For a class of models of adaptive queueing systems an exact diffusion approximation is derived with the aim of obtaining information on the evolution of the systems. Our approximating diffusion process includes the Wiener and the Ornstein-Uhlenbeck processes with reflecting boundaries at 0. The goodness of the approximations is thoroughly discussed and the closed-form solutions obtained for the diffusion processes are compared with those holding for the queueing system in order to investigate the conditions under which reliable information can be obtained from the approximating continuous models. For the latter the transient behaviour is quantitatively analysed and the distribution of the busy period is determined in closed form.
On some diffusion approximations to queueing systems / V., Giorno; A. G., Nobile; Ricciardi, LUIGI MARIA. - In: ADVANCES IN APPLIED PROBABILITY. - ISSN 0001-8678. - STAMPA. - 18:4(1986), pp. 991-1014. [10.2307/1427259]
On some diffusion approximations to queueing systems
RICCIARDI, LUIGI MARIA
1986
Abstract
For a class of models of adaptive queueing systems an exact diffusion approximation is derived with the aim of obtaining information on the evolution of the systems. Our approximating diffusion process includes the Wiener and the Ornstein-Uhlenbeck processes with reflecting boundaries at 0. The goodness of the approximations is thoroughly discussed and the closed-form solutions obtained for the diffusion processes are compared with those holding for the queueing system in order to investigate the conditions under which reliable information can be obtained from the approximating continuous models. For the latter the transient behaviour is quantitatively analysed and the distribution of the busy period is determined in closed form.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
