Performance of two-stage tandem queues with blocking: The impact of several flows of signals

Abstract

This paper considers a two-stage tandem G-queue with blocking, service requirements of phase type and arrivals of units and of signals - which cancel one unit waiting in line or in service - both assumed to be Markovian arrival processes. The main characteristic of the service process in this tandem queue is blocking, which occurs according to a BAS (blocking after service) mechanism. A finite queue of capacity K >= 0 is allowed between servers, so that a unit having completed processing on Station I attempts to join Station 2. If K + 1 units are accommodated into Station 2, then the completed unit is forced to wait at Station I occupying the server space until a space becomes available at Station 2. Thus the first server becomes blocked or not available for service on incoming units. Our purpose is to study the influence of several flows of signals on the performance evaluation of the queueing model through various probabilistic descriptors. By means of a numerical investigation, we study four two-stage tandem G-queues with blocking depending on the existence of flows of signals affecting Station 1 and/or Station 2. The essential tool in our analysis is the general theory of quasi-birth-and-death processes.