In previous research on urban rail operations, capacities have been calculated using fully deterministic procedures based on the calculation of the minimum time interval between successive arrivals at a station. This paper adds to previous contributions on the analysis of traffic flow of railway systems in that a stochastic model for the passage of trains is derived in terms of queueing theory. Statistical fluctuations in station stop times occur in urban commuter railways at bottleneck stations and furthermore some randomness is present in the time headways of trains passing the entry point to the station. Thus it is appropriate to extend the deterministic models by considering a railway block signalling section (from the outer home signal to the station starter) as the service component of a classical single server queue. Various time headway distributions are considered as inputs to the station approach and particular attention is given to a semi-poisson model of headway, similar to certain models used for analysing road traffic headways. The work is valid for a general class of distributions in both input and service and admits of wide application in modelling railway signalling systems. As an example data collected from a study of london transport underground railways were used to calibrate headway models and then applied to model a typical block section including a station stop. It is believed that a queue-theoretic basis for mean waiting time in the system and mean queue length for a given traffic intensity provides a better approach to the planning of levels of service than the present operating procedure of some railway bodies who calculate the capacity under the deterministic minimum time headway criterion and then operate at some proportion of that level. (a). For the covering abstract of the symposium, please see irrd abstract no. 224453.
Abstract