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access icon free Retrial queues with starting failure and service interruption

  • Author(s): Jau-Chuan Ke 1 ; Tzu-Hsin Liu 1 ; Dong-Yuh Yang 2
    • View affiliations
  • Source: Volume 12, Issue 12, 31 July 2018, p. 1431 – 1437
    DOI:  10.1049/iet-com.2017.0820 , Print ISSN 1751-8628, Online ISSN 1751-8636
© The Institution of Engineering and Technology
Received 10/09/2017, Accepted 18/03/2018, Revised 12/03/2018, Published 22/03/2018

The purpose of this study is to investigate an M/M/R retrial queue with geometric loss and Bernoulli feedback, in which all servers are subject to breakdowns and starting failures. After the completion of service, unsatisfied customers can join the retrial group with probability p or depart from the system with probability 1 − p. All servers may breakdown at any time, and the failed server undergoes repair immediately when a breakdown occurs. An arriving customer finding all servers unavailable (busy or down), will either join the orbit with probability b or leave the system with probability 1 − b. For such a queuing model, the authors apply the matrix-geometric method to compute the stationary probabilities and develop system performance measures in the steady state. Moreover, they construct a cost model and formulate an optimisation problem of minimising the expected cost per unit time. Finally, numerical results are given for illustrative purposes.

Inspec keywords: probability; queueing theory

Other keywords: queuing model; stationary probabilities; server starting failures; geometric loss; system performance measures; servers breakdowns; Bernoulli feedback; matrix-geometric method; M/M/R retrial queue; service interruption

Subjects: Queueing theory; Applications of systems theory

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