A Transient Analysis of a Data Network with a Processor-Sharing Switch

Abstract

This paper gives a simple, accurate, first-order asymptotic analysis of the transient behavior of a data network. The network is based on a switch, such as the Datakit® virtual circuit switch, which receives packetized traffic from many message sources of diverse classes and multiplexes the traffic over a trunk line. The network has a regulatory mechanism based on acknowledgments that produces a closed model. Assuming that the switch has a processor-sharing discipline, and assuming an asymptotic regime of high loading of the switch and high-capacity trunks, we derive the explicit, first-order transient behavior of the means of queue lengths — and hence response times. We then give a simple procedure for finding the time constants (eigenvalues) that govern the approach to steady state. Our numerical experiments show that the analysis is quite accurate.