Transient analysis of a single server queue with catastrophes, failures and repairs

Kumar, Barun; Krishnamoorthy, A.; Madheswari, S. Pavai; Basha, S. Sadiq

doi:10.1007/s11134-007-9014-0

Cited by 53 publications

(12 citation statements)

References 20 publications

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“…For example, Di Crescenzo et al [7] provides an example of a queueing system working under two alternating regimes. Also, in many queueing systems, the server is prone to failure, for example Krishna Kumar et al [8], Choudhury and Tadj [9], Kalidass et al [10], Ammar [11], and Di Crescenzo et al [12,13] deal with queueing models subject to failures (breakdowns) and repairs.…”

Section: Introductionmentioning

confidence: 99%

Steady-State Analysis of a Flexible Markovian Queue with Server Breakdowns

Bounkhel

Tadj

Hedjar

2019

Entropy

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A flexible single-server queueing system is considered in this paper. The server adapts to the system size by using a strategy where the service provided can be either single or bulk depending on some threshold level c. If the number of customers in the system is less than c, then the server provides service to one customer at a time. If the number of customers in the system is greater than or equal to c, then the server provides service to a group of c customers. The service times are exponential and the service rates of single and bulk service are different. While providing service to either a single or a group of customers, the server may break down and goes through a repair phase. The breakdowns follow a Poisson distribution and the breakdown rates during single and bulk service are different. Also, repair times are exponential and repair rates during single and bulk service are different. The probability generating function and linear operator approaches are used to derive the system size steady-state probabilities.

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Section: Introductionmentioning

confidence: 99%

Steady-State Analysis of a Flexible Markovian Queue with Server Breakdowns

Bounkhel

Tadj

Hedjar

2019

Entropy

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“…Most of them investigated mathematically the simplest queueing models -Markovian queueing systemsor mathematically the most difficult queueing models with general distribution of costumers inter-arrival times, service times etc. For example paper [4] is devoted to modelling of the unreliable M/M/1/m queueing system, paper [5] introduces a model of the unreliable M/M/1/∞ queueing system with impatient costumers, papers [6] a [7] are focused on unreliable M/M/1/∞ queueing systems with failures causing departure of all customers finding in the system. Some unreliable M/G/1/∞ queueing systems are studied in paper [8].…”

Section: Introductionmentioning

confidence: 99%

Modelling and Simulation of Unreliable e2/e2/1/m Queueing System

Dorda¹

2011

TransVSBms

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This paper is devoted to modelling and simulation of an E 2 /E 2 /1/m queueing system with a server subject to breakdowns. The paper introduces a mathematical model of the studied system and a simulation model created by using software CPN Tools, which is intended for modelling and a simulation of coloured Petri nets. At the end of the paper the outcomes which were reached by both approaches are statistically evaluated.

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“…Introduction. Queueing models with disaster and repair have been studied by many researchers in the past few decades as they possess wide applications in modeling many practical situations related to computer networks, communication systems, etc (refer [3], [4], [7], [8], [13], [14], [15], [19], [20], [25]). Closedown the system when it becomes empty and setup the system before starting the service, play a key role in various real life situations as they support economically to minimize the expenses of an organization.…”

mentioning

confidence: 99%

“…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]).…”

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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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Transient analysis of a single server queue with catastrophes, failures and repairs

Cited by 53 publications

References 20 publications

Steady-State Analysis of a Flexible Markovian Queue with Server Breakdowns

Steady-State Analysis of a Flexible Markovian Queue with Server Breakdowns

Modelling and Simulation of Unreliable e2/e2/1/m Queueing System

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

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