On the stationary distribution of tandem queue consisting of a finite number of stations

Abstract

In this paper we consider a tandem queueing system consisting of a finite number of multi-server queues (stations) without buffers. Customers arrive to the first station in the MAP (Markovian Arrival Process). The service times at the servers of the tandem are exponentially distributed with different parameters for different stations. We describe the output flows from the stations of the tandem as MAPs and present the simple method for recursive constructing the infinitesimal generator of the multi-dimensional Markov chain describing the operation of the system, calculating the stationary distributions and loss probabilities associated with the tandem. It is shown that the marginal stationary distribution of any station can be calculated as stationary distribution of the system of MAP/M/N/N type. © 2012 Springer-Verlag.