A double-ended queue with catastrophes and repairs, and a jump-diffusion   approximation
  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. 
Antonio Di Crescenzo, Virginia Giorno, Balasubramanian Krishna Kumar,   Amelia G. Nobile
math.PR