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.
|Titolo:||A Double-ended Queue with Catastrophes and Repairs,and a Jump-diffusion Approximation|
|Autori interni:||DI CRESCENZO, Antonio|
NOBILE, Amelia Giuseppina
|Data di pubblicazione:||2012|
|Rivista:||METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY|
|Appare nelle tipologie:||1.1.2 Articolo su rivista con ISSN|