An M/G/1 queue with two phases of service subject to the server breakdown and delayed repair

a b s t r a c tThis paper deals with the steady-state behavior of an M X /G/1 retrial queue with an additional second phase of optional service and service interruption where breakdowns occur randomly at any instant while the server is serving the customers. Further, the concept of delay time is also introduced in the model. This model generalizes both the classical M X /G/1 retrial queue with service interruption as well as the M X /G/1 queue with second optional service and service interruption. We carry out an extensive analysis of this model.

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“…Note that for the single unit arrival case with = 1, the above formula (3.45) is consistent with the result obtained by Choudhury and Tadj [16].…”

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confidence: 90%

“…This model can be generalized straight away by considering that the second optional service time is also governed by a general distribution. In this context, recently, Choudhury and Tadj [16] generalized this type of model by introducing the concept of a delay period.…”

Section: Introductionmentioning

confidence: 98%

A batch arrival retrial queueing system with two phases of service and service interruption

Choudhury

Tadj

Deka

2010

Computers & Mathematics with Applications

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“…Madan (2000) considered the classical M/G/1 queuing system in which the server provides the first essential service (FES) to all the arriving customers whereas some of them receive SOS. The steady state analysis of an M/G/1 queue with repeated attempts and additional second phase of service has been done in different frameworks by Artelejo and Choudhury (2004), Choudhury (2008), and Choudhury and Tadj (2009).…”

Section: Survey Of Literaturementioning

confidence: 99%

A batch arrival retrial queuing system for essential and optional services with server breakdown and Bernoulli vacation

Jain

Sharma

Sharma³

2012

IJIEM

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This paper studies a general retrial M X /G/1 queue with an additional phase of second optional service and Bernoulli vacation where breakdowns occur randomly at any instant while servicing the customers. If an arriving batch finds that the server is busy in providing either first essential service (FES)/second optional service (SOS) or on vacation then arriving batch enters an orbit called retrial queue. Otherwise, one customer from arriving batch starts to be served by the server while the rest join the orbit. The vacation times and service times of both first essential and second optional services are assumed to be general distributed while the retrial times are exponential distributed. Introducing supplementary variables and by employing embedded Markov chain technique, we derive some important performance measures of the system such as average orbit size, average queue size, mean waiting time, expected lengths of busy period, etc. Numerical results have been facilitated to illustrate the effect of different parameters on several performance measures.

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“…Further, Wang and Xu (2009) obtained the solution of an M/G/1 queue with second optional service and server breakdown using the method of functional analysis. The work on an M/G/1 queue with second optional service and server breakdown has been done by Choudhury and Tadj (2009). They derived the Laplace-Stieltjes transform of busy period distribution and waiting time distribution.…”

Section: Introductionmentioning

confidence: 99%

Multiple vacation policy for MX/Hk/1 queue with un-reliable server

Jain

Sharma

Sharma³

2013

J Ind Eng Int

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This paper studies the operating characteristics of an M X /H k /1 queueing system under multiple vacation policy. It is assumed that the server goes for vacation as soon as the system becomes empty. When he returns from a vacation and there is one or more customers waiting in the queue, he serves these customers until the system becomes empty again, otherwise goes for another vacation. The breakdown and repair times of the server are assumed to follow a negative exponential distribution. By using a generating function, we derive various performance indices. The approximate formulas for the probability distribution of the waiting time of the customers in the system by using the maximum entropy principle (MEP) are obtained. This approach is accurate enough for practical purposes and is a useful method for solving complex queueing systems. The sensitivity analysis is carried out by taking a numerical illustration.

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An M/G/1 queue with two phases of service subject to the server breakdown and delayed repair

Cited by 61 publications

References 36 publications

A batch arrival retrial queueing system with two phases of service and service interruption

A batch arrival retrial queueing system with two phases of service and service interruption

A batch arrival retrial queuing system for essential and optional services with server breakdown and Bernoulli vacation

Multiple vacation policy for MX/Hk/1 queue with un-reliable server

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