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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 byexponentially-distributed repair times. After any repair the system starts anewfrom state zero. We study both the transient and steady-state probability lawsof the stochastic process that describes the state of the system. We thenderive a heavy-traffic approximation to the model that yields a jump-diffusionprocess. The latter is equivalent to a Wiener process subject to randomlyoccurring jumps, whose probability law is obtained. The goodness of theapproximation is finally discussed.

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