A dual tandem queueing system with a finite intermediate buffer and cross traffic

Abstract

We analyze a dual tandem queue having a single server queueing system with infinite buffer at the first station and a multi-server queueing system with a finite buffer at the second station. Arrival flow is described by the Batch Markovian Arrival Process (BMAP). Service time at the first station is generally distributed while at the second station it is exponentially distributed. In situation when the intermediate buffer between the stations is full at the service completion of a customer at the first station, this customer is lost or blocks the server until service completion in one of the servers at the second station. Besides the customers, which got service at the first station, an additional MAP flow (cross traffic) arrives to the second station directly, not entering the first station.Ergodicity condition for this system is derived. Stationary state distribution of the system at embedded and arbitrary time epochs is computed as well as the main performance measures of the system. Numerical results show possibility of optimization of the system operation by means of appropriate choosing the capacity of an intermediate buffer and the intensity of cross traffic. Necessity of the account of correlation in the arrival processes is illustrated.