Impact of the degradation in service rate in MAP/PH/1 queueing system with phase type vacations, breakdowns, and repairs

Document Type

Article

Publication Date

11-4-2023

Publication Title

Annals of Operations Research

Abstract

In many service systems, the service rates of the servers or the machines degrade over time due to a variety of reasons like fatigue, deficiency (due to manufacturing defect or energy loss, deformation, or excessive heat), and lack of proper maintenance. To make a service system beneficial for both customers and management points of view, it is imperative that models are developed to understand the impact of degradation. In this paper, we study MAP/P H/1−type queueing models incorporating degradation, failures/breakdowns and repairs. The degradation and to restore to normalcy in the service rate we look at two scenarios. In the first one, the service is restored to normalcy immediately after the server becomes idle or a fixed number of services is offered. In the second one, the restoration takes a random time that is modeled using a phase type distribution. Also, there are a variety of reasons that lead to failures/breakdowns of the server. We model these using (possibly) different phase type distributions. Both the models are studied analytically using matrixanalytic methods and illustrative numerical examples bringing out the qualitative behavior of the impact of degrading services are discussed. Two cost optimization problems whose solutions are obtained using particle swarm optimization technique along with a few illustrative examples are presented

First Page

1

Last Page

42

DOI

https://doi.org/10.1007/s10479-023-05628-4

ISSN

Electronic ISSN: 1572-9338

Rights

© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023

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