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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
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