Multiserver queueing systems with retrials and losses

Abstract

The interest in retrial queueing systems mainly lies in their application to telephone systems. This paper studies multiserver retrial queueing systems with n servers. The arrival process is a quite general point process. An arriving customer occupies one of the free servers. If upon arrival all servers are busy, then the customer waits for his service in orbit, and after a random time retries in order to occupy a server. The orbit has one waiting space only, and an arriving customer, who finds all servers busy and the waiting space occupied, is lost from the system. Time intervals between possible retrials are assumed to have arbitrary distribution (the retrial scheme is explained more precisely in the paper). The paper provides analysis of this system. Specifically the paper studies the optimal number of servers to decrease the loss proportion to a given value. The representation obtained for the loss proportion enables us to solve the problem numerically. The algorithm for numerical solution includes effective simulation, which meets the challenge of a rare events problem in simulation. © Australian Mathematical Society 2007.