A Double-ended Queue with Catastrophes and Repairs, and a Jump-diffusion Approximation

By A. Di Crescenzo, V. Giorno, B. Krishna Kumar, A. G. Nobile. 2011

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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.

Subfields: Management Information Systems, Management Science and Operations Research, Safety, Risk, Reliability and Quality

View Paper: https://www.semanticscholar.org/paper/68cc72f14345cd50119b7aac3e5a7723d631c3b6