M<sup>x</sup>/G/1 retrial vacation queue for multi-optional services, phase repair and reneging

Jain, Madhu; Bhagat, Amita

doi:10.1080/16843703.2016.1189025

Cited by 16 publications

(5 citation statements)

References 29 publications

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“…Similarly, utilizing P 0 in equation (A. 16) and further substituting the outcome in (A.11), we can easily obtain equation (4.3) and hence equations (4.4-4.6).…”

Section: Appendix Amentioning

confidence: 98%

“…Using (A.1), (A.4), (A.11), (A.18-A.20) in normalizing condition (3.14) and further using (A.12), (A.13) and (A. 16), (A.17), we can obtain value of P 0 as…”

Section: Appendix Amentioning

confidence: 99%

“…Some queueing theorists have done research works in different frameworks by considering unreliable server [8,21]. M X /G/1 queueing system with reneging having unreliable server, and multi optional services was analyzed by Jain and Bhagat [16] by employing SVT. The balking behaviour in the arriving units may also emerged due to sudden failure of system; this concept was incorporated in the investigation done by Singh et al [32] for the study of queueing system with bulk input, Bernoulli feedback, breakdown and multiphase repairs.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Similarly, utilizing P 0 in equation (A. 16) and further substituting the outcome in (A.11), we can easily obtain equation (4.3) and hence equations (4.4-4.6).…”

Section: Appendix Amentioning

confidence: 98%

“…Using (A.1), (A.4), (A.11), (A.18-A.20) in normalizing condition (3.14) and further using (A.12), (A.13) and (A. 16), (A.17), we can obtain value of P 0 as…”

Section: Appendix Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…Some of the works in this area have been done in this area are Kumar et al Also, returning to the orbit (feedback) is considered in many of the studied systems. For example, Kumar et al [ [19], modified vacation by Jain and Bhagat [20], Bernoulli vacation by Choudhury and Ke [21], working vacation by Azhagappan [22] and variant vacation by Ke [23].…”

Section: Introduction *mentioning

confidence: 99%

Reliability and Sensitivity Analysis of a Batch Arrival Retrial Queue with k-Phase Services, Feedback, Vacation, Delay, Repair and Admission

Abdollahi

Rad

2020

IJRRS

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Queueing theory is a way for real-world problems modeling and analyzing. In many processes, the input is converted to the desired output after several successive steps. But usually limitations and conditions such as Lack of space, feedback, vacation, failure, repair, etc. have a great impact on process efficiency.This article deals with the modeling the steady-state behavior of a‫ܯ‬ Ȁ‫ܩ‬Ȁ ͳretrial queueing system with ݇ phases of service. The arriving batches join the system with dependent admission due to the server state.If the customers find the server busy, they join the orbit to repeat their request. Although, the first phase of service is essential for all customers, any customer has three options after the completion of the ݅ െ ‫݄ݐ‬phaseሺ݅ ൌ ͳǡʹǡ ǥ ǡ ሻ. They may take the ሺ݅ ͳሻ െ ‫݄ݐ‬ phase of service with probabilityɅ ୧ , otherwise return the orbit with probability ୧ or leave the system with probability ሺͳ െ ୧ െ Ʌ ୧ ሻ. Also, after each phase, the probabilistic failure, delay, repair and vacation are considered.In this article, after finding the steady-state distributions, the probability generating functions of the system and orbit size have been found. Then, some important performance measures of the system have been derived. Also, the system reliability has been defined. Eventually, to demonstrate the capability of the proposed model, the sensitivity analysis of performance measures via some model parameters (arrival/retrial/vacation rate) in different reliability levels have been investigated in a specific case of this model. Additionally, for optimizing the performance of system, some technical suggestions are presented.

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“…Queuing systems with repeated attempts have been widely studied in the literature (see, e.g. Chang and Ke [4], Kim et al [5], Jain and Bhagat [6], Gao et al [7], and Ke et al [8]). However, one encounters that the server may breakdown in practical situations.…”

Section: Introductionmentioning

confidence: 99%

Retrial queues with starting failure and service interruption

Liu

Yang

2018

IET Communications

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M^x/G/1 retrial vacation queue for multi-optional services, phase repair and reneging

Cited by 16 publications

References 29 publications

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

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

Reliability and Sensitivity Analysis of a Batch Arrival Retrial Queue with k-Phase Services, Feedback, Vacation, Delay, Repair and Admission

Retrial queues with starting failure and service interruption

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Mx/G/1 retrial vacation queue for multi-optional services, phase repair and reneging

Cited by 16 publications

References 29 publications

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

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

Reliability and Sensitivity Analysis of a Batch Arrival Retrial Queue with k-Phase Services, Feedback, Vacation, Delay, Repair and Admission

Retrial queues with starting failure and service interruption

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Product

Resources

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M^x/G/1 retrial vacation queue for multi-optional services, phase repair and reneging

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

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