An M/G/1 Retrial G-Queue with General Retrial Times and Working Breakdowns

Li, Tao; Zhang, Liyuan

doi:10.3390/mca22010015

Cited by 11 publications

(2 citation statements)

References 34 publications

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“…Reliability estimates and queueing measures for a bulk advent G-queue under general reiterate times, malfunction, and single vacation policy have been provided by Yang et al (2013). Li and Zhang (2017) explored an M/G/1 reiterate G-queue with general reiterate times and working malfunction. Only one operator reiterate G-queue involving second phase assistance was recently explored by Upadhyaya (2020) who also discussed its use in local network environments.…”

Section: Literature Reviewmentioning

confidence: 99%

Maximum Entropy Solution for M^X/G/1 Priority Reiterate G-queue Under Working Breakdown and Working Vacation

Nisha,

Upadhyaya,

Shekhar

2024

Int. j. math. eng. manag. sci.

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The maximum entropy principle has grown progressively more pertinent to queueing systems. The principle of maximum entropy (PME) presents an impartial framework as a promising method to examine complex queuing processes. This principle can be employed to assess the most appropriate probability distributions for queueing scenarios in a variety of widespread industrial issues. The aspects of general service bulk arrival retrial G-queue including working vacation, state-dependent arrival, priority users, and working breakdown are all explored in this article. Real-world applications for this kind of waiting line include computer systems, industrial companies, packet-switching networks, and communication facilities, etc. The adverse users (or negative arrivals) can make an appearance when the server (operator) is preoccupied with a positive user. Consumer’s arrival patterns follow the Poisson distribution. Priority consumers and regular (ordinary) consumers are the two groups of consumers that are considered in this investigation. Priority consumers do not have to wait in line and are granted a special right of prevention that allows them to receive services before ordinary consumers. Initially, we have estimated performance metrics including orbit size and long-run probabilities in this research work. The maximum entropy approach is then used to give a comparative perusal between the system’s exact and estimated waiting times. Apart from that a bi-objective optimization model is developed to diminish both consumers waiting times and estimated costs simultaneously. It is manageable to establish an effective balance between the standard of service and operating expenses using the analytical strategy that has been provided.

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Section: Literature Reviewmentioning

confidence: 99%

Maximum Entropy Solution for M^X/G/1 Priority Reiterate G-queue Under Working Breakdown and Working Vacation

Nisha,

Upadhyaya,

Shekhar

2024

Int. j. math. eng. manag. sci.

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“…In their work, the supplementary variable has been used. Li and Zhang (2017) have analyzed an M/G/1 retrial G − queue with working breakdowns. They have supposed that during the breakdown period, the service still continues with a lower rate.…”

Section: Introductionmentioning

confidence: 99%

An unreliable single server retrial queue with collisions and transmission errors

Lakaour

Aı̈ssani

Adel-Aissanou

et al. 2020

Communications in Statistics - Theory and Methods

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The present paper deals with the performance evaluation of an M/M/1 retrial queue with collisions, transmission errors and unreliable server. To the best of our knowledge, there are no works that have dealt with retrial queues by considering all the above-mentioned aspects (collisions, transmission errors and unreliable server). This queue can be used as a mathematical model of several computer systems and telecommunication networks. We apply the generating function method to derive the joint distribution of the server state and the orbit length in the steady state, and we obtain some performance measures. Finally, we provide numerical illustrations to show the effectiveness and the applicability of the model.

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