A Two Stage Batch Arrival Queue with Reneging during Vacation and Breakdown Periods

Baruah, Monita; Madan, Kailash C.; Eldabi, Tillal

doi:10.4236/ajor.2013.36054

Cited by 13 publications

(8 citation statements)

References 17 publications

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“…If we assume there is no delay, standby server, extended vacation and second optional repair with two stages of service having single vacation policy then The above result agrees with the result given Monita Baruah et al, [6]…”

Section: Case (Ii) No Delay No Standby Server No Extended Vacationsupporting

confidence: 87%

M[x]/G/1 Multistage Queue with Stand-by Server During Main Server’s Interruptions

Chandrasekaran

Vijayalakshmi

2018

IJEECS

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<p>This paper investigates a multistage batch arrival queue with different server interruptions and a second server replaces the main server during the interruptions. The different server interruptions are assumed to be: multiple vacation, extended vacation, breakdown with delay time and server under two phases of repair. Customers are assumed to arrive in batches according to Poisson process and a single server provides service to the customers. When the main server is inactive due to the interruptions, stand-by server provide service to the arrivals. In addition, customers may renege during server breakdown or during server vacation due to impatience. Transient solution and the corresponding steady state solution is derived using supplementary variable technique.</p>

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Section: Case (Ii) No Delay No Standby Server No Extended Vacationsupporting

confidence: 87%

M[x]/G/1 Multistage Queue with Stand-by Server During Main Server’s Interruptions

Chandrasekaran

Vijayalakshmi

2018

IJEECS

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“…Arumugananathan and Maliga [24] also examined a bulk queue with re-service of the service station and setup time. Baruah et al [25] studied a batch arrival queue with two types of service, balking, re-service and vacation. Ayyappan and Sathiya [11] derived the PGF of the non-Markovian queue with two types of service and optional re-service with a general vacation distribution.…”

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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“…Also, derived certain queueing models as special cases. Baruah et al (2013) studied a batch arrival queue where service is offered in two stages with customer reneging during the system breakdown or vacation periods. They obtained the mean queue length and mean waiting time.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Two-Phase Queuing System With Impatient Customers, Server Breakdowns and Delayed Repair

Rao¹,

Kumar²,

Kumar³

et al. 2017

Int. J. of Pure and Appl. Math.

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Abstract:We study a two-phase Markovian queueing model where the first phase of service is for all waiting customers in batch mode and second phase of service is in individual mode to each of them. The server may breakdown during any phase of service and may not be repaired immediately due to non-availability of the repair facility. Arriving customers may balk with certain probability and may depart after joining the queue without getting the service due to impatience. Customers reneging is assumed to occur when the server is in individual service or during breakdown rate of individual service. We derive the probability generating functions for the number of customers present in the system when the server is in different states. Further, closed form of expressions for the mean system size for various states of the server, balking rate, reneging rate and loss rate are derived. Numerical examples are presented.

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A Two Stage Batch Arrival Queue with Reneging during Vacation and Breakdown Periods

Cited by 13 publications

References 17 publications

M[x]/G/1 Multistage Queue with Stand-by Server During Main Server’s Interruptions

M[x]/G/1 Multistage Queue with Stand-by Server During Main Server’s Interruptions

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

Analysis of Two-Phase Queuing System With Impatient Customers, Server Breakdowns and Delayed Repair

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