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

This paper analyzes the morning peak-period commuting pattern in a one-to-many transit system. Commuters make their optimal time-of-use decision by trading o_ the travel time and crowding cost against the schedule delay cost. An equivalent mathematical programming model is proposed to characterize the equilibrium state. we deduce five equilibrium properties of the morning peak-period commuting in a one-to-many mass transit system. 1) Commuters of the same destination disperse in continuous train services and the number of commuters reaches its peak value in the train which arrives the destination at desired time. 2) Earlier trains which are choosed by short distance commuters carry long distance commuters simultaneously. 3) When earlier trains arrive at specific stations, the numbers of commuters in vehicle are constant independent of the train number. 4) When later trains leave specific stations, the number of commuters in vehicle are constant independent of the train number. 5) In specific region of trains, the number of commuters in later trains is less than earlier trains. Illustrated by two numerical examples, all equilibrium states accord with these properties.