Convergence of Dual Algorithm with Arbitrary Communication Delays

Abstract

We study the issue of convergence of user rates and resource prices under a family of rate control schemes called dual algorithms with arbitrary communication delays. We first consider a case where a single resource is shared by many users. Then, we study a general network shared by heterogeneous users and derive sufficient conditions for convergence. We show that in the case of a single user utilizing a single resource, our condition is also necessary. Using our results we derive a sufficient condition for convergence with a family of popular utility and resource price functions. We present numerical examples to validate our analysis.

A Differential Equation with a State-Dependent Queueing Delay

“…The papers of Ranjan et al [17,15,16,23,24,25,26] and [1,3] consider similar systems, starting from discrete ones, through ordinary and delay differential equations with constant or state-dependent delays, to general network systems. They examine these models from the engineering point of view, comparing the different rate control schemes, like the TCP (transmission control protocol) and its modifications.…”