A large deviation analysis of retrial models with constant and classic retrial rates

Abstract

In this paper, a large deviation analysis of the retrial systems is developed. We consider both classical and constant retrial rate models. We focus on the (overflow) probability that the orbit size in the single-server system reaches a high level N within a regeneration period. Under natural assumptions, it is shown that, as N→∞, the overflow probability has an exponential decay rate. We find a lower bound and an upper bound for the exponential decay rate. At that these bounds have different exponential rates, because, to construct these bounds, we consider different (majorant and minorant) classical buffered systems. Then we apply the technique that has been developed earlier to analyze large deviation in a tandem queueing network. We also establish analogous large deviation result for a multiserver retrial system. Stability conditions are discussed as well. Simulation results are also included to demonstrate the accuracy of the obtained lower and upper bounds.