A discrete-time retrial queueing system with starting failures, Bernoulli feedback and general retrial times

Atencia, Iván; Ruiz, Inmaculada Fortes; Sánchez, Sixto E.

doi:10.1016/j.cie.2009.06.011

Cited by 32 publications

(15 citation statements)

References 38 publications

(35 reference statements)

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“…Ke and Chang [18] presented a steady-state analysis of a retrial system with general retrial times, where the server is subjected to starting failures and operates the Bernoulli vacation policy for two phases of heterogeneous service. For recent literature on the retrial queues with feedback and starting failures, see Atencia et al [3], Wang and Zhou [33] for details.…”

Section: Introductionmentioning

confidence: 99%

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

Yang

2014

International Journal of Computer Mathematics

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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.

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Section: Introductionmentioning

confidence: 99%

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

Yang

2014

International Journal of Computer Mathematics

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“…Such phenomena occur in day-to-day life, for example, the components of the computer and communication systems are subject to random breakdowns. Discrete-time retrial queues that take into account server breakdowns were studied by Atencia and Moreno [6,7], Moreno [8], Wang and Zhao [9], Wang [10], Wang and Zhang [11], and Atencia et al [12].…”

Section: Introductionmentioning

confidence: 99%

A Discrete-TimeGeo/G/1Retrial Queue withJVacations and Two Types of Breakdowns

Zhao

Zhu

2013

Journal of Applied Mathematics

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This paper is concerned with a discrete-time / /1 retrial queueing model with vacations and two types of breakdowns. If the orbit is empty, the server takes at most vacations repeatedly until at least one customer appears in the orbit upon returning from a vacation. It is assumed that the server is subject to two types of different breakdowns and is sent immediately for repair. We analyze the Markov chain underlying the considered queueing system and derive the system state distribution as well as the orbit size and the system size distributions in terms of their generating functions. Then, we obtain some performance measures through the generating functions. Moreover, the stochastic decomposition property and the corresponding continuous-time queueing system are investigated. Finally, some numerical examples are provided to illustrate the effect of vacations and breakdowns on several performance measures of the system.

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“…For example, the continuous-time retrial queueing systems which take into account servers breakdowns and repairs were discussed by Kulkarni and Choi [16], Wang et al [17,18], and Li et al [19]. Parallel to the continuous-time unreliable retrial queues, the discrete-time retrial queues with starting failure were studied by Atencia and Moreno [20], Wang and Zhao [21], and Atencia et al [22]. The discretetime unreliable retrial queueing systems caused by negative customers were discussed by Wang and Zhang [23].…”

Section: Introductionmentioning

confidence: 99%

A Discrete-Time UnreliableGeo/G/1Retrial Queue with Balking Customers, Second Optional Service, and General Retrial Times

Zhao

Zhu

2013

Mathematical Problems in Engineering

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This paper deals with the steady-state behavior of a discrete-time unreliableGeo/G/1retrial queueing system with balking customers and second optional service. The server may break down randomly while serving the customers. If the server breaks down, the server is sent to be repaired immediately. We analyze the Markov chain underlying the considered system and its ergodicity condition. Then, we obtain some performance measures based on the generating functions. Moreover, a stochastic decomposition result of the system size is investigated. Finally, some numerical examples are provided to illustrate the effect of some parameters on main performance measures of the system.

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A discrete-time retrial queueing system with starting failures, Bernoulli feedback and general retrial times

Cited by 32 publications

References 38 publications

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

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

A Discrete-TimeGeo/G/1Retrial Queue withJVacations and Two Types of Breakdowns

A Discrete-Time UnreliableGeo/G/1Retrial Queue with Balking Customers, Second Optional Service, and General Retrial Times

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