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

Authors: Alexander Dudin; Anatoly Nazarov

Addresses: Department of Applied Mathematics and Cybernetics, Tomsk State University, Tomsk, Russia ' Department of Applied Mathematics and Cybernetics, Tomsk State University, Tomsk, Russia

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.

Keywords: retrial queue; tandem queue; state dependent parameters; stationary distribution.

DOI: 10.1504/IJOR.2017.083954

International Journal of Operational Research, 2017 Vol.29 No.2, pp.170 - 182

Received: 28 Mar 2014
Accepted: 21 Sep 2014
Published online: 28 Apr 2017 *

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