Modelling and optimisation of a two-server queue with multiple vacations and working breakdowns

Dong-Yuh Yang, Yi-Hsuan Chen and Chia-Huang Wu

International Journal of Production Research, 2020, vol. 58, issue 10, 3036-3048

Abstract: This paper presents a steady-state analysis of an M/M/2 queue with heterogeneous servers (Server 1 and Server 2). Server 1 is reliable and may leave for a vacation when the system becomes empty. Sever 2 is unreliable and may break down while serving customers. When a breakdown occurs, Server 2 reduces the service rate rather than halting service. We formulate this queueing model as a quasi birth-and-death (QBD) process, using the matrix geometric method to compute the stationary distribution of system size. We also develop several measures to evaluate the performance of the system. A cost model based on system performance measures is formulated as a heuristic cost optimisation problem subject to stability conditions. A canonical particle swarm optimisation algorithm is used to obtain numerical solutions for the approximate optimal service rates of Server 1 and Server 2. Moreover, we present numerical results showing the effects of various parameters on the approximate optimal service rates as well as a practical example illustrating the application of the proposed model.

Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1080/00207543.2019.1624856

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