On a tandem queue with retrials and losses and state dependent arrival, service and retrial rates

Abstract

We consider the M/M/1 → •, M/M/1/0 type retrial queueing system with state dependent parameters. The intensities of input, service (at both stations) and retrials depend in an arbitrary way on the current number of customers in the orbit. Because operation of the first station of this tandem does not depend on the state of the second station, analysis of the system is implemented in two steps. At the first step, we compute the marginal distribution of the states of the first station in a simple form. At the second step, analytical formulas are presented for computation of the steady state-distribution of the tandem. Formulas for computing the most important performance measures of the system are derived. Results can be used for solving various problems of optimal control by the system operation.