Unreliable bulk retrial queues with delayed repairs and modified vacation policy

Jain, Madhu; Bhagat, Amita

doi:10.1007/s40092-014-0063-9

Cited by 21 publications

(5 citation statements)

References 28 publications

(17 reference statements)

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“…Chakravarthy (2013) investigated a single server queue with vacation on the premise that customers might use two optional services depending on their needs and that both optional and essential services were provided by the same server. Jain and Bhagat (2014) described a model for a retrial bulk input queuing system with k-essential phases of service offered to all users under a modified vacation policy, assuming that the server may go down at any time during the service. Govindan and Shyamala (2014) used the additional variable technique to analyse the performance characteristics of the M [X] /G/1 retrial queue with second optional service and random breakdown of the server under Bernoulli vacation policy.…”

Section: Introductionmentioning

confidence: 99%

A multi-server with backup system employs decision strategies to enhance its service

R¹,

S²

2023

Preprint

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The queueing paradigm is frequently applied in the manufacturing, inventory, and service industries. The effectiveness of the queuing model can be greatly enhanced by specifying the real properties of queuing. This research examines impatient client behaviors that may lead to renege in a multi-server queuing system, as well as the strategic behavior of the service provider that tries to enhance the service by adding a backup server. A very intricate multi-dimensional continuous-time Markov chain that has been successfully analysed accurately describes the system's behavior. The decision rules are used to frame the value function and the iteration algorithm is used to get the total expected cost and the optimal average cost of the entire system. By enabling the numerical results for the relevant case, the sensitivity analysis is carried out.

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Section: Introductionmentioning

confidence: 99%

A multi-server with backup system employs decision strategies to enhance its service

R¹,

S²

2023

Preprint

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“…In the queueing literature, a few researchers including Medhi [23], Wang [35], Choudhury and Deka [5] worked on this aspect under varied assumptions. Bulk queue with multiphase services was discussed by Jain and Bhagat [15] by considering the features of retrial, unreliable server and modified vacation policy. Recently, Jain et al [31] explored the bulk arrival queue with optional service by incorporating the balking behaviour of customers, unreliable server and multiphase repairs.…”

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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“…But sometimes due to some limitations, these repairs are delayed.Madhu Jain and AmitaBhagat [26] and Choudhury and Ke [21] have been considered this issue in their model. Some systems aren't able to respond to all customers.…”

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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Unreliable bulk retrial queues with delayed repairs and modified vacation policy

Cited by 21 publications

References 28 publications

A multi-server with backup system employs decision strategies to enhance its service

A multi-server with backup system employs decision strategies to enhance its 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

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Unreliable bulk retrial queues with delayed repairs and modified vacation policy

Cited by 21 publications

References 28 publications

A multi-server with backup system employs decision strategies to enhance its service

A multi-server with backup system employs decision strategies to enhance its 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

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