A Two-Server Queue with Interdependence between Arrival and Service Processes

Sindhu S, Achyutha Krishnamoorthy () and Dmitry Kozyrev ()
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Sindhu S: Department of Mathematics, Model Engineering College, Ernakulam 682021, India
Achyutha Krishnamoorthy: Centre for Research in Mathematics, CMS College, Kottayam 686001, India
Dmitry Kozyrev: V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Street, 117997 Moscow, Russia

Mathematics, 2023, vol. 11, issue 22, 1-25

Abstract: In this paper, we analyse a queueing system with two servers where the arrival and service processes are interdependent. The evolution of these processes is governed by transitions on the product space of three Markov chains, which are descriptors of the arrival and service processes. The transitions in this Markov chain follow a semi-Markov rule and the exponential distribution governs the sojourn times in the states. The stability condition of the system is derived and the stationary distribution is calculated for the system in equilibrium. Several important performance measures are provided, and numerical illustrations of the model are presented.

Keywords: interdependent; Markov chain; semi-Markov process; sojourn time; heterogeneous servers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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