A heuristic algorithm for the optimization of a retrial system with Bernoulli vacation

Jau Chuan Ke*, Chia-Huang Wu, W.l. Pearn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this study, we consider an M/M/c retrial queue with Bernoulli vacation under a single vacation policy. When an arrived customer finds a free server, the customer receives the service immediately; otherwise the customer would enter into an orbit. After the server completes the service, the server may go on a vacation or become idle (waiting for the next arriving, retrying customer). The retrial system is analysed as a quasi-birth-and-death process. The sufficient and necessary condition of system equilibrium is obtained. The formulae for computing the rate matrix and stationary probabilities are derived. The explicit close forms for system performance measures are developed. A cost model is constructed to determine the optimal values of the number of servers, service rate, and vacation rate for minimizing the total expected cost per unit time. Numerical examples are given to demonstrate this optimization approach. The effects of various parameters in the cost model on system performance are investigated.

Original languageEnglish
Pages (from-to)299-321
Number of pages23
JournalOptimization
Volume62
Issue number3
DOIs
StatePublished - 1 Mar 2013

Keywords

  • Bernoulli vacation schedule
  • matrix-geometric method
  • quasi-Newton method
  • retrial
  • single vacation policy

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