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

Abstract

This paper considers the stationary queue length distribution of a Markov-modulated MX/M/∞ queue with binomial catastrophes. Binomial catastrophes occur according to a Poisson process, and each customer is removed with a probability and retained with the complementary probability upon the arrival of a binomial catastrophe. 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 the heavy traffic regime. The central limit theorem can be used to approximate the queue length distribution of our model with large arrival rates.