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Atomic hierarchical routing games in communication networks

Theoretical studies on routing games in networks have so far dealt with reciprocal congestion effects between routing entities. But, with the advent of technologies like Cognitive Radio, we have networks which support differentiation of flows. In a two priority level model a user can be high priority or low priority and there is a cost for such a classification. The point of departure of this model from the traditional routing scenarios is the absence of reciprocity in the congestion effects: The low priority flow faces congestion from both high priority as well as low priority flow while the high priority flow is immune to the congestion effects from the low priority flow. This hierarchy is naturally present in contexts where there are primary (licensed) users and secondary (unlicensed) users who can sense their environment because there are equipped with a cognitive radio. We study such kind of routing scenarios for the cases of atomic users. We establish the existence and the uniqueness of Nash equilibrium and further we show the existence of a potential function for linear congestion costs and a certain priority classification pricing scheme. Natural applications of this model to Cognitive Radio are also pointed out.