A Model to Simulate Delay in Train Schedule Caused by Crowded Passengers

We propose a network flow model to study problems in commuting traffic in the railway network of the Tokyo Metropolitan area. Through this network, about seven million passengers commute, and about 7,500 trains transport them in morning rush hours. Trains are usually crowded and subject to delay caused by overcrowded passengers. In addition to the huge traffic volume, such facts intensify the situation that the commuters concentrate in commuting during short time period, traveling radial lines directing to the central district, and choosing a “better (higher speed)†train service. In order to relieve such conditions, not only investments in hardware but also soft approach are important to fully utilize the existing capacity of the network to average the number of passengers across the trains. Our model consists of a time–space network (or schedule-based network) and detailed traffic data on route choice of commuters. The former has been intensively studied to consider traffic problems where each vehicle service is operated according to a timetable. Using this network, every train services and actions of passengers can be represented by nodes and edges of the network. The latter is the questionnaire survey of commuting traffic in Metropolitan area being done in every five years. We use the survey conducted in 2005, which has about 140,000 respondents. Another important point of our model is that it is able to consider the whole railway network universally in one system.