Title :
Fast Mixing of Parallel Glauber Dynamics and Low-Delay CSMA Scheduling
Author :
Jiang, Libin ; Leconte, Mathieu ; Ni, Jian ; Srikant, R. ; Walrand, Jean
Author_Institution :
Qualcomm, Bridgewater, NJ, USA
Abstract :
Glauber dynamics is a powerful tool to generate randomized, approximate solutions to combinatorially difficult problems. It has been recently used to design distributed carrier-sense multiple-access (CSMA) scheduling algorithms for multihop wireless networks. In this paper, we derive bounds on the mixing time of a generalization of Glauber dynamics where multiple links update their states in parallel and the fugacity of each link can be different. The results are used to prove that the average queue length (and hence, the delay) under the parallel-Glauber-dynamics-based CSMA grows polynomially in the number of links for wireless networks with bounded-degree interference graphs when the arrival rate lies in a fraction of the capacity region. Other versions of adaptive CSMA can be analyzed similarly. We also show that in specific network topologies, the low-delay capacity region can be further improved.
Keywords :
approximation theory; carrier sense multiple access; graph theory; radio links; radio networks; scheduling; telecommunication network topology; adaptive CSMA; approximate solutions; average queue length; bounded-degree interference graphs; combinatorially difficult problems; distributed CSMA scheduling algorithms; distributed carrier-sense multiple-access scheduling algorithms; low-delay CSMA scheduling; low-delay capacity region; network topologies; parallel-Glauber-dynamic-based CSMA; wireless networks; Algorithm design and analysis; Delay; Heuristic algorithms; Markov processes; Multiaccess communication; Schedules; Scheduling algorithms; Carrier-sense multiple-access (CSMA); Glauber dynamics; Markov chain; delay performance; mixing time; scheduling algorithm;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2012.2204032