy cost per household.

3.2 Regression framework

Ordinary Least Squares (OLS) regression is used as the primary modelling framework, due to its transparency and interpretability. Coefficients are interpreted as marginal associations with average annual household energy costs. All models are estimated with heteroscedasticity-robust (HC1) standard errors.

The preferred specification is:

where i indexes MSOAs and γᵣ denotes region fixed effects.

Variables capture four structural dimensions:

  1. Housing age and efficiency (share pre-1945, share EPC D–G)

  2. Housing scale and form (log floor area, share detached)

  3. Household composition and income (log income, share 4+ households)

  4. Heating infrastructure (fuel mix indicators)

Multicollinearity is assessed using variance inflation factors and remains within accepted thresholds.

4. Regression Findings

Across all specifications, structural housing characteristics and household composition emerge as the primary drivers of variation in annual household energy costs.

  • A higher share of energy-inefficient dwellings (EPC D–G) and pre-1945 housing is consistently associated with higher energy costs, even after controlling for income and dwelling size. These effects remain stable across all model specifications, indicating that housing efficiency and age exert an independent influence on energy expenditure.

  • Dwelling size and housing type are also strongly associated with energy costs. Larger median floor areas and a higher share of detached housing are linked to higher expenditure, reflecting greater baseline energy demand.

  • Household composition also plays an important role. MSOAs with a higher share of households containing four or more persons exhibit substantially higher energy costs across all models, with this variable showing the largest coefficients throughout.

  • The inclusion of fuel mix variables materially improves explanatory power, with the adjusted increasing from to . Electric-only heating is associated with significantly higher energy costs, while solid and liquid fuels and renewables are associated with lower average expenditure.

  • Adding region fixed effects further improves model fit (final adjusted = ), likely capturing residual climatic variation and regional housing patterns, without materially altering the main coefficient estimates.

regression_table

Residual diagnostics (Figure A3) indicate satisfactory linearity and variance homogeneity, with mild right-skewness. Checks reveal a small number of high-cost MSOAs that tend to have larger dwellings and higher reliance on electricity.

Regression diagnostics dashboard

Variable VIF Plot Label
reg_North East 1.686154 Var_1
share_epc_DG 1.902158 Var_2
share_hh_4plus 1.927551 Var_3
reg_Yorkshire 2.067431 Var_4
reg_South West 2.071966 Var_5
reg_West Midlands 2.102305 Var_6
share_pre1945 2.106134 Var_7
urban_dummy 2.147526 Var_8
share_electric 2.224277 Var_9
reg_East of England 2.245763 Var_10
share_renewable 2.277739 Var_11
reg_North West 2.469844 Var_12
reg_South East 2.849354 Var_13
share_solid_liquid 3.225414 Var_14
share_detached 3.631050 Var_15
log_median_floor_area 3.815178 Var_16
log_income 4.066691 Var_17
share_low_central 4.577141 Var_18
reg_London 5.265254 Var_19

5. Investigating spatial dependence

Global Moran’s I tests on OLS residuals show positive spatial autocorrelation (), indicating that neighbouring MSOAs share some unobserved characteristics influencing energy costs.

5.1 Spatial Error Model (SEM)

To account for this, a Spatial Error Model (SEM) was estimated using maximum likelihood. The SEM identifies strong spatial correlation in the error term , consistent with possible omitted spatially structured factors such as housing typologies, retrofit histories or local infrastructure.

Spatial Error Model

Notwithstanding, the findings are robust: coefficient signs and magnitudes remain consistent with OLS estimates. This suggests that while spatially clustered unobserved factors influence energy cost exposure, core structural relationships are correctly specified.

5.2 Geographically Weighted Regression (GWR)

To further explore spatial heterogeneity in coefficients, Geographically Weighted Regression (GWR) was employed to examine how the impact of income and housing efficiency vary spatially. An adaptive bandwidth was selected via AICc.

GWR

Additional findings include:

  • Income-Driven Areas: Higher energy costs align with income, suggesting consumption-led demand.

  • Efficiency-Driven Areas: High EPC D–G coefficients indicate that poor housing quality drives costs regardless of household wealth.

While GWR reached an of 0.88, the elevated fit likely reflects GWR’s inherent local overfitting and results serve an exploratory purpose rather than a formal refutation of the global model’s performance.

6. Reflections and Limitations

6.1 Limitations

Several constraints qualify the findings above.

Area-level inference. The analysis operates on MSOA averages, so it cannot capture heterogeneity within areas. Two neighbourhoods with identical average costs may contain very different distributions of household circumstances, and relationships observed between area averages may not necessarily hold for individual households. Findings should therefore be read as identifying where structural exposure is concentrated, not which households experience it.

Behavioural adaptation is invisible. Observed consumption reflects energy used, not energy needed. Households that ration heating in response to cost appear in the data as low consumers, which cannot be disentangled from those in efficient homes with genuinely low demand. Under-heating is a documented response to affordability pressure, which means measured costs may understate exposure precisely where it is more acute.

EPC coverage and currency. EPC records are generated at points of sale, letting or new build rather than continuously, so coverage is uneven and skewed toward recently transacted stock. Records are sparser in rural areas and in stable owner-occupied neighbourhoods, and an EPC issued several years ago may not reflect subsequent retrofit work. The share_epc_DG variable is best read as a proxy for housing quality rather than a current census of it.

Metering and off-grid households. DESNZ consumption data is reported per meter rather than per household, which introduces error where properties share meters or hold multiple. More importantly, gas figures cover only gas-metered properties, so households off the gas grid which are concentrated in rural areas and reliant on oil, LPG or solid fuel, are absent from the gas component of the cost calculation, likely understating their true energy expenditure.

Temporal alignment. Consumption and price data are drawn from different reference periods, and prices are held at a single national cap value. The resulting cost estimates are therefore best understood as a consistent comparative index across areas rather than an accurate reconstruction of any particular year’s bills.

6.2 Reflections

The analysis reinforces that variation in energy costs across England is structural rather than incidental. Housing age, efficiency, dwelling size and household composition consistently explain more of the variation than income alone, and these relationships held across every specification tested, including after accounting for spatial dependence.

It also underlines that a nationally uniform price does not produce a uniform burden. Because the same tariff interacts with very different housing stock, the geography of energy cost tracks the geography of building quality more closely than it tracks the geography of income. This has practical implications for delivery, since housing stock is precisely the domain where local authorities and councils hold both knowledge and levers, through retrofit programmes, targeted efficiency schemes and local housing interventions that national income thresholds cannot replicate.

Methodologically, the exercise was a useful demonstration of the usefulness of spatial regression techniques. The Spatial Error Model served primarily as a robustness check with the persistence of coefficient signs and magnitudes under an explicitly spatial error structure giving more confidence in the core specification than OLS diagnostics alone could. GWR was an interesting exploratory instrument for asking where relationships differ rather than whether they exist. Its high local fit is a reason for caution rather than confidence, but the spatial patterning affirmed that income mattered more in some regions, efficiency in others, complementing the findings of the global model.

7. Annex: Additional Visualisation

Annex: How does energy cost and income vary across England

This article was submitted as part of my coursework for the CASA0007 Quantitative Methods (QM) assignment. Source code and data can be found here.

References

Advani, A. et al. (2013) Household energy use in britain: A distributional analysis. Institute for Fiscal Studies. doi: 10.1920/re.ifs.2013.0085.
Bolton, P. (2025) “Gas and electricity prices during the ‘energy crisis’ and beyond.” Available at: https://commonslibrary.parliament.uk/research-briefings/cbp-9714/ (Accessed: December 29, 2025).
Cornwall Insights (2025) “Bills Remain Stable But New Forecast Signals Increases in April.” Available at: https://www.cornwall-insight.com/press-and-media/press-release/bills-remain-stable-but-new-forecast-signals-increases-in-april/ (Accessed: December 29, 2025).
Department for Energy Security and Net Zero (2025a) Electricity and gas consumption estimates at MSOA level. Available at: https://www.data.gov.uk/dataset/ed629618-7b69-465d-8e0a-0546b1809fc7/electricity_and_gas_consumption_at_middle_layer_super_output_area_mlsoa_and_intermediate_geography_z (Accessed: December 27, 2025).
Department for Energy Security and Net Zero (2025b) MSOA estimates of properties not connected to the gas network. Available at: https://www.gov.uk/government/statistics/msoa-estimates-of-households-not-connected-to-the-gas-network (Accessed: December 22, 2025).
Department for Energy Security and Net Zero (2025c) Subnational electricity and gas consumption summary report 2024. Available at: https://www.gov.uk/government/statistics/subnational-electricity-and-gas-consumption-summary-report-2024/subnational-electricity-and-gas-consumption-summary-report-2024--2 (Accessed: December 27, 2025).
DLUHC (2025) Energy Performance of Buildings Data England and Wales. Available at: https://epc.opendatacommunities.org/ (Accessed: December 27, 2025).
Ipsos (2025) Almost nine in ten britons are concerned about energy prices. Available at: https://www.ipsos.com/en-uk/almost-nine-ten-britons-are-concerned-about-energy-prices (Accessed: December 22, 2025).
Office for National Statistics (2022a) Census 2021: Accomodation type (TS044). Available at: https://www.ons.gov.uk/datasets/TS044/editions/2021/versions/4 (Accessed: December 27, 2025).
Office for National Statistics (2022b) Census 2021: Central heating (TS017). Available at: https://statistics.ukdataservice.ac.uk/dataset/ons_2021_demography_household_size (Accessed: December 27, 2025).
Office for National Statistics (2022c) Census 2021: Central heating (TS046). Available at: https://statistics.ukdataservice.ac.uk/dataset/england-and-wales-census-2021-ts046-central-heating (Accessed: December 27, 2025).
Office for National Statistics (2022d) Regions (December 2022) Boundaries EN BFE. Available at: https://geoportal.statistics.gov.uk/datasets/ons::regions-december-2022-boundaries-en-bfe/about (Accessed: December 27, 2025).
Office for National Statistics (2022e) Rural/urban classifications - Office for National Statistics. Available at: https://www.ons.gov.uk/methodology/geography/geographicalproducts/ruralurbanclassifications/2021ruralurbanclassification (Accessed: December 27, 2025).
Office for National Statistics (2024) Income estimates for small areas, england and wales.
Office for National Statistics (2025) Public opinions and social trends, great britain. Available at: https://www.ons.gov.uk/peoplepopulationandcommunity/wellbeing/bulletins/publicopinionsandsocialtrendsgreatbritain/june2025 (Accessed: December 16, 2025).
Ofgem (2024) New energy price cap level for january to march 2024. Available at: https://www.ofgem.gov.uk/news/new-energy-price-cap-level-january-march-2024-starts-today (Accessed: December 22, 2025).
Ofgem (2025a) Debt and arrears indicators. Available at: https://www.ofgem.gov.uk/data/debt-and-arrears-indicators (Accessed: December 27, 2025).
Ofgem (2025b) Energy price cap explained. Available at: https://www.ofgem.gov.uk/information-consumers/energy-advice-households/energy-price-cap-explained (Accessed: December 27, 2025).
Oshan, T. M. et al. (2019) “Mgwr: A python implementation of multiscale geographically weighted regression,” ISPRS International Journal of Geo-Information, 8(6), p. 269. doi: 10.3390/ijgi8060269.
Prime Minister’s Office (2022) Government announces energy price guarantee for families and businesses. Available at: https://www.gov.uk/government/news/government-announces-energy-price-guarantee-for-families-and-businesses-while-urgently-taking-action-to-reform-broken-energy-market (Accessed: December 22, 2025).
Robinson, E. (2025) Energy bills and debt are rising yet again – here are three things that would help vulnerable households, The Conversation. doi: 10.64628/AB.9r55r7hns.
Tilly Cook, A. W. (2025) “Energy affordability: How to reduce bills for majority of households Joseph Rowntree Foundation.” Available at: https://www.jrf.org.uk/cost-of-living/energy-affordability-how-to-reduce-bills-for-majority-of-households (Accessed: December 29, 2025).
Valuation Office Agency (2021) Dwelling Ages and Prices - Geographic Data Service. Available at: https://data.geods.ac.uk/dataset/dwelling-ages-and-prices (Accessed: December 27, 2025).

Footnotes

  1. Russia-Ukraine War (Bolton, 2025)↩︎

  2. In Sep 22, then-Prime Minister Elizabeth Truss implemented the Energy Price Guarantee (EPG) to cap the typical UK household energy bill at £2,500 a year for the next two years (Prime Minister’s Office, 2022).↩︎

  3. Cornwall insights forecasts that the price cap for energy bills is expected to rise by 3.2% in 2Q26, to account for increases in network costs for electricity (Cornwall Insights, 2025).↩︎

  4. https://www.ipsos.com/en-uk/almost-nine-ten-britons-are-concerned-about-energy-prices↩︎

]]> OLS GWR Energy Inequality https://benjamintee.github.io/projects/Household-Energy-Costs/ Tue, 30 Dec 2025 00:00:00 GMT