Equilibrium properties of the morning peak-period commuting in a many-to-one mass transit system

This paper analyzes the equilibrium properties of the morning peak-period commuting pattern on a many-to-one transit system with in-vehicle crowding effect and schedule delay cost in a monocentric city. Commuters are assumed to choose their optimal time-of-use decision from various stations/home locations to a single destination/workplace by trading off the travel time and crowding cost against the schedule delay cost. An equivalent mathematical programming model is proposed to characterize the equilibrium state, in which no commuter can reduce his/her total commuting cost by unilaterally changing his/her departure time or train service. Solution of the model yields many insights including the following: (1) commuters living closer to the destination choose trains also chosen by those living farther from the destination; (2) the train arriving at the time desired by everyone is utilized by commuters from all stations; (3) the farther a station is from the workplace, the longer is the peak-period departure duration from that station; (4) finally, a 'saturated' time period exists for each station during which the departure rate of commuters is identical and maximal.