A new method for approximating blocking probability in overflow loss networks

Abstract

In this paper, we present a new approximation for estimating blocking probability in overflow loss networks and systems. Given a system for which an estimate of blocking probability is sought, we first construct a second system to act as a surrogate for the original system. Estimating blocking probability in the second system with Erlang's fixed point approximation (EFPA) provides a better estimate for blocking probability in the original system than if we were to use the conventional approach of directly using EFPA in the original system. We present a combination of numerical and theoretical results that indicate our new approximation offers a better estimate than EFPA for a certain pure overflow loss network. Moreover, we demonstrate the accuracy of our new approximation for circuit-switched networks using alternative routing. We argue that the success of our new approximation is due to its ability to utilize congestion information imbedded in overflow traffic, whereas the conventional approach fails to utilize such information.