A Queueing System with Batch Renewal Input and Negative Arrivals

Gupta, Umesh C.; Kumar, Nitin; Barbhuiya, F. P.

doi:10.1007/978-981-15-5951-8_10

Cited by 9 publications

(2 citation statements)

References 31 publications

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“…For related work on discrete-time G-queues with negative customers, the reader is referred to [3,7,14,[16][17][18][19][20][21][22][23]. For work on continuous-time queueing models with negative customers and/or disasters, we refer to the bibliography in [24,25] and the more recent papers [26][27][28][29][30][31][32][33][34][35][36]. Additionally, somewhat related to this paper in the sense that customers may leave the system before their service is completed are queueing models with customer impatience or deadlines; we refer to [37] and the references therein for an overview of such models.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Discrete-Time Queueing Model with Disasters

2021

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Queueing models with disasters can be used to evaluate the impact of a breakdown or a system reset in a service facility. In this paper, we consider a discrete-time single-server queueing system with general independent arrivals and general independent service times and we study the effect of the occurrence of disasters on the queueing behavior. Disasters occur independently from time slot to time slot according to a Bernoulli process and result in the simultaneous removal of all customers from the queueing system. General probability distributions are allowed for both the number of customer arrivals during a slot and the length of the service time of a customer (expressed in slots). Using a two-dimensional Markovian state description of the system, we obtain expressions for the probability, generating functions, the mean values, variances and tail probabilities of both the system content and the sojourn time of an arbitrary customer under a first-come-first-served policy. The customer loss probability due to a disaster occurrence is derived as well. Some numerical illustrations are given.

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Section: Introductionmentioning

confidence: 99%

Analysis of a Discrete-Time Queueing Model with Disasters

2021

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“…[ 7 ] and for total catastrophes see, Gupta et al. [ 15 ], Kumar et al. [ 22 ], and reference therein.…”

Section: Introductionmentioning

confidence: 99%

Computational and Numerical Investigation of the Batch Markovian Arrival Process Subject to Renewal Generated Geometric Catastrophes

Kumar

Gupta

Singh

2021

Int. J. Appl. Comput. Math

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In this paper, we consider a stochastic model in which the population grows according to the batch Markovian arrival process and is subjected to renewal generated geometric catastrophes. Our analytical work starts from the vector generating function (VGF) of the population size at post-catastrophe epoch. We develop a methodology for extracting the population size distribution at post-catastrophe epoch from the VGF, which is based on the inversion of VGF using the roots method. The method is analytically quite simple and easy to implement. Further, we obtain the population size distribution at arbitrary, pre-catastrophe and pre-arrival epochs along with their factorial moments. To show the applicability and correctness of the proposed methodology, we match our results with the available ones in special cases and present several numerical examples for different inter-catastrophe time distributions. Moreover, we investigate the effect of key parameters on the system performance and display the results in the form of graphs along with a detailed description.

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