Title: Optimal routing control of a retrial queue with two-phase service

Authors: Zineb Dahmane; Amar Aissani

Addresses: Department of Mathematics, Faculty of Science, Blida 1 University, Blida, Algeria ' Department of Informatics, Faculty of Electronics and Informatics, USTHB Bab Ezzouar University, Algiers, Algeria

Abstract: Consider the problem of dynamic routing control in a retrial queue with a single server that provides two phases of service. All arriving customers join an ordinary queue and wait to be served. Every customer must receive service in both phases before leaving the system. After completion of the first phase, the server can either continue with the second phase for the same customer or stop the current service sequence in the first phase (to support a new customer that is on hold). In the latter case, the customer is placed in the retrial box, from where he is recalled for the second phase before leaving the system. Using Markov decision theory, we prove that an optimal policy exists that minimises the expected waiting cost for the system. We show that such a policy can be described by a switching curve that divides the state space into two contiguous regions. We present two conjectures regarding the structure of this policy, taking into account two different retrial policies.

Keywords: dynamic routing? two-phase service? ordinary queue? retrial box? Markov decision theory? threshold policy? classical retrial? constant retrial.

DOI: 10.1504/IJMOR.2021.117631

International Journal of Mathematics in Operational Research, 2021 Vol.20 No.1, pp.20 - 40

Received: 05 Dec 2019
Accepted: 11 Jun 2020
Published online: 17 Sep 2021 *

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