Time dependent traffic assignment model for commuter traffic in Tokyo metropolitan railway network

In this paper we propose a traffic assignment model based on user equilibrium principle for commuters traveling through the public railway network in Tokyo Metropolitan area. Our model covers about seven million commuters in seventy five hundred trains traveling along 128 railway routes of JR and other private railway companies. Since the census data of commuter traffic that describes for each commuter his/her origin station, departure time and destination station are available, we formulate this problem as being time dependent. In order to treat the time dependent problem where OD traffic demand depends on time and commuters are assigned to each train running according to a timetable, we adopt such approach to construct a time–space network which honestly expresses the timetable of trains in the network. We extend a usual network to a time–space network by representing each train arrival/departure at a station by a node, each train travel between successive stations by an edge. Using this kind of network, the time dependent problem could be formulated as to find static equilibrium flow pattern being realized through “user-optimal” route choice of commuters, i.e. Wardrop's first principle. In order to obtain OD traffic demand as an input to the traffic assignment problem, we edit the census data for commuter traffic in Tokyo area in 2000. The calculated results show good coincidence with the commuters' flow pattern reproduced by aggregating commuters on every train according to records in the census data. After this preliminary calculation, we considered two applications to demonstrate usefulness of our model. One is to forecast how many commuters would change their routes to use newly opened railway line “Nanboku-sen”. The other is to estimate the effect of staggered departure of commuters to their offices in order to reduce congestion during the morning rush hours. We believe that we could propose a useful tool to analyze precisely commuter traffic flow in a widespread public transportation network.