Transient Analysis for State-Dependent Queues with Catastrophes

Kumar, Barun; Vijayakumar, A.; Sophia, S.

doi:10.1080/07362990802405786

Cited by 16 publications

(17 citation statements)

References 21 publications

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“…Note that Equation 19is the suitable extension of (2.7) of [10], which refers to the case of constant rates. Furthermore, we remark that from (18) and (19), one obtains:…”

Section: Transient Probabilitiesmentioning

confidence: 98%

“…Making use of (6) and (18) in (19), for t ≥ t 0 and n ∈ Z, one has the following expression for the transition probabilities of N(t):…”

Section: Transient Probabilitiesmentioning

confidence: 99%

“…The literature on the area of stochastic systems evolving in the presence of catastrophes is very broad. We restrict ourselves to mentioning the papers by Economou and Fakinos [15,16], Kyriakidis and Dimitrakos [17], Krishna Kumar et al [18], Di Crescenzo et al [19], Zeifman and Korotysheva [20], Zeifman et al [21] and Giorno et al [22]. The analysis of some time-dependent queueing models with catastrophes has been performed in Di Crescenzo et al [23] and, more recently, in Giorno et al [24], with special attention to the M(t)/M(t)/1 and M(t)/M(t)/∞ queues.…”

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confidence: 99%

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A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation

et al. 2018

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We consider a time-non-homogeneous double-ended queue subject to catastrophes and repairs. The catastrophes occur according to a non-homogeneous Poisson process and lead the system into a state of failure. Instantaneously, the system is put under repair, such that repair time is governed by a time-varying intensity function. We analyze the transient and the asymptotic behavior of the queueing system. Moreover, we derive a heavy-traffic approximation that allows approximating the state of the systems by a time-non-homogeneous Wiener process subject to jumps to a spurious state (due to catastrophes) and random returns to the zero state (due to repairs). Special attention is devoted to the case of periodic catastrophe and repair intensity functions. The first-passage-time problem through constant levels is also treated both for the queueing model and the approximating diffusion process. Finally, the goodness of the diffusive approximating procedure is discussed.

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“…Note that Equation 19is the suitable extension of (2.7) of [10], which refers to the case of constant rates. Furthermore, we remark that from (18) and (19), one obtains:…”

Section: Transient Probabilitiesmentioning

confidence: 98%

“…Making use of (6) and (18) in (19), for t ≥ t 0 and n ∈ Z, one has the following expression for the transition probabilities of N(t):…”

Section: Transient Probabilitiesmentioning

confidence: 99%

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confidence: 99%

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A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation

et al. 2018

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“…Krishnakumar et.al. [21] analyzed infinite server and discouraged arrivals queueing systems with catastrophes.…”

Section: Introductionmentioning

confidence: 99%

Exact Solution to Tandem Fluid Queues with Controlled Input

Sophia¹,

Vijayakumar²

2014

Stochastic Analysis and Applications

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We consider a tandem fluid system composed of multiple buffers connected in a series. The first buffer receives input from a number of independent homogeneous on-off sources and each buffer provides input to the next buffer. The active (on) periods and silent (off) periods follow general and exponential distribution, respectively. Furthermore, the generally distributed active periods are controlled by an exponential timer. Under this assumption, explicit expressions for the distribution of the buffer content for the first buffer fed by a single source is obtained for the fluid queue driven by discouraged arrivals queue and infinite server queue. The buffer content distribution of the subsequent buffers when the first buffer is fed by multiple sources are found in terms of confluent hypergeometric functions. Numerical results are illustrated to compare the trend of the average buffer content for the models under consideration.

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“…They derived its transient solution using the continued fractions approach. The transient solution of a queuing system with catastrophes and state-dependent arrival and service rates was obtained by Kumar et al [26]. Montazer-Hagighi [30] obtained the transient solution to a parallel multi-processor queuing system with task-splitting and feedback.…”

Section: Literature Reviewmentioning

confidence: 99%

A transient solution to the M/M/c queuing model equation with balking and catastrophes

Kumar

2017

Croat. Oper. Res. Rev.

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Abstract. In this paper, we consider a Markovian multi-server queuing system with balking and catastrophes. The probability generating function technique along with the Bessel function properites is used to obtain a transient solution to the queuing model. The transient probabilities for the number of customers in the system are obtained explicitly. The expressions for the time-dependent expected number of customers in the system are also obtained. Finally, applications of the model are also discussed.

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Transient Analysis for State-Dependent Queues with Catastrophes

Cited by 16 publications

References 21 publications

A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation

A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation

Exact Solution to Tandem Fluid Queues with Controlled Input

A transient solution to the M/M/c queuing model equation with balking and catastrophes

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