Performance analysis and optimization of a retrial queue with working vacations and starting failures

Dong Yuh Yang*, Chia-Huang Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


This paper presents a steady-state analysis of an M/M/1 retrial queue with working vacations, in which the server is subject to starting failures. The proposed queueing model is described in terms of the quasi-birth-death (QBD) process. We first derive the system stability condition. We then use the matrix-geometric method to compute the stationary probability distribution of the orbit size. Some performance measures for the system are developed. We construct a cost model, and our objective is to determine the optimal service rates during normal and vacation periods that minimize the expected cost per unit time. The canonical particle swarm optimization (CPSO) algorithm is employed to deal with the cost optimization problem. Numerical results are provided to illustrate the effects of system parameters on the performance measures and the optimal service rates. These results depict the system behaviour and show how the CPSO algorithm can be used to find numerical solutions for optimal service rates.

Original languageEnglish
Pages (from-to)463-481
Number of pages19
JournalMathematical and Computer Modelling of Dynamical Systems
Issue number5
StateAccepted/In press - 1 Jan 2019


  • Matrix-geometric method
  • starting failure
  • working vacation


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