A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation

Details A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation

2011-01-26

arxiv.org/abs/1101.5073v1

Mathematics

Probability

18 pages, 5 figures, paper accepted by "Methodology and Computing in Applied Probability", the final publication is available

Scientific paper

10.1007/s11009-011-9214-2

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.

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