Analysis of MAP / PH /1 Queueing System with Degrading Service Rate and Phase Type Vacation

Alka Choudhary, Srinivas R. Chakravarthy and Dinesh C. Sharma
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Alka Choudhary: Department of Mathematics, Central University of Rajasthan, Ajmer 305817, India
Srinivas R. Chakravarthy: Departments of Industrial and Manufacturing Engineering and Mathematics, Kettering University, Flint, MI 48504, USA
Dinesh C. Sharma: Department of Mathematics, Central University of Rajasthan, Ajmer 305817, India

Mathematics, 2021, vol. 9, issue 19, 1-17

Abstract: Degradation of services arises in practice due to a variety of reasons including wear-and-tear of machinery and fatigue. In this paper, we look at M A P / P H / 1 -type queueing models in which degradation is introduced. There are several ways to incorporate degradation into a service system. Here, we model the degradation in the form of the service rate declining (i.e., the service rate decreases with the number of services offered) until the degradation is addressed. The service rate is reset to the original rate either after a fixed number of services is offered or when the server becomes idle. We look at two models. In the first, we assume that the degradation is instantaneously fixed, and in the second model, there is a random time that is needed to address the degradation issue. These models are analyzed in steady state using the classical matrix-analytic methods. Illustrative numerical examples are provided. Comparisons of both the models are drawn.

Keywords: queueing model; degrading service rate; server vacation; Markovian arrivals; phase type service (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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