Time-non-homogeneous diffusion approximations to single server-single queue-FCFS discipline systems are considered. Under various assumptions on the nature of the time-dependent functions appearing in the infinitesimal moments the transient and the regime behaviour of the approximating diffusions are analysed in some detail. Special attention is then given to the study of a diffusion approximation characterized by a linear drift and by a periodically time-varying infinitesimal variance. Unlike the behaviour of transition functions and moments, the p.d.f. of the busy period is seen to be unaffected by the presence of such periodicity.
On some time non-homogeneous diffusion approximations to queueing systems / V., Giorno; A. G., Nobile; Ricciardi, LUIGI MARIA. - In: ADVANCES IN APPLIED PROBABILITY. - ISSN 0001-8678. - STAMPA. - 19:4(1987), pp. 974-994. [10.2307/1427111]
On some time non-homogeneous diffusion approximations to queueing systems
RICCIARDI, LUIGI MARIA
1987
Abstract
Time-non-homogeneous diffusion approximations to single server-single queue-FCFS discipline systems are considered. Under various assumptions on the nature of the time-dependent functions appearing in the infinitesimal moments the transient and the regime behaviour of the approximating diffusions are analysed in some detail. Special attention is then given to the study of a diffusion approximation characterized by a linear drift and by a periodically time-varying infinitesimal variance. Unlike the behaviour of transition functions and moments, the p.d.f. of the busy period is seen to be unaffected by the presence of such periodicity.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
