Morning commute in congested urban rail transit system: A macroscopic model for equilibrium distribution of passenger arrivals

In many metropolises, the congestion and delay of rail transit have brought about tremendous psychological stress to commuters and considerable economic loss to the society. For example, according to a report by the Ministry of Land, Infrastructure, Transport and Tourism of Japan, on an average, train delays (more than 5 min) were observed for 45 railway lines in the Tokyo metropolitan area in 11.7 days of 20 weekdays in a month, and more than half of the short delays (within 10 min) were caused by extended dwell time (MLIT, 2020). Kariyazaki et al (2015) estimated that in Japan, train delays resulted in social cost in excess of 1.8 billion dollars per year. In a high-frequency operated rail transit system, when a train delay occurs because of either an accident or extended dwell time, the subsequent trains are forced to decelerate or stop between stations to maintain a safety clearance, which is a so-called "knock-on delay" on the rail track (Carey and Kwieci nski, 1994). Meanwhile, more passengers are kept waiting on the platform when trains decelerate or stop (because headways of trains are extended), which results in a longer dwell time of trains.