Steady state analysis of a non-Markovian bulk queueing system with overloading and multiple vacations

Balasubramanian, M.; Arumuganathan, R.; Vadivu, A. Senthil

doi:10.1504/ijor.2010.034362

Cited by 5 publications

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“…Arumuganathan and Jeyakumar [1] analyzed a bulk queue with multiple vacations, setup times with N -policy and closedown times. Lee et al [15] analyzed an M x /G/1queue with N-policy and multiple vacation Balasubramanian et al [2] discussed steady state analysis of a Non-Markovian bulk queueing system with overloading and multiple vacations. Haridass and Arumuganathan [8] discussed a batch arrival general bulk service queueing system with variant threshold policy for secondary jobs.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a M^X/G(a,b)/1 queueing system with vacation interruption

Haridass

Arumuganathan

2012

RAIRO-Oper. Res.

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In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least 'a' customers waiting for service say ξ, he serves a batch of min (ξ, b) customers, where b ≥ a. On the other hand, if the queue length is at the most 'a-1', the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary job is interrupted abruptly and the server resumes for primary service, if the queue size reaches 'a', during the secondary job period. On completion of the secondary job, the server remains in the system (dormant period) until the queue length reaches 'a'. For the proposed model, the probability generating function of the steady state queue size distribution at an arbitrary time is obtained. Various performance measures are derived. A cost model for the queueing system is also developed. To optimize the cost, a numerical illustration is provided.

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Section: Introductionmentioning

confidence: 99%

Analysis of a M^X/G(a,b)/1 queueing system with vacation interruption

Haridass

Arumuganathan

2012

RAIRO-Oper. Res.

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“…Jeyakumar and Arumuganathan [17] have discussed steady state analysis of an M [X] ]/G/1 queue with two service modes and multiple vacation, in which they obtained PGF of the queue size and some performance measures. Balasubramanian et al [18] discussed steady state analysis of a non-Markovian bulk queueing system with overloading and multiple vacations. Haridass and Arumuganathan [19] discussed a batch arrival general bulk service queueing system with a variant threshold policy for secondary jobs.…”

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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“…Doshi (1985) discussed an M/G/1 system with variable vacations. Balasubramanian et al (2010) discussed steady state analysis of a non-Morkovian bulk queueing system with overloading and multiple vacations. Xu et al (2009) have discussed an M/M/1 with single working vacation and set-up times.…”

Section: Literature Surveymentioning

confidence: 99%

An M<SUP align="right">x</SUP>/G/1 retrial queue with two phase service under active server breakdowns, two types of repair and multiple vacations with N-policy

Jailaxmi

Arumuganathan

Rathinasamy

2013

IJOR

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This paper analyses a single server batch arrival retrial queue with active breakdowns, two types of repair, a second optional service and multiple vacations with N-policy. The server may breakdown while providing first essential service. When the server fails, it is repaired immediately. On successful completion of first essential service, the customer may opt for second optional service with probability α. At a service completion epoch, without any request for re-service and the orbit size being zero, the server does a secondary job (vacation) repeatedly until the number of customers in the orbit reaches the threshold value N. At a secondary job completion epoch, if the orbit size in at least N, then the server remains in the system to render service for customers from main pool or from retrial group. The steady state queue size distribution of number of customers in the orbit and expected number of customers in the retrial group are obtained. Some particular cases and reliability measures are discussed. Also, some performance measures are obtained. Numerical illustrations are also provided.

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Steady state analysis of a non-Markovian bulk queueing system with overloading and multiple vacations

Cited by 5 publications

References 0 publications

Analysis of a M^X/G(a,b)/1 queueing system with vacation interruption

Analysis of a M^X/G(a,b)/1 queueing system with vacation interruption

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

An M<SUP align="right">x</SUP>/G/1 retrial queue with two phase service under active server breakdowns, two types of repair and multiple vacations with N-policy

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Steady state analysis of a non-Markovian bulk queueing system with overloading and multiple vacations

Cited by 5 publications

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Analysis of a MX/G(a,b)/1 queueing system with vacation interruption

Analysis of a MX/G(a,b)/1 queueing system with vacation interruption

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

An M<SUP align="right">x</SUP>/G/1 retrial queue with two phase service under active server breakdowns, two types of repair and multiple vacations with N-policy

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Analysis of a M^X/G(a,b)/1 queueing system with vacation interruption

Analysis of a M^X/G(a,b)/1 queueing system with vacation interruption