Equilibrium of Heterogeneous Congestion Control: Existence and Uniqueness
When heterogeneous congestion control protocols that react to different pricing signals share the same network, the resulting equilibrium may no longer be interpreted as a solution to the standard utility maximization problem. We prove the existence of equilibrium in general multiprotocol networks under mild assumptions. For almost all networks, the equilibria are locally unique, finite, and odd in number. They cannot all be locally stable unless there is a globally unique equilibrium. Finally, we show that if the price mapping functions, which map link prices to effective prices observed by the sources, are sufficiently similar, then global uniqueness is guaranteed.
© Copyright 2007 IEEE. Reprinted with permission. Manuscript received April 8, 2005; revised December 29, 2005 and May 9, 2006; approved by IEEE/ACM TRANSACTIONS ON NETWORKING Editor M. Ajmone Marsan. [Posted online: 2007-07-02] This work was performed as part of the Caltech FAST Project supported in part by the National Science Foundation, by the Caltech Lee Center for Advanced Networking, by ARO, by AFOSR, and by Cisco, and through Grants CCF-0448012, CNS-0417607, CNS-0519880, and DARPA D-DOT, AFOSR ION. The authors would like to thank K. Border and J. Ledyard of Caltech, and R. Johari of Stanford for their useful discussions, and R. Srikant of UIUC for helpful references.