Computational algorithm and parameter optimization for a multi-server system with unreliable servers and impatient customers

Chia-Huang Wu, Jau Chuan Ke*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We consider an infinite capacity M/M/c queueing system with c unreliable servers, in which the customers may balk (do not enter) and renege (leave the queue after entering). The system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition of system equilibrium is obtained. System performance measures are explicitly derived in terms of computable forms. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is derived to determine the optimal values of the number of servers, service rate and repair rate simultaneously at the minimal total expected cost per unit time. The parameter optimization is illustrated numerically by the Quasi-Newton method.

Original languageEnglish
Pages (from-to)547-562
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume235
Issue number3
DOIs
StatePublished - 1 Dec 2010

Keywords

  • Balk
  • Cost
  • Matrix analytic approach
  • Quasi-Newton method
  • Renege

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