Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging

Bouchentouf, Amina Angelika; Medjahri, Latifa; Boualem, Mohamed; Kumar, Amit

doi:10.22363/2658-4670-2022-30-1-21-38

Cited by 6 publications

(4 citation statements)

References 29 publications

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“…Singla [24] provided a re-service facility to the unsatisfied customers in retrial queueing model with two servers and feedback where feedback customers may join the orbit with retrial customers and re-try for service. Optional re-service is also provided by Boutchentouf [9] in Markovian multi-server feedback queue with impatient customers and variant of multiple vacations. Comparison of M/M/2 and M/M/1 queueing models having particular service interruption and feedback customers was done by Mahla [20].…”

Section: State Of Artmentioning

confidence: 99%

Study of markovian queueing model with F-policy, impatience customers, feedback and re-service, server vacation and breakdown

Mahla

Sharma

2022

Preprint

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A system with two heterogeneous servers with impatient customers and finite capacity is considered. The admission control of customers is based on F-policy. This paper is based on M/M/2 queues, and presents the study of two heterogeneous servers where one server is the primary server and other is secondary. Customers are primarily served by the main server, who also takes customer's feedback into account. If customers are unsatisfied and opt for further service, the second server will serve them. The main server considered is unreliable, that is, it may breakdown at any time. The main server will go for vacation whenever there is no customer to serve. To analyze the performance of the model, we calculated the measures of performance and did the cost analysis. Impact of F-policy on system's estimated profit is shown. At last, conclusions are drawn.

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Section: State Of Artmentioning

confidence: 99%

Study of markovian queueing model with F-policy, impatience customers, feedback and re-service, server vacation and breakdown

Mahla

Sharma

2022

Preprint

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“…A heterogeneous queuing system with reverse balking and reneging was discussed by Som and Kumar [20]. In another work Bouchentouf et al [21] presented the mathematical modelling of a multi-server Markovian queue with Bernoulli feedback under variant of multiple vacation policy in the absence of retention strategy. In these papers [15][16][17][18][19] authors did not assume the concept of discouraged arrival.…”

Section: Introductionmentioning

confidence: 99%

Analysis of single server finite buffer queue under discouraged arrival and retention of reneging

Medhi

Choudhury

2023

Yugosl J Oper Rres

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Queuing models where arrival rates go down consequent to increase in the number of customers are called systems with discouraged arrivals. Discouraged arrivals are distinct from balking in the sense that balking implies that arriving customers do not join. In this paper, we model a single server finite buffer Markovian queuing model with discouraged arrival, balking, reneging and retention of reneged customers. The steady state probabilities are obtained using Markov process method. Closed form expression of traditional as well as some freshly designed performance measures are presented. We also perform sensitivity analysis to examine the variations in performance measures with the variations in system parameters. Our results are numerically illustrated through a field level problem with design connotations.

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“…In the existing literature, for example [22] and [24], the customer has only two options such as opting for the feedback if he/she is not happy with the quality of service or leaving the system after completing the service. Further, the arriving customers decide to enter the queue with a certain probability or balk with a certain probability when the server is on vacation period or during a busy period.…”

Section: Introductionmentioning

confidence: 99%

“…Substituting equation(22) in equation (28), we obtain the result. Lemma Based on the previous results, we have…”

mentioning

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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Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging

Cited by 6 publications

References 29 publications

Study of markovian queueing model with F-policy, impatience customers, feedback and re-service, server vacation and breakdown

Study of markovian queueing model with F-policy, impatience customers, feedback and re-service, server vacation and breakdown

Analysis of single server finite buffer queue under discouraged arrival and retention of reneging

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

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