Heavy traffic performance of a class of channel assignment algorithms

Abstract

In this paper we present a study of the performance of a general class of channel assignment algorithms. These algorithms, which we call Ω-algorithms, are completely characterized by the set of carried-traffic "states" which they allow. We shall see that for any such algorithm, there is a closed-form expression for the carried traffic function, which lends itself to several kinds of asymptotic analysis. As an application, we shall study a particular Ω-algorithm, which has been previously studied under the name "maximum packing algorithm," and which is a "greedy" dynamic channel assignment algorithm, and show that its performance is in many cases inferior to that of simple fixed channel assignment algorithms. We shall see that the cause of this unexpected phenomenon, which was first observed by Kelly [3], it the tendency of dynamic algorithms to get trapped in states that are locally, but not globally, maximal.