Some decomposition formulae for M/M/r/r+ d queues with constant retrial rate

Abstract

The M/M/r/r-d queue with constant retrial rate has many important applications in teletraffic theory and computer and communication networks. An analytical solution of this queue is difficult and would not necessarily lend itself to numerical implementation in the case r+≥ 3. In this paper, we extend the decomposition formulae for the stationary distributions of the standard M/M/r/r+d queue to the M/M/r/r+d queue with constant retrial rate. In the case r+< 3, we show that the stationary distributions of the number of customers in orbit and the total number of servers and waiting positions occupied can be expressed as mixtures of two random variables weighted by the probability of entering the orbit. In the case r+≥ 3, we propose and heuristically explore decomposition formulae for the stationary distribution of the number of customers in orbit