PaperlayerView exact revision on arXiv

Source-linked AI summary

The Multilayer Temporal Network of Public Transport in Great Britain

Riccardo Gallotti, Marc Barthelemy

arXiv:1501.02159v1physics.soc-ph

TL;DR

The paper addresses the lack of a complete national-scale picture of public transport by integrating heterogeneous timetable sources. It constructs a weighted, directed, temporal multilayer network with explicit intermodal connections and distributes the resulting dataset in accessible formats. The dataset supports multimodal analysis of Great Britain’s transport system, while short bus traveltimes remain a major reliability limitation.

  • Problem

    Complete national-scale analysis of public transport is difficult because relevant information is distributed across heterogeneous sources and multimodal systems.

    Source: Background & Summary · p. 1

  • Method

    The authors integrate timetable data, correct inconsistent times, coarse-grain stops into multimodal areas, and encode rides and walking transfers as temporal multilayer-network edges.

    Source: Background & Summary · p. 1, Timetables correction · p. 3, Coarse graining procedure · p. 4

  • Results

    The resulting dataset represents Great Britain’s public transport as a weighted, directed, temporal multilayer network with geo-referenced nodes, travel-time weights, and ride events.

    Source: Data Records · pp. 6–7

  • Takeaways & Limitations

    The shared dataset provides a reusable basis for studying multimodal public-transport structure and time-respecting journeys across Great Britain.

    Source: Data Records · pp. 6–7, Multilayer aspects · p. 9

    Short bus traveltimes have low reliability because of imprecise source timetables, although their effect becomes less relevant for total journey times on longer trajectories.

    Source: Temporal aspects · p. 8

Abstract

from arXiv · show

Despite the widespread availability of information concerning Public Transport from different sources, it is extremely hard to have a complete picture, in particular at a national scale. Here, we integrate timetable data obtained from the United Kingdom open-data program together with timetables of domestic flights, and obtain a comprehensive snapshot of the temporal characteristics of the whole UK public transport system for a week in October 2010. In order to focus on the multi-modal aspects of the system, we use a coarse graining procedure and define explicitly the coupling between different transport modes such as connections at airports, ferry docks, rail, metro, coach and bus stations. The resulting weighted, directed, temporal and multilayer network is provided in simple, commonly used formats, ensuring easy accessibility and the possibility of a straightforward use of old or specifically developed methods on this new and extensive dataset.

Background & Summary

The paper addresses the difficulty of analyzing complex public-transport systems by integrating multimodal timetable data into a national-scale temporal multilayer network. It combines land, water, and domestic-air schedules, aggregates stops into multimodal nodes, and distributes the resulting data in accessible formats.

Motivation

  • Public-transport systems are difficult to manage and analyze because multimodal data cross organizational boundaries and require complex journey-planning services.The paper frames public transport as important for mobility, quality of life, fairness, air quality, and economic growth.Source: Background & Summary · p. 1

Integrated sources

  • The dataset integrates UK land and water timetables with all non-stop domestic-flight schedules to provide multimodal coverage at urban and inter-urban scales.Land and water data come from the NPTDR, while flight schedules come from Innovata for October 2010.Source: Background & Summary · p. 1, Original datasources · pp. 2–3

Multilayer representation

  • Each transport mode is represented as a separate layer, while hierarchical coarse graining aggregates stops into nodes that can participate in multiple layers.The procedure corrects NAPTAN grouping information and represents modal interconnections explicitly.Source: Background & Summary · p. 1

Temporal representation

  • Each ride is modeled as a directed temporal edge with departure and arrival events, travel-time weight, and a static minimum-travel-time counterpart.The temporal edge remains active during the trip, while the static network retains the minimum travel time among observed events.Source: Background & Summary · p. 1

Dataset scale

  • The resulting network covers six transport layers and provides geo-referenced nodes, multilayer edges, and approximately 130M weekly events for October 2010.The data are distributed using node-list, edge-list, and temporal-event files.Source: Background & Summary · pp. 1–2

Timetables correction

The timetable-cleaning and stop-aggregation workflow corrects inconsistent times and restructures heterogeneous stop records into spatially coherent interchange areas. It combines interpolation, distance thresholds, hierarchy rules, and special handling for airports and transport modes.

Timetables correction

  • Rail timetable errors marked by invalid zero strings are corrected by estimating missing arrival times from the preceding time and average travel times on the same connection.The procedure addresses erroneous values that can also represent valid midnight times.Source: Timetables correction · p. 3
  • Inconsistent stop times are temporally interpolated when possible, while events that cannot be repaired are excluded; the excluded fraction is negligible.For A-B-C trajectories, the total interval is split according to the Euclidean-distance ratio between consecutive segments.Source: Timetables correction · p. 3

Coarse graining procedure

  • Stop Points are organized into Stop Areas representing facilities or interchange points, then corrected because original areas can span distances of 10 kilometres or more.The procedure uses a maximal walking-distance parameter wd = 500 m to define consistent multimodal nodes.Source: Coarse graining procedure · p. 4
  • Area centers are recalculated from stop-point coordinates when existing centers fail the distance criterion, and bus stops outside the threshold are removed.Bus-only areas are iteratively pruned until their points fit within a radius wd/2.Source: Coarse graining procedure · p. 4
  • Airports sharing an IATA code are joined, while rail, metro, and ferry areas are merged using mode-specific distance thresholds.The rules also promote selected stop points or areas, absorb nearby lower-rank elements, and assign representative points and area codes.Source: Coarse graining procedure · p. 4
  • The workflow applies additional hierarchy rules for promotion, absorption, declassification, representative-point selection, and administrative area-code assignment.Rail areas use wd for merging, whereas ferry and metro areas use wd/2.Source: Coarse graining procedure · p. 4

Defining the network

Intermodal edges encode walking connections between transport layers, while temporal links preserve service availability at minute-level resolution throughout the week. The representation favors straightforward reading and reuse over memory minimization.

Intermodal connections

  • Inter-layer edge weights are walking times computed from average distances between points in two layers within the same interchange area.Distances are converted using a 5 km/h walking speed and include a one-minute minimum connection time.Source: Defining the network · p. 5

Temporal encoding

  • The temporal network represents whether links exist at each minute from Monday 00:00, directly translating the operating-day information in the source data.This choice does not optimize memory space but makes the dataset straightforward to read.Source: Defining the network · p. 5

Code availability

The dataset-generation workflow and source data are shared to support reproducibility and adaptation. It corrects timetables, aggregates stops, constructs links, computes travel times, and produces the final dataset format.

Code and inputs

  • The authors share Python 2.7 code together with the required NPTDR snapshot and Innovata flight timetables.The workflow is designed to reproduce the October 2010 dataset.Source: Code availability · p. 5

Workflow stages

  • The workflow first corrects rail timetables, then performs stop coarse graining, timetable correction, and intra-layer distance computation.The stops.py stage produces intermediate node, event, and intra-layer-edge files.Source: Code availability · p. 5
  • The links.py stage sorts events and computes minimum travel times for intra-layer edges.Its outputs feed the final-format stage.Source: Code availability · p. 5
  • The finalformat.py stage computes inter-layer travel times, corrects zero minimum travel times, and writes the final dataset format.The final output is built after the preceding correction and link-construction stages.Source: Code availability · p. 5

Configurability

  • Workflow parameters include walking distance, walking speed, flight connection times, minimum connection time, and the lower travel-time threshold.The same workflow can be applied to NPTDR data from 2004–2011.Source: Code availability · p. 5

Data Records

The dataset records a geo-referenced, directed, weighted multilayer transport network alongside temporal ride events. Its files use node, layer, edge, and compressed event-list representations.

Network structure

  • The network uses layers for transport modes, and the same node can appear once in each layer where it is present.Nodes are identified by nodeid and layerid, while layers have numerical identifiers and mode labels.Source: Data Records · p. 6

Metadata fields

  • Node records can link transport-network nodes to administrative metadata through area codes, while edge records can also include Euclidean distance in kilometres.The areacode links nodes to administrative-area information, and km records the origin–destination Euclidean distance.Source: Data Records · pp. 6–7

Edge records

  • Edges are directed and weighted, with intra-layer links joining nodes within a mode and inter-layer links joining modal copies of the same node.Each edge weight is the minimal travel time in minutes; origin and destination nodes and layers are listed explicitly.Source: Data Records · pp. 6–7

Temporal events

  • Each edge record can include temporal rides as successive pairs of start time and duration values.The events file lists the origin and destination node-layer pairs first, followed by t_i and dt_i values in minutes.Source: Data Records · p. 7
  • The events file uses variable-length comma-delimited rows rather than a standard CSV event list because edges have different numbers of events.This adjacency-list structure reduces the space required to store the approximately varied event sequences.Source: Data Records · pp. 6–7

NaPTAN and NPTG metadata

The dataset includes original NaPTAN and NPTG files plus field definitions for stops, groups, administrative areas, and travel regions. These files provide geographic, administrative, and regional metadata.

Source metadata

  • The dataset includes original NaPTAN and NPTG files and directs readers to the NaPTAN schema guide for their interpretation.The accompanying metadata files cover stops, groups, administrative areas, and travel regions.Source: NaPTAN and NPTG metadata · p. 7

Stop metadata

  • Stops.csv contains stop identifiers, geographic coordinates, names, locality information, transport-stop classifications, and record-management fields.Its fields include ATCOCode, coordinates, common names, locality hierarchy, stop types, registration status, and change information.Source: NaPTAN and NPTG metadata · p. 7

Group metadata

  • Groups.csv records group identifiers, names, types, geographic coordinates, and last-change information for grouped transport locations.The file includes GroupID, GroupName, Type, spatial-reference fields, longitude and latitude, and LastChanged.Source: NaPTAN and NPTG metadata · p. 7

Administrative metadata

  • Admin Areas.csv links administrative areas to names, Traveline regions, countries, ATCO codes, call-centre identifiers, and version dates.These fields support connections between transport locations and administrative or regional classifications.Source: NaPTAN and NPTG metadata · p. 7

Regional metadata

  • Travel Region.csv provides region names, primary, secondary, and tertiary URLs, issue dates, issue versions, and JW versions.Traveline Region ID is the linking field for the regional records.Source: NaPTAN and NPTG metadata · p. 7

Innovata LLC timetables

The dataset includes the original Innovata LLC timetable files to support reproducibility.

Reproducibility

  • The original timetable supplied by Innovata LLC is included to ensure dataset reproducibility.The timetable is provided as part of the dataset materials.Source: Innovata LLC timetables · p. 7

UKDOMESTICOCT10.csv

UKDOMESTICOCT10.csv contains domestic-flight timetable and operational fields for airports, routes, schedules, equipment, capacity, and operating frequency.

Flight timetable fields

  • UKDOMESTICOCT10.csv lists airline, origin, destination, distance, flight, stop, equipment, seat, terminal, and schedule fields.The file also records arrival flags and operating-day information.Source: UKDOMESTICOCT10.csv · p. 7

Schedule and capacity

  • The file includes departure and arrival times, block minutes, operating days, operations per week, and seats per week.These fields describe both flight timing and service frequency or capacity.Source: UKDOMESTICOCT10.csv · p. 7

Technical Validation

Technical validation is limited by dependence on transport-agency source data and the absence of independent datasets for direct technical validation. Statistical checks and time-respecting paths provide supporting evidence for dataset reliability.

  • Reliability depends largely on the spatial and temporal information supplied by transport agencies to the NPTDR.Source: Technical Validation · p. 8

Spatial aspects

The dataset’s spatial representation was checked against maps and expected geographic patterns, with reasonable node positions and layer-specific edge-distance ranges. Coarse-graining errors remain possible, but multimodal trajectories broadly agree with external route results.

  • Node positions and Stop Area centres were reasonable at approximately 500 m scale when visualized on satellite maps.The resulting coordinates produced sensible intra-layer distances and a distribution matching the imposed walking-distance constraint.Source: Spatial aspects · p. 8
  • Layer-specific edge lengths fell within reasonable ranges, including short Air edges mostly associated with local or low-capacity flights.Source: Spatial aspects · p. 8
  • Short-edge travel-time errors become less relevant for total trajectory times, with London path speeds showing a reasonable extreme of approximately 60 km/h over 500–750 m.Source: Temporal aspects · p. 8
  • Coarse-graining introduces unavoidable small errors, although major airports and stations were often correctly defined in the NaPTAN scheme.Source: Multilayer aspects · p. 8
  • Trajectories were similar over large portions to Google-derived routes when using the “less walking” option, despite deviations between data sources and routing choices.Source: Multilayer aspects · pp. 8–9

SUPPLEMENTARY INFORMATION

The supplementary analysis characterizes the network’s spatial, temporal, and speed distributions while identifying data-quality anomalies. It shows distinct geographic and modal patterns, alongside implausible speeds linked to very short travel times.

Spatial distributions

  • Bus nodes cover the largest geographic area, while Ferry and Metro nodes are concentrated in northern Scottish islands and large English urban areas.Source: Figure 3 · p. 11
  • Inter-layer distances are relatively uniform below 300 m, decay rapidly thereafter, and reach a maximum of approximately 2 km.The distribution is consistent with walking-distance constraints and larger facilities such as airports.Source: Figure 4 · p. 12
  • Bus and Metro edges are mostly shorter than 2 km, whereas Rail, Coach, and Ferry characteristic distances begin near 2 km, 5 km, and 10 km.Source: Figure 5 · p. 13

Temporal distributions

  • Air, Rail, and Bus minimal travel times reach approximately 2 h, Metro reaches approximately 20 min, and Ferry and Coach extend higher.Bus contains many one-minute minimal travel times, while timetable sparsity is especially visible for Air, Coach, and Ferry.Source: Figure 6 · p. 14

Speed distributions

  • Expected maximum speeds are approximately 350 km/h for Air, 60 km/h for Rail, and 15 km/h for Ferry and Bus, with anomalies in Metro, Coach, and Bus.Seven percent of Bus edges exceed 50 km/h and 1% exceed 90 km/h; these extremes are associated with very short travel times.Source: Figure 7 · p. 15

Temporal distributions

  • Events are distributed across the week in a daily urban activity cycle, with weekdays broadly similar and weekend schedules differing.Source: Figure 9 · p. 17

Speed distributions

  • Zero travel times were retained for some events to preserve temporal causality, allowing infinite speeds on individual edges.Source: Figure 10 · p. 18

Related papers

Loading 1501.02159v1…