"Cap and Trade" for Congestion Control

We study a "cap and trade" scheme for congestion control: the planner sets constraints for aggregate utilization on certain critical links in a given network and competitive trading of usage rights in a secondary market is expected to identify over time prices clearing demand for the utilization of the constrained links. If prices in a "cap and trade" scheme stabilize relatively quickly, a social planner can fine-tune the caps for aggregate utilization on critical links. However, it is not clear that prices would necessarily stabilize as users dynamically adjust their route and/or flow choices. In this paper we show that prices and flows (or routes) do stabilize in a "cap and trade" scheme for congestion control when users are assumed to adjust their flow (or route) choices by optimizing vis-à-vis current conditions. A sufficient condition for this result pertains to the relative speed of trading versus users' adjustments. We find that prices stabilize and flows (or routes) converge to an equilibrium if the pace at which prices are updated is faster than that at which users adjust their decisions.