Analysis of Reversible and Nonreversible Queueing Networks with Rejection Blocking

Abstract

Queueing networks which contain finite capacities have proved useful in modeling actual computer systems and communication networks. The finite capacity of stations introduces blocking events which should be considered in the performance evaluation. Specifically, we shall examine the effects of rejection blocking upon queueing networks. Rejection blocking is defined in the following manner. Upon completion of its service of a particular station’s server, a job attempts to proceed to its next station. If, at that moment, its destination station is full, the job is rejected. The job goes back to the server of the source station and immediately receives a new service. This is repeated until the next station releases a job and a place becomes available. In the first part of this work the well known exact product form solution for the equilibrium state probabilities is presented for closed rejection blocking networks which have reversible routing. An algorithm is given for computation of performance measures in reversible networks with rejection blocking. In the second part nonreversible networks with rejection blocking are analyzed. The analysis is based on the transformation of the state space of a blocking queueing network into an equivalent state space of a nonblocking network with infinite station capacities. It is shown that the state spaces of both systems are isomorphic under a given condition. Markov processes describing the evolution of both networks over time have the same structure. This leads to the product form solution for blocking networks. Based on product form solution new formulae are given for the exact computation of performance measures.Key WordsPerformance EvaluationQueueing NetworksBlockingEquilibrium State Probabilities