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

Springer Science and Business Media LLC - Tập 331 - Trang 1207-1248 - 2023
Alka Choudhary1, Srinivas R. Chakravarthy2, Dinesh C. Sharma1
1Department of Mathematics, Central University of Rajasthan, Bandarsindri, Ajmer, India
2Departments of Industrial and Manufacturing Engineering and Mathematics, Kettering University, Flint, USA

Tóm tắt

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 $$MAP/PH/1-$$ 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 matrix-analytic 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.

Tài liệu tham khảo

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