A Queueing Theory Approach to Railway Capacity in Urban Commuter Railways

Abstract

A notable deficiency in the planning of urban railways lies in the treatment of statistical variation inherent in the day-to-day operation of the system. Thus in peak periods on lines which carry heavy train flows, it is of great importance to know the penalties associated with running more trains. In the case of urban passenger railways operating on single tracks through single track platforms considerable random variations are expected in the time interval between trains.The method proposed is a mixture of stochastic and diffusion type mathematical approximations to describe the queue length, delay and relaxation times found in the operation of the section. It is the perturbations in the times between trains and in the station stop times that give rise to queuing and the delays to the trains. The traffic intensity and a queue growth factor are key parameters in determining the practical capacity which is related to the deterministic or basic capacity, a concept derived entirely from the signalling characteristic of the station layout.It is believed that this framework represents an important contribution to the understanding of London Transport type railway operations in practice. The problems of time dependency in the operation are shown to be surmountable and that sensible approximations are given very quickly and without recourse to an elaborate simulation model.