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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 off 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. [ABSTRACT FROM AUTHOR]

In the present paper, hyper-Erlang distribution (HErD) which is a restricted class of phase-type distribution (PH) with good versatility and analyticity and seven common distributions are used to fit the distribution of time interval between arriving passengers. From the comparison of a large number of experiments, the fitting effect of HErD is proven to be the best and the applicability of all distributions is given. Then, the fitting parameters of HErD are extracted to analyze the law of their variations, and it demonstrates that when the coefficient of variation is smaller than 1, the distribution is mixed by one exponential distribution (ED) and one 4-order Erlang distribution (ErD), in which there's a power functional relationship between the mixing ratio of ED and the square of coefficient of variation. However, when the coefficient of variation is larger than 1, the distribution is mixed by two EDs, in which there's an S functional relationship between the mixing ratio of one ED and square of coefficient of variation. As a result, the parameters of HErD are simplified into 2 scale parameters determined by the given long-term peak traffic and super- peak coefficient, and thus the PH distribution and PH queuing model can be introduced to the systemic planning and design of urban rail transit station, which will improve the rationality of the design. [ABSTRACT FROM AUTHOR]