The multi-server retrial system with Bernoulli feedback and starting failures

Dong Yuh Yang*, Jau Chuan Ke, Chia-Huang Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


In this paper, we present a detailed analysis of a multi-server retrial queue with Bernoulli feedback, where the servers are subject to starting failures. Upon completion of a service, a customer would decide either to leave the system with probability p or to join the retrial orbit again for another service with complementary probability 1−p. We analyse this queueing system as a quasi-birth–death process. Specifically, the equilibrium condition of the system is given for the existence of the steady-state analysis. Applying the matrix-geometric method, the formulae for computing the rate matrix and stationary probabilities are obtained. We further develop the matrix-form expressions for various system performance measures. A cost model is constructed to determine the optimal number of servers, the optimal mean service rate and the optimal mean repair rate subject to the stability condition. Finally, we give a practical example to illustrate the potential applicability of this model.

Original languageEnglish
Pages (from-to)954-969
Number of pages16
JournalInternational Journal of Computer Mathematics
Issue number5
StatePublished - 4 May 2015


  • Bernoulli feedback
  • cost
  • matrix-geometric method
  • retrial queue
  • starting failure

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