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A central limit theorem for a Markov-modulated infinite-server queue with batch Poisson arrivals and binomial catastrophes

Authors:

M. Yajima,

T. Phung-DucAuthors Info & Claims

ACM SIGMETRICS Performance Evaluation Review, Volume 46, Issue 3

Pages 33 - 34

https://doi.org/10.1145/3308897.3308911

Published: 25 January 2019 Publication History

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Abstract

This paper considers the stationary queue length distribution of a Markov-modulated MX/M/∞queue with binomial catastrophes. When a binomial catastrophe occurs, each customer is either removed with a probability or is retained with the complementary probability. We focus on our model under a heavy traffic regime because its exact analysis is difficult if not impossible. We establish a central limit theorem for the stationary queue length of our model in a heavy traffic regime. The central limit theorem can be used to approximate the queue length distribution of our model with large arrival rates.

Reference

[1]

J. Blom, K. de Turck, M. Mandjes, Analysis of Markov-modulated in nite-server queues in the central-limit regime, Probability in the Engineering and Informational Sciences 29 (3) (2015) 433{459.

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A central limit theorem for a Markov-modulated infinite-server queue with batch Poisson arrivals and binomial catastrophes
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Information & Contributors

Information

Published In

cover image ACM SIGMETRICS Performance Evaluation Review

ACM SIGMETRICS Performance Evaluation Review Volume 46, Issue 3

December 2018

174 pages

ISSN:0163-5999

DOI:10.1145/3308897

Editor:
Nidhi Hegde
Borealis AI

Issue’s Table of Contents

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 25 January 2019

Published in SIGMETRICS Volume 46, Issue 3

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A central limit theorem for a Markov-modulated infinite-server queue with batch Poisson arrivals and binomial catastrophes

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