Unreliable retrial queueing system with working vacation

Shanmugam, Bharanidharan; Saravanarajan, M.C.

doi:10.3934/math.20231234

Cited by 3 publications

(2 citation statements)

References 38 publications

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“…Pazhani et al [19] used the supplementary variable technique to obtain the probability generating function for the number of customers and the mean number of customers in the invisible waiting area of a retrial queue with working vacation and a single waiting server. Shanmugam and Saravanarajan [20] investigated an unreliable retrial queueing system with working vacation. The orbit and system lengths were derived through the supplementary variable method.…”

Section: Introductionmentioning

confidence: 99%

Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

Liu,

Chiou,

Chen

et al. 2024

Mathematics

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This work investigates a two-way communication retrial queue with synchronous working vacation and a constant retrial policy. During the idle time, a server makes an outgoing call after a random length. The service time of the incoming call and outgoing call obeys exponential distribution with different rates. If the incoming call finds all servers to be unavailable, it may or may not enter orbit. All servers immediately go on vacation simultaneously as soon as they find an empty system after the service finishes. During vacation, the servers can provide a service to those incoming calls, but this is at a lower-speed rate. The stationary probability distribution and the ergodic condition are obtained utilizing the matrix geometric technique. Some system characteristics are developed. Using MATLAB software, the variation in average orbit length, idle ratio, and the average number of servers in different server states is plotted for different values of the incoming/outgoing call rate and retrial rate. We further propose a multi-objective optimization model from which the optimal rate of outgoing calls and optimal vacation rate are explicitly obtained.

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Section: Introductionmentioning

confidence: 99%

Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

Liu,

Chiou,

Chen

et al. 2024

Mathematics

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“…In further development of the M/M/1/WV queueing model, Wu and Takagi [24] have constructed an M/G/1 model that established a WV extension. Bharathy and Saravanarajan [25] investigate unreliable retrial queues by including WV. Bouchentouf et al [26] have investigated finite capacity Markovian queues with different WV.…”

Section: Introductionmentioning

confidence: 99%

Non-Markovian Feedback Retrial Queue with Two Types of Customers and Delayed Repair Under Bernoulli Working Vacation

2024

Contemp. Math.

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This paper deals with an M/G/1 feedback retrial G-queue and delayed repair incorporating Bernoulli working vacation. Arrivals of both favorable and unfavorable consumers are two independent Poisson processes. The server is subjected to breakdown during the regular busy period due to the arrival of unfavorable customers and then the server will be down for a short period of time. Further, the concept of delay time is also discussed. After the fulfillment of regular service, the dissatisfied consumer may re-join the orbit to receive another service as a feedback consumer. During the working vacation period, the server provides the service to consumers at a reduced rate. By applying the supplementary variable technique (SVT), we have analyzed the steady-state probability generating function (PGF) for the system size and orbit size. In addition, we have presented the system performance, reliability indicators, and stochastic decomposition property. Finally, we provided numerical examples to illustrate our model’s mathematical results.

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Sensitivity analysis of a non-Markovian feedback retrial queue, reneging, delayed repair with working vacation subject to server breakdown

Sundarapandiyan,

Nandhini

2024

MATH

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This study investigated the steady-state characteristics of a non-Markovian feedback retrial queue with reneging, delayed repair, and working vacation. In this scenario, we assumed that consumers arrive through Poisson processes and the server provides service to consumers during both regular and working vacation periods. However, it is subject to breakdowns at any moment, resulting in a service interruption for a random duration. Additionally, the concept of delay time was also presented. The consumer that is dissatisfied with the service may re-enter the orbit to receive another service; this individual is considered a feedback consumer. The server will go on a working vacation if the orbit is empty after successfully serving a satisfied consumer. By utilizing the supplementary variable technique (SVT), we examined the steady-state probability generating function of the system and orbit sizes. Finally, numerical outcomes and a sensitivity analysis were given to verify the analytical findings of important performance indicators.

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Unreliable retrial queueing system with working vacation

Cited by 3 publications

References 38 publications

Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

Non-Markovian Feedback Retrial Queue with Two Types of Customers and Delayed Repair Under Bernoulli Working Vacation

Sensitivity analysis of a non-Markovian feedback retrial queue, reneging, delayed repair with working vacation subject to server breakdown

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