Analysis of a population model with batch Markovian arrivals influenced by Markov arrival geometric catastrophes

Kumar Nitin; Gupta U. C.

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Analysis of a population model with batch Markovian arrivals influenced by Markov arrival geometric catastrophes

机译：Markov抵达几何灾难影响批次马尔维亚峡谷人口模型分析

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We consider a population model in which individuals arrive as per the batch Markovian arrival process. The population is influenced by catastrophes which occur according to Markovian arrival process and it eliminates each individual of the population in a sequential order with probability p until the one individual survives or the entire population is annihilated. We first obtain the steady-state vector generating function of the population size distribution at arbitrary epoch and then the distribution is extracted in term of roots of the associated characteristic equation. Further, we obtain the population size distribution at post-catastrophe and pre-arrival epochs. Finally, a few numerical results are given.

机译：我们考虑一个人口模型，其中个人按照批量马克洛维亚到达过程到达。人口受到根据马尔可维亚到达过程发生的灾难的影响，并且它以概率p顺序消除了每个人口的每个人，直到一个人存活或整个人口被歼灭。我们首先在任意时期获得群体大小分布的稳态向量，然后在相关特性方程的根部提取分布。此外，我们在灾区后和抵达前的纪念碑中获得人口大小分布。最后，给出了一些数值结果。

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来源
《Communications in Statistics》 |2021年第15期|3137-3158|共22页
作者
Kumar Nitin; Gupta U. C.;
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作者单位

Indian Inst Technol Kharagpur Dept Math Kharagpur 721302 W Bengal India;

Indian Inst Technol Kharagpur Dept Math Kharagpur 721302 W Bengal India;

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原文格式 PDF
正文语种 eng
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关键词
Batch Markovian arrival process; catastrophes; geometric; population;

机译：批量马尔可夫到达过程;灾难;几何;人口;

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1. THE BATCH MARKOVIAN ARRIVAL PROCESS SUBJECT TO RENEWAL GENERATED GEOMETRIC CATASTROPHES [J] . A. Economou, A. Gomez-Corral Stochastic models . 2007,第2期

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2. Elucidating the Short Term Loss Behavior of Markovian-Modulated Batch-Service Queueing Model with Discrete-Time Batch Markovian Arrival Process [J] . Yung-ChungWang, Dong-LiangCai, Li-HsinChiang, Mathematical Problems in Engineering: Theory, Methods and Applications . 2014,第3期

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3. A Renewal Generated Geometric Catastrophe Model with Discrete-Time Markovian Arrival Process [J] . Kumar Nitin, Gupta U. C. Methodology and computing in applied probability . 2020,第3期

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4. A Batch-Service Queueing Model with a Discrete Batch Markovian Arrival Process [C] . Dieter Claeys, Joris Walraevens, Koenraad Laevens, Analytical and stochastic modeling techniques and applications . 2010

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5. Analysis of a time-limited polling system with Markovian arrival process and phase-type service. [D] . Frigui, Imed. 1997

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6. Markovian and Non-Markovian Protein Sequence Evolution: Aggregated Markov Process Models [O] . Carolin Kosiol, Nick Goldman -1

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7. A batch-service queueing model with a discrete batch Markovian arrival process [O] . Claeys Dieter, Walraevens Joris, Laevens Koenraad, 2010

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8. Batch Markovian Arrival Processes (BMAP) (PREPRINT) [R] . Cordeiro, J. D., Kharoufeh, J. P. 2011

机译：批量马尔可夫抵达过程（Bmap）（pREpRINT）

Analysis of a population model with batch Markovian arrivals influenced by Markov arrival geometric catastrophes

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