A mathematical model of joint congestion control and routing in multisource networks

Abstract

In this paper we study a model of joint congestion control and routing in a ring network of sources with a single destination at the center (Figure 2). A utility maximization problem subject to routing constraints is posed and equations for its solution are presented. The distribution of traffic on routes available to a source is subject to an entropy constraint that controls the path diversity or degree of robustness of the allocation. Thus the utility/stability issue can be addressed directly and quantitatively in a way that differs from previous work on multiroute NUM problems. The dynamics of the model equations will be analyzed in the case of a constant route allocation defined by the allocation distribution entropy for a source. Motivated by earlier work on a two link network, the dynamics of the mean route costs for each source in the ring network are studied by deriving a continuous time approximation of the equations they satisfy. The equilibrium solutions of this approximation are used to greatly simplify the analysis of the model equations and the solution of the original optimization problem. We conclude with a discussion of the tradeoff between utility and path diversity (robustness) for two contrasting assignment of link capacities. Given a homogeneous assignment of capacities the network behaves like a two link model (Fig 1), while a heterogeneous assignment produces utilities displaying different tradeoffs for different sources.