For the M/M/1 queue in the presence of catastrophes the transition probabilities, densities of the busy period and of the catastrophe waiting time are determined. A heavy-traffic approximation to this discrete model is then derived. This is seen to be equivalent to a Wiener process subject to randomly occurring jumps for which some analytical results are obtained. The goodness of the approximation is discussed by comparing the closed-form solutions obtained for the continuous process with those obtained for the M/M/1 catastrophized queue.
On the M/M/1 queue with catastrophes and its continuous approximation / A., DI CRESCENZO; V., Giorno; A. G., Nobile; Ricciardi, LUIGI MARIA. - In: QUEUEING SYSTEMS. - ISSN 0257-0130. - STAMPA. - 43:4(2003), pp. 329-347. [10.1023/A:1023261830362]
On the M/M/1 queue with catastrophes and its continuous approximation
RICCIARDI, LUIGI MARIA
2003
Abstract
For the M/M/1 queue in the presence of catastrophes the transition probabilities, densities of the busy period and of the catastrophe waiting time are determined. A heavy-traffic approximation to this discrete model is then derived. This is seen to be equivalent to a Wiener process subject to randomly occurring jumps for which some analytical results are obtained. The goodness of the approximation is discussed by comparing the closed-form solutions obtained for the continuous process with those obtained for the M/M/1 catastrophized queue.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.