RETRACTED ARTICLE: Transient analysis of an M/M/1 queue with variant impatient behavior and working vacations

Sudhesh, R.; Azhagappan, A.

doi:10.1007/s12597-018-0339-8

Cited by 8 publications

(3 citation statements)

References 15 publications

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“…There are many practical situations where the steady state solutions are not applicable. As a result, the development of transient solutions for various queueing models is mainly focused by many researchers for the past three decades (refer [1], [9], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22]).…”

mentioning

confidence: 99%

“…They obtained the time-dependent system size distributions, average and variance of size of the system explicitly. Sudhesh and Azhagappan [22] obtained the transient system size probabilities for the M/M/1 queueing model with working vacation and variant impatient behavior of customers using continued fraction. They also derived the expected system size and variance of system size for the time-dependent case.…”

mentioning

confidence: 99%

“…Taking Laplace inversion of (31), we get (22). The expressions given in (10), (16), (17), (18), (19), (20), (21) and (22) together represent the transient system size probabilities of the proposed model.…”

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confidence: 99%

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Transient analysis of N-policy queue with system disaster repair preventive maintenance re-service balking closedown and setup times

Azhagappan¹,

Deepa²

2020

Journal of Industrial &Amp; Management Optimization

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This paper investigates the transient behavior of a M/M/1 queueing model with N-policy, system disaster, repair, preventive maintenance, balking, re-service, closedown and setup times. The server stays dormant (off state) until N customers accumulate in the queue and then starts an exhaustive service (on state). After the service, each customer may either leave the system or get immediate re-service. When the system becomes empty, the server resumes closedown work and then undergoes preventive maintenance. After that, it comes to the idle state and waits N accumulate for service. When the N th one enters the queue, the server commences the setup work and then starts the service. Meanwhile, the system suffers disastrous breakdown during busy period. It forced the system to the failure state and all the customers get eliminated. After that, the server gets repaired and moves to the idle state. The customers may either join the queue or balk when the size of the system is less than N. The probabilities of the proposed model are derived by the method of generating function for the transient case. Some system performance indices and numerical simulations are also presented.

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