Diffusion Approximations for Time-Dependent Queueing Systems

This paper deals with queueing systems which reveal timedependent behavior. The goal of the paper is to present a set of results which can be applied to the analysis of computer-communication systems. Some new results on the time-dependent analysis of the queue and of general queueing networks are given. All these results are based on a transient diffusion model of a single server queue. A parametric-decomposition method of the time-dependent analysis of queueing networks is presented. The method permits the analysis, of the networks where the arrival, service processes and also the routing matrix are time-dependent. It makes possible the analysis of various aspects of computer-communication systems, especially the adaptive routings, the strategies of flow and congestion control, the influence of short overload peaks and other time-varying phenomena in such systems. To illustrate these applications, a simple example of the analysis of the centralized adaptive routing in packet-switching networks is presented.