A heuristic algorithm for the optimization of M/M/s queue with multiple working vacations

Chia-Huang Wu*, Kuo Hsiung Wang, Jau Chuan Ke, Jyh Bin Ke

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

This paper focuses on an M/M/s queue with multiple working vacations such that the server works with different service rates rather than no service during the vacation period. We show that this is a generalization of an M/M/1 queue with working vacations in the literature. Service times during vacation period, or during service period and vacation times are all exponentially distributed. We obtain the useful formula for the rate matrix R through matrix-geometric method. A cost function is formulated to determine the optimal number of servers subject to the stability conditions. We apply the direct search algorithm and Newton-Quasi algorithm to heuristically find an approximate solution to the constrained optimization problem. Numerical results are provided to illustrate the effectiveness of the computational algorithm.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalJournal of Industrial and Management Optimization
Volume8
Issue number1
DOIs
StatePublished - 1 Feb 2012

Keywords

  • Newton-quasi algorithm
  • Optimization
  • Rate matrix
  • Sensitivity analysis
  • Working vacations

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