Abstract
AbstractIn this paper, we consider the flow control in a general multi‐node multi‐link communication network with competing users. Each user has a source node, a destination node, and an existing route for its data flow over any set of links in the network from its source to its destination node. The flow rate for each user is a control variable that is determined by optimizing a user‐specific utility function which combines maximizing the flow rate and minimizing the network congestion for that user. A preference parameter in the utility function allows each user to adjust the trade‐off between these two objectives. Since all users share the same network resources and are only interested in optimizing their own utility functions, the Nash equilibrium of game theory represents a reasonable solution concept for this multi‐user general network. The existence and uniqueness of such an equilibrium is therefore very important for the network to admit an enforceable flow configuration. In this paper, we derive an expression for the Nash equilibrium and prove its uniqueness. We illustrate the results with an example and discuss some properties and observations related to the network performance when in the Nash equilibrium. Copyright © 2007 John Wiley & Sons, Ltd.
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