Transient solution of an M&lt;SUP align="right"&gt;[X]&lt;/SUP&gt;/G/1 queueing model with feedback, random breakdowns, Bernoulli schedule server vacation and random setup time

Ayyappan, G.; Shyamala, S.

doi:10.1504/ijor.2016.073956

Cited by 9 publications

(7 citation statements)

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“…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%

“…A detailed survey on queues with interruptions was undertaken by Krishnamoorthy et al [10]. Ayyappan and Shyamala [11] derived the transient solution to an M [X] /G/1 queueing system with feedback, random breakdowns, Bernoulli schedule server vacation and random setup time. An M/G/1 queue with two phases of service subject to random breakdown and delayed repair was examined by Choudhury and Tadj [12].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Literature Surveymentioning

confidence: 99%

Section: Introductionmentioning

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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“…They consider the service times as independent and identically distributed with different rates when the customer is served with feedback or without feedback. Other studies on feedback are found in [9][10][11][12][13], etc.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Batch Arrival General Service Queue with Balking, Feedback and Second Optional Service

Vijaya Laxmi,

Qrewi,

George

2023

Contemp. Math.

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This paper aims to analyze the steady-state behavior of bulk input general service queue with a second optional service (SOS), balking, and feedback facility. In this study, the server provides two kinds of services such as first essential service (FES) and SOS. The FES is provided to all arriving customers to the system while SOS is only to those customers who demand additional service. When the customer completes FES and is not satisfied with the service, he may choose to rejoin the queue (feedback) or opt for SOS or depart from the system with a certain probability. We have computed the probability-generating function of the queue-length distribution after converting the non-Markovian to Markovian process by using a supplementary variable technique. This technique is used to solve the non-Markov queue model by taking the elapsed service times as the supplementary variable so that the process becomes Markovian. This study contributes to filling the gap in the analysis of batch arrival general service queues with balking, feedback, and SOS. Furthermore, we have presented the numerical results and cost optimization. The results reveal that the higher service rate in both FES and SOS helps the system manager to run the system effectively. Similarly, in cost optimization, the system manager should make emphasize choosing optimal service rates to have a cost-benefit and less congestion in the queueing system.

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“…An M/G/1 retrial queue having optional feedback along with a pair of heterogeneous essential service, was investigated by Lakshmi and Ramanath [20]. Ayyappan and Shyamala [3] have studied the bulk arrival feedback queueing model by utilizing Laplace Stieltjes transform. Lately, Chang et al [4] have discussed unreliable server queue with impatient customers and Bernoulli feedback and derived steady state queue size probabilities using quasi progression algorithm.…”

Section: Introductionmentioning

confidence: 99%

Bernoulli vacation model for M^X/G/1 unreliable server retrial queue with bernoulli feedback, balking and optional service

Jain

Kaur

2021

RAIRO-Oper. Res.

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The study of unreliable server retrial bulk queue with multiphase optional service is analyzed by incorporating the features of balking, Bernoulli vacation and Bernoulli feedback. On the occasion when the server is occupied with the service of the customers, an arriving customer finding the long queue, can join the retrial orbit and receives its service later on by making re-attempt. The system is reinforced with multi phase optional service along with essential service and joining customer can opt any one of optional services after getting essential service. Furthermore, the essential/ optional service can be aborted due to abrupt failure of the server. There is an immediate support of multi phase repair facility to take care of the failed server, but sometimes repair may be put on hold by virtue of any unexpected cause. If the service is unsatisfactory, the customer can rejoin the queue as feedback customer. Bernoulli vacation is permitted to the server following the respective busy period. For evaluating the queue size distribution and other system performance metrics, supplementary variable technique (SVT) is used. The approximate solutions for the steady state probabilities and waiting time are suggested using maximum entropy principle (MEP). To verify the outcomes of the model, numerical illustrations and cost analysis have been accomplished.

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Transient solution of an M<SUP align="right">[X]</SUP>/G/1 queueing model with feedback, random breakdowns, Bernoulli schedule server vacation and random setup time

Cited by 9 publications

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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[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 Batch Arrival General Service Queue with Balking, Feedback and Second Optional Service

Bernoulli vacation model for M^X/G/1 unreliable server retrial queue with bernoulli feedback, balking and optional service

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Transient solution of an M<SUP align="right">[X]</SUP>/G/1 queueing model with feedback, random breakdowns, Bernoulli schedule server vacation and random setup time

Cited by 9 publications

References 0 publications

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[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 Batch Arrival General Service Queue with Balking, Feedback and Second Optional Service

Bernoulli vacation model for MX/G/1 unreliable server retrial queue with bernoulli feedback, balking and optional service

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Bernoulli vacation model for M^X/G/1 unreliable server retrial queue with bernoulli feedback, balking and optional service