Modelling passenger service rate at a transport hub serviced by a single urban bus route as a queueing system

Abstract

In this paper the daily service rate at a bus stop from the urban passenger transport network is reviewed. The bus stop is located close to a railway and a bus station. A mathematical model has been developed for the average daily incoming flows of passengers to the monitored bus stop. The service rate has been modelled using pulse Dirac delta functions. The daily irregularity of operation of a particular bus line at this bus stop has been evaluated and the operation of the system has been modelled as a queueing system, in order to assess the capacity of the bus line and the organisation of work. The type of incoming flow, as well as the service rate has been defined as a non-stationary Poisson flow. A system of differential-algebraic equations has been chosen as a model according to Kolmogorov's model for stochastic processes. A specific numerical method for solving system differential equations has been devised with Dirac delta functions in the right part of the equations. Under non-stationary conditions, the basic values of the system parameters have been calculated and an application has been created in a MatLab environment. The results are suitable for accurately determining the routing speed and the average waiting time of the passengers at the bus stop. They can also determine the refusal of passengers to wait at the passenger stop.