Mean delay approximations for polling systems with batch Poisson input

Abstract

This paper presents a method for approximating mean message delays in a polling system where each message consists of a random number (batch) of packets. Each station can send at most one packet per visit by the server (token), and thus multiple visits by the server are typically necessary to transmit a single message. The number of packets per message is assumed to follow a general distribution. By applying a pseudo-conservation law, we are able to obtain an explicit, simple approximation for the average message (not packet) delay. The approximation is tested against simulation results and found to be quite accurate. For the case of a completely symmetrical system with geometrically distributed batch-sizes, the result becomes exact. © 1991.