  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.
