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Parthasarathy, P. R.; Vijayashree, K. V.; Lenin, R. B.

doi:10.1023/a:1020157021703

Cited by 36 publications

(6 citation statements)

References 15 publications

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“…The above results coincide with the results of Parthasarathy, Vijayashree and Lenin [10] discussed for stationary solution when there is no catastrophe and restoration takes place.…”

Section: Particular Casesupporting

confidence: 90%

“…Van Doorn and Scheinhardt [13] have obtained explicit expressions for the stationary distribution of the buffer content for fluid queues driven by an M/M/1 queue with constant arrival service rates. A continued fraction method to analyse fluid queues has been proposed by Parthasarathy, Lenin and Vijayashree [10]. Transmission Control Protocol (TCP) is able to guarantee that each data packet transmitted from a server (computer) and leave it momentarily inactivated until the new arrival occurs, such infected cells may be modeled by catastrophes.…”

Section: Introductionmentioning

confidence: 99%

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A Fluid Model Driven by an M/M/1 Queue With Catastrophe and Restoration Time

Vijayalakshmi¹,

Thangaraj²

2013

Int. J. of Appl. Math.

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In this paper, we discuss a fluid queue driven by an M/M/1 queue with catastrophe and restoration. Using the continued fraction technique, we derive the Laplace transform of the transient state probability distribution of the buffer content, transient solution for this fluid queue and the corresponding steady state results explicitly. Also we analyze the queue when there are no catastrophes and no restoration.

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“…The above results coincide with the results of Parthasarathy, Vijayashree and Lenin [10] discussed for stationary solution when there is no catastrophe and restoration takes place.…”

Section: Particular Casesupporting

confidence: 90%

Section: Introductionmentioning

confidence: 99%

A Fluid Model Driven by an M/M/1 Queue With Catastrophe and Restoration Time

Vijayalakshmi¹,

Thangaraj²

2013

Int. J. of Appl. Math.

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“…We prove the above results by mathematical induction on m for every j . Now, using (15) in (12), we have…”

Section: Analysis Of the Modelmentioning

confidence: 99%

“…Later, Adan and Resing [11] shown the results of Virtamo and Norros [10] in the form of the modified Bessel function of the first kind of order one by observing at embedded time points. Parthasarathy et al [12] carried out explicit expressions for the steady-state distribution of buffer occupancy and buffer content of a fluid queueing model driven by an / /1 MM queue based on the continued fraction technique. Barbot and Sericola [13] derived the solution of buffer level and state of the / /1 MM fluid queueing model using the generating function approach associated with exponential matrix.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Stationary Fluid Queue Driven by State-Dependent Birth-Death Process Subject to Catastrophes

Ammar¹,

Samanta²,

Kilany³

et al. 2022

Scientia Iranica

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This paper investigates an infinite buffer fluid queueing model driven by a state-dependent birth-death process prone to catastrophes.We use the Laplace-Stieltjes transform and continued fraction approaches to establish precise expression for the joint probability of the content of the buffer and the number of customers in an / /1 MM queueing model. The importance of the proposed system is that, in numerous practical situation, the service facility has defence mechanisms in place to deal with long waits. Under the strain of a significant backlog of work, the servers may improve their service rate. Therefore,considering the state-dependent character of queueing systems is of relevance. For example, congestion control technologies prevent long queues forming in computer and communication systems by adjusting packet transmission speeds based on the length of the queue (of packets) at the source or destination. Theoretical results are supported by numerical illustrations.

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“…The busy period for the buffer content has been analysed in Boxma and Dumas [5] for the case where the fluid queue is fed by an arbitrary number of on-off arrival streams. Parthasarathy et al [17] have presented the stationary buffer occupancy distribution of the fluid queue controlled by the M/M/1 queue employing a continued fraction technique. Barbot and Sericola [4] have introduced a new analytic expression for the stationary buffer content by adopting the generating function method.…”

mentioning

confidence: 99%

Performance analysis of a fluid flow system modulated by a single server queue prone to catastrophic failures and repairs

Kumar

Krishnan

Sankar

et al. 2023

JIMO

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<p style='text-indent:20px;'>This article deals with a new class of fluid flow queue regulated by an <inline-formula><tex-math id="M1">\begin{document}$ M/M/1 $\end{document}</tex-math></inline-formula> queueing system in the presence of active catastrophic failures and subsequent repairs of the server. The distribution of the stationary buffer-content is determined in terms of modified Bessel function of first kind. Besides, an explicit closed-form analytical expression for the probability density function of the fluid level in the stationary regime is derived in an elegant manner. Some important and essential performance measures are obtained. Finally, numerical results are provided to illustrate the behaviour of the buffer content distribution and the performance measures for the proposed fluid flow queueing model.</p>

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Cited by 36 publications

References 15 publications

A Fluid Model Driven by an M/M/1 Queue With Catastrophe and Restoration Time

A Fluid Model Driven by an M/M/1 Queue With Catastrophe and Restoration Time

Analysis of Stationary Fluid Queue Driven by State-Dependent Birth-Death Process Subject to Catastrophes

Performance analysis of a fluid flow system modulated by a single server queue prone to catastrophic failures and repairs

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