User-based representation of time-resolved multimodal public

transportation networks

Laetitia Gauvin

in collaboration with Laura Maria Alessandretti and Márton Karsai

Calculation of shortest temporal pathsIntroduction

Structure and dynamics of transport networks studied as complex networks

- In opposition to other networks (Internet, collaborations, social networks ) :

transportation networks design and evolution are physically constrained

→ spatial networks

The embedding in a two dimensional space has important effects on the topological properties and consequently on processes which take place on the network

- Transportation networks are multimodal

Public transportation network data

Theoretical motivation : multimodal + spatiality

Pattern identification and efficiency of the system

Focus on commuters

Overview

GTFS datasets :

agency.txt

One or more transit agencies that provide the data in this feed.

stops.txt

Individual locations where vehicles pick up or drop off passengers.

routes.txt

Transit routes. A route is a group of trips that are displayed to riders as a single service.

trips.txt

Trips for each route. A trip is a sequence of two or more stops that occurs at specific time.

stop_times.txt

Times that a vehicle arrives at and departs from individual stops for each trip.

calendar.txt

Dates for service IDs using a weekly schedule. Specify when service starts and ends, as well as days of the week where service is available.

ParisStrasbourgNantesToulouse

trip_id arrival time departure time stop_id stop_sequence44000942075 16:10:00 16:10:00 4025388 144000942075 16:11:00 16:11:00 4025390 244000942075 16:12:00 16:12:00 4025392 344000942075 16:13:00 16:13:00 4025393 444000942075 16:15:00 16:15:00 4025394 5

Google Transit Feed Specification dataset

GTFS datasets

City Period Companies

Paris agglomeration Sep-Oct 2013 RATP (Bus, Metro, Tram, RER)/SNCF (RER,Train)

Toulouse agglomeration Sep-Oct 2014 Tisséo (Bus, Tram, Metro)SNCF (Train)

Nantes agglomeration Jan 2015 Semitain (Bus, Tram, Ferry)/SNCF (Train)

Strasbourg agglomeration Jan 2015 CTS (Bus, Tram)/SNCF (Train)

Datasets

Pre-processing : coarse graining / identification of the transfer nodes

For identifying the transfer nodes between different lines,

we do coarse graining of the nodes using transfer files

→ merging of the stops in walking distances

- transfer files

- parent station files

.

Paris 11850 → 4596

Strasbourg 1329 → 594

Nantes 3411 → 1035

Toulouse 5693 →

For matching the 2 datasets for each city (train + others), one identifies stops/stations present in both (i.e ”Gare du Nord” is both a RER station and a metro stop).

One uses a grid with step size of 0.25 Km (the typical distance between two bus stops), and assigns a cell for each of the train stations. Each train station was associated tothe closest RATP stops present in that cell or in neighbors cells, if there was one.

1913

Pre-processing : choice of a representative day

Schedule for several months (no perturbation due to traffic jam or system breakdown)

Selection of 4 weeks without school breaks or public holiday

One considers trips between 7AM and 10 AM to focus on commuters and average the system behaviour during these hours.

nodes : groups of stops/stationsEdges : connections between two stopsweights : average number of transits on the edge per day

A straightforward network representation

Nodes 4524 282 494Edges 9662 668 1292Density 4.10-4 4.10-3 2.10-3

Bus Metro Train

A straightforward network representation

Community detection on spatial networks : well ...

Motivationnal factors : car versus public transportation

Choice mainly affected by : - average travel time needed to commute

- weak variability of the total travel time

Less determinant factors : - travel cost - comfort

Asperges, T., Cornelis, E., Steenbergen, T. et al. Déterminants des choix modaux dans les chaînes de d éplacements. Résumé, Plan d’Appui scientifique à une politique de Développement Durable (PADD II), Partie 1 (2007).Le Jeanic, T., Armoogum, J., Bouffard-Savary, E. et al. La mobilit e des fran cais, panorama issu de l'enquête nationale transports et déplacements 2008. Paris: ministère de l' Ecologie, du Développement durable, destransports et du Logement (2010).

Representation of the network :

- privileging such determinants

- reducing effects due to spatial embeddedness

P-space multiedge representation

Combination of a graph multi-edge and P-space representations

Graph multi-edge accounts for the presence of different transportation lines

P-space representation accounts for the fact that changing lines is time-consuming : -linking all stops

P space reduces effect due to the spatial extension of the network, as it takesinto account connections between stops located at large distance

Framework to study the public transportation network from the user perspective

choice not to model the system as a temporal graph

Choice of a representation with average characteristic temporal quantities

total travel time is subject to variability

P-space multiedge representation

P-space multiedge representation

Calculation of shortest temporal paths

average time needed on the line

average transfer time

Time-distance correlations

Calculation of the shortest paths and the corresponding physical distances

Paris

Time-distance correlations

Calculation of the shortest paths and the corresponding physical distances

Nantes Strasbourg Toulouse

Comparison of average travel time of selected paths with the average travel time needed to cover the same distance by car

Car commuting times extracted from the French 2008 Enquête Nationale Transports et Déplacements 2007-2008

→

Individuals were asked :

- how far they travelled every day with a resolution of 1 Km, by - which transportation mean, and for how long with the resolution of 1 minute

We computed the typical time needed to commute a particular distance by car as the median of the distribution of times over the entire sample.

Similarly, we calculate the median time needed by PT using only privileged connections

Privileged connections

dataset describing the global mobility of people living in France.

Privileged connections

Selection of the best 1% of all paths : at most 1.71 the time needed by car.

Such result motivates the choice of our selection as studies have revealed that commuters typically consider commuting by public transportation an interesting choice if the travel time factor (the ratio between the travel time with PT and by car) does not exceed 1.5-1.6.

Paris

Global efficiency of the transportation network systems

Privileged connections

1) The structural properties of the transportationnetwork are geographically constrained

2) Going beyond the geographical informations: the privileged connections are the results of the design of the transportation network

How are these fast connections distributed in the city ?

- at which extent are they linked to home- work commuting ?

- which part is devoted to tourism ?

- which part is devoted to other moves ?

Map of the privileged connections

Analysis of the privileged connections

Intuition : stations with similar connectivity patterns can exhibit some similarities

For instance :

1) we expect that some stops located in a residential neighborhood have similar connections with respect to the rest of the network, as they might be all linked via similar routes to stops located in the city center and in working areas : Functional areas

2) nearby stops having the same connectivity patterns can yield some resilience to the system

→ Building of an adjacency matrix of the privileged connections

Jaewon Yang, Julian McAuley, and Jure Leskovec. Detecting cohesive and 2-mode communities indirected and undirected networks. In Proceedings of the 7th ACM international conference on Web search and data mining, pages 323–332. ACM, 2014.

Analysis of the privileged connections

Inverse problem : In fact, if two nodes interact through more then one community they are more likely to be connected with a strong weight.

Extraction of the underlying structure of the emergent graph

The existence of a connection between two nodes depend on how many affiliation communities the nodes share

Analysis of the privileged connections : a set of structures

Analysis of the privileged connections : a set of structures

Minimization problem

Update rules : element by element

Approximation of the networks as a set of elementary structures :strong signal of the design of the network

Analysis of the privileged connections : a set of structures

We run the method for different cities :

- 1) representation of the transportation network as a P-space multiedge

- 2) calculation of the shortest paths

- 3) extraction of structures for different interval of distances relevant for the city scale

Some transportations networks do not exhibit any structure. In this case, it meansthat there is not a strong signal in the design of the network. It is somehowhomogeneous

For each structure one looked at the main stations. This gives :

- main axes in the cities

- different centers in the cities...

Analysis of privileged connections

Nantes (5-10 kms) Strasbourg (5-10kms)

Analysis of the privileged connections : a set of structures

Art B Owen and Patrick O Perry. Bi-cross-validation of the svd and the nonnegative matrix factorization. The Annals of Applied Statistics, pages 564–594, 2009.

Example of structures detected

Example of structures detected

Paris (5-6 kms)

Comparison with commuting patterns

Comparison with commuting patterns

Discussion

Framework :

- gives insights on the structure of transportation network from theuser point of view : free of the constraint imposed by spatial embedness

-characterize the public transportation system of different cities by identifying wheresome efforts have been put, not only structurally, but also in term of the frequency of the connections

Illustration :

-provides hints about the efficiency of transportation systems regarding the flow of Commuters

-quantifying how well the transportation system answer the need of some of its users

Further studies :

-measure of efficiency to refine and structures to explore

Characteristics of the shortest paths

One allows at most 2 changes

Comparison with commuting patterns