On a single server queue with two-stage heterogeneous service and deterministic server vacations

Madan, Kailash C.

doi:10.1080/00207720121488

Cited by 45 publications

(29 citation statements)

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“…Levy, U. Yechilai,1976), (Doshi, B. T., 1986), (Takagi, H., 1990) and (Madan, 1991(Madan, , 2000b have studied queues with vacations. Also queueing systems with breakdowns have been studied by several authors including (Federgruen & So, 1990), (Aissani & Artalejo, 1998), (Wang, Cao & Li, 2001) and (Madan, Abu-Dayyeh, Gharaibeh, 2003b).…”

Section: Introductionmentioning

confidence: 99%

An M[X]/G/1 Queue with Bernoulli Schedule General Vacation Times, General Extended Vacations, Random Breakdowns, General Delay Times for Repairs to Start and General Repair Times

Khalaf¹,

Madan²,

Lukas³

2011

JMR

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This paper studies a batch arrival queueing system in which the server may face occasional random breakdowns. The repair process does not start immediately after a breakdown and there is a delay time waiting for repairs to start. Further, after every service completion the server has the option to leave for a vacation with probability p or continue serving with probability1 − p. The main new assumption in this paper is that the server has the option to go on extended vacation after the original vacation completion with probability r or rejoins the system to provide service directly after the original vacation with probability 1 − r. The service times, vacation times, extended vacation times, delay times and repair times are all assumed to follow general arbitrary distributions, while only the breakdown times are exponentially distributed.

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Section: Introductionmentioning

confidence: 99%

An M[X]/G/1 Queue with Bernoulli Schedule General Vacation Times, General Extended Vacations, Random Breakdowns, General Delay Times for Repairs to Start and General Repair Times

Khalaf¹,

Madan²,

Lukas³

2011

JMR

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“…Madan [21] analyzed a queueing system with feedback. Madan [22], generalized his previous model by incorporating server vacation. Medhi [23] discussed a single server Poisson input queue with a second optional channel.…”

Section: Literature Surveymentioning

confidence: 99%

An M[X]/G(a,b)/1 Queueing System with Breakdown and Repair, Stand-By Server, Multiple Vacation and Control Policy on Request for Re-Service

Ayyappan

Karpagam

2018

Mathematics

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Abstract:In this paper, we discuss a non-Markovian batch arrival general bulk service single-server queueing system with server breakdown and repair, a stand-by server, multiple vacation and re-service. The main server's regular service time, re-service time, vacation time and stand-by server's service time are followed by general distributions and breakdown and repair times of the main server with exponential distributions. There is a stand-by server which is employed during the period in which the regular server remains under repair. The probability generating function of the queue size at an arbitrary time and some performance measures of the system are derived. Extensive numerical results are also illustrated.

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“…Vacation Queues have been studied by numerous researchers including Kleinrock (1983) , Keilson and Servi (1986), Baba (1986), Doshi (1986Doshi ( ,1990, Cramer (1989), Choi & Park (1990), Borthakur & Choudhury 1997), Madan (1992Madan ( , 1999Madan ( , 2001, to mention a few. Most of these authors have investigated single server queues assuming Bernoulli schedules or exhaustive service or generalized vacations among several other vacation policies with a single or multiple vacations.…”

Section: Introductionmentioning

confidence: 99%

“…Most of these authors have investigated single server queues assuming Bernoulli schedules or exhaustive service or generalized vacations among several other vacation policies with a single or multiple vacations. , 2001, 2001 have studied a single server queue with exponential service and deterministic vacatio ns, deterministic service with exponential vacations and deterministic service with deterministic vacations, assuming Bernoulli schedules.…”

Section: Introductionmentioning

confidence: 99%

Steady State Analysis Of An M/D/2 Queue With Bernoulli Schedule Server Vacations

Madan

Abu–Dayyeh

Tayyan

2003

J. Mod. App. Stat. Meth.

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We examine an M/D/2 queue with Bernoulli schedules and a single vacation policy. We have assumed Poisson arrivals waiting in a single queue and two parallel servers who provide identical deterministic service to customers on first-come, first-served basis. We consider two models; in one we assume that after completion of a service both servers can take a vacation while in the other we assume that only one may take a vacation. The vacation periods in both models are assumed to be exponential. We obtain steady state probability generating functions of system size for various states of the servers.

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On a single server queue with two-stage heterogeneous service and deterministic server vacations

Cited by 45 publications

References 0 publications

An M[X]/G/1 Queue with Bernoulli Schedule General Vacation Times, General Extended Vacations, Random Breakdowns, General Delay Times for Repairs to Start and General Repair Times

An M[X]/G/1 Queue with Bernoulli Schedule General Vacation Times, General Extended Vacations, Random Breakdowns, General Delay Times for Repairs to Start and General Repair Times

An M[X]/G(a,b)/1 Queueing System with Breakdown and Repair, Stand-By Server, Multiple Vacation and Control Policy on Request for Re-Service

Steady State Analysis Of An M/D/2 Queue With Bernoulli Schedule Server Vacations

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