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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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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

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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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