An MX/G/1 unreliable retrial queue with two phases of service and Bernoulli admission mechanism

Choudhury, Gautam; Deka, Kandarpa

doi:10.1016/j.amc.2009.06.015

Cited by 26 publications

(6 citation statements)

References 43 publications

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“…By employing the embedded Markov chain technique, they obtained the steady state distribution of the server state and number of the customers in the retrial group. Choudhury and Deka (2009) analysed the steady state behaviour of an M X /G/1 unreliable retrial queue with Bernoulli admission mechanism. Further, Sharma (2010) suggested threshold N-policy for un-reliable server queue with vacations.…”

Section: Literature Reviewmentioning

confidence: 99%

Maximum entropy analysis of bulk arrival retrial queue with second optional service and Bernoulli vacation

Jain

Sharma

2015

IJISE

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This paper deals with the maximum entropy principle (MEP) to explore the steady state behaviour of the bulk arrival retrial queuing system. The concepts of Bernoulli vacation schedule and second optional service are taken into consideration. After the completion of first essential service (second optional service), the server has an option to go for vacation with probability ( ) p q or may continue to serve the next customer, if any with complementary probability. During vacation, the server is allowed to do some secondary work and is called on working vacation. By introducing supplementary variables and using generating function technique, we obtain the expected number of the customers and expected waiting time of the customers in the retrial group. By employing the maximum entropy approach, we derive various system performance measures. By taking the numerical illustrations we perform a comparative study between the exact waiting time and the approximate waiting time based on MEP analysis. The sensitivity analysis is also carried out to validate the analytical results.

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Section: Literature Reviewmentioning

confidence: 99%

Maximum entropy analysis of bulk arrival retrial queue with second optional service and Bernoulli vacation

Jain

Sharma

2015

IJISE

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“…An M/M/1 retrial queue with constant retrial rate, unreliable server and threshold-based recovery was examined by Efrosinin and Winkler [14]. There are some other papers on retrial queues with server breakdowns, and we refer the readers to Choudhury and Deka [8,9], Gharbi and Dutheillet [16], Choudhury and Ke [10] for details and further references.…”

Section: Introductionmentioning

confidence: 98%

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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“…Although numerous papers dealt with retrial queuing systems with server breakdowns in different frameworks, which still is an interesting topic due to a variety of applications. Choudhury and Deka [9,10] examined M/G/1 and M X /G/1 unreliable retrial queuing systems with generally distributed repair time. Krishnamoorthy et al [11] also gave a detailed literature review on the retrial queue with server breakdown.…”

Section: Introductionmentioning

confidence: 99%