A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation
Abstract
Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero. We study both the transient and steady-state probability laws of the stochastic process that describes the state of the system. We then derive a heavy-traffic approximation to the model that yields a jump-diffusion process. The latter is equivalent to a Wiener process subject to randomly occurring jumps, whose probability law is obtained. The goodness of the approximation is finally discussed.
Cite
@article{arxiv.1101.5073,
title = {A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation},
author = {Antonio Di Crescenzo and Virginia Giorno and Balasubramanian Krishna Kumar and Amelia G. Nobile},
journal= {arXiv preprint arXiv:1101.5073},
year = {2011}
}
Comments
18 pages, 5 figures, paper accepted by "Methodology and Computing in Applied Probability", the final publication is available at http://www.springerlink.com