Transient diffusion approximation for some queuening systems.

Authors:
Andrzej Duda
Affiliations:
I.S.E.M. - Bät. 508, Université de Paris-Sud, 91405 ORSAY (France)
Venue:
SIGMETRICS '83 Proceedings of the 1983 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Year:
1983

Citing 3
Cited 1

Application of the Diffusion Approximation to Queueing Networks II: Nonequilibrium Distributions and Applications to Computer Modeling

Journal of the ACM (JACM)
A Simple Approximation to the Average Queue Size in the Time-Dependent M/M/1 Queue

Journal of the ACM (JACM)
Theory, Volume 1, Queueing Systems

Theory, Volume 1, Queueing Systems

A simple approximation for modeling nonstationary queues

INFOCOM'96 Proceedings of the Fifteenth annual joint conference of the IEEE computer and communications societies conference on The conference on computer communications - Volume 1

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Abstract

There are many situations where information about the transient behaviour of computer systems is wanted. In this paper a diffusion approximation to the transient behaviour of some queueing systems is proposed. The solution of the forward diffusion equation on the real positive line with the elementary return barrier having almost general holding time distribution provides the approximation for the GI/G/1 queue. The solution of the diffusion equation in a finite region approximates the transient behaviour for the two-server cyclic system and gives approximations for the first overflow time in the GI/G/1/N system and for the maximum number of customers in the GI/G/1 system. Also the approximation for the busy period of the GI/G/1 system and of the two-server cyclic system are presented.