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

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish
JournalInternational Journal of Production Research
DOIs
StatePublished - Jun 2019

Keywords

  • canonical particle swarm optimisation algorithm
  • heterogeneous servers
  • matrix geometric method
  • multiple vacations
  • working breakdown

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