Equilibrium of Heterogeneous Congestion Control: Optimality and Stability
When heterogeneous congestion control protocols that react to different pricing signals share the same network, the current theory based on utility maximization fails to predict the network behavior. The pricing signals can be different types of signals such as packet loss, queueing delay, etc, or different values of the same type of signal such as different ECN marking values based on the same actual link congestion level. Unlike in a homogeneous network, the bandwidth allocation now depends on router parameters and flow arrival patterns. It can be non-unique, suboptimal and unstable. In Tang et al. ("Equilibrium of heterogeneous congestion control: Existence and uniqueness," IEEE/ACM Trans. Netw., vol. 15, no. 4, pp. 824–837, Aug. 2007), existence and uniqueness of equilibrium of heterogeneous protocols are investigated. This paper extends the study with two objectives: analyzing the optimality and stability of such networks and designing control schemes to improve those properties. First, we demonstrate the intricate behavior of a heterogeneous network through simulations and present a framework to help understand its equilibrium properties. Second, we propose a simple source-based algorithm to decouple bandwidth allocation from router parameters and flow arrival patterns by only updating a linear parameter in the sources' algorithms on a slow timescale. It steers a network to the unique optimal equilibrium. The scheme can be deployed incrementally as the existing protocol needs no change and only new protocols need to adopt the slow timescale adaptation.
© 2009 IEEE. Manuscript received September 23, 2007; revised June 28, 2008 and July 28, 2009; approved by IEEE/ACM TRANSACTIONS ON NETWORKING Editor S. Shakkottai. First published December 01, 2009; current version published June 16, 2010. The research is supported by the NSF under Grants CCF-0835706 and CNS-0519880, the DARPA under Grant HR0011–06–1–0008, the ARO, and the Caltech Lee Center for Advanced Networking. The authors thank C. Jin of Caltech for help on some WAN-in-Lab experiments, S. Simsek and A. Ozdaglar of MIT, D. Palomar of HKUST, and J. Lui of CUHK for useful discussions. The authors would also like to thank the anonymous reviewers and the associate editor for their comments that have helped improve this paper significantly.
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