A flow and routing control policy for communication networks with multiple competitive users

This paper is concerned with deriving an optimal flow and routing control policy for two-node parallel link communication networks with multiple competing users. The model assumes that each user has a flow demand which needs to be optimally selected and routed on the network links. The flow and routing control policy for each user seeks to maximize the user's total throughput and minimize its expected delay. To derive such a policy, we consider a utility function for each user that combines these two objectives in an additive fashion with preference constants that can be adjusted to reflect the user's own preferences between maximizing throughput and minimizing delay. Additionally, we provide each user with the ability to make these preferences link-dependent to reflect the user's preferences for certain links over others in the network. A condition that depends on the link capacities and preference constants is derived to guarantee the existence and uniqueness of a non-symmetric flow and routing control policy solution which satisfies the Nash equilibrium of non-cooperative game theory. The Nash equilibrium is a desirable solution for such networks because it insures that no user can improve its utility by unilaterally deviating from its Nash control policy. We discuss in detail several interesting properties of this equilibrium and in particular, its relationship to the users’ preference constants. Two illustrative examples are also presented.