# Convergence Analysis of a Distributed CSMA Algorithm for Maximal Throughput in a General Class of Networks

### Libin Jiang and Jean Walrand

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/EECS-2008-185

December 29, 2008

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-185.pdf

In [1] [2], we proposed a family of distributed scheduling and rate control algorithms to achieve the maximal throughput in a general class of networks with interference constraints, as well as approaching the optimal fairness among different data flows. These algorithms were inspired by CSMA (Carrier Sense Multiple Access). In this paper, we analyze and prove the convergence of such a scheduling algorithm and the queue stability it guarantees, with properly-chosen step sizes and adjustment periods. Convergence of other algorithms in [1] [2] can be proved similarly.

BibTeX citation:

@techreport{Jiang:EECS-2008-185, Author = {Jiang, Libin and Walrand, Jean}, Title = {Convergence Analysis of a Distributed CSMA Algorithm for Maximal Throughput in a General Class of Networks}, Institution = {EECS Department, University of California, Berkeley}, Year = {2008}, Month = {Dec}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-185.html}, Number = {UCB/EECS-2008-185}, Abstract = {In [1] [2], we proposed a family of distributed scheduling and rate control algorithms to achieve the maximal throughput in a general class of networks with interference constraints, as well as approaching the optimal fairness among different data flows. These algorithms were inspired by CSMA (Carrier Sense Multiple Access). In this paper, we analyze and prove the convergence of such a scheduling algorithm and the queue stability it guarantees, with properly-chosen step sizes and adjustment periods. Convergence of other algorithms in [1] [2] can be proved similarly.} }

EndNote citation:

%0 Report %A Jiang, Libin %A Walrand, Jean %T Convergence Analysis of a Distributed CSMA Algorithm for Maximal Throughput in a General Class of Networks %I EECS Department, University of California, Berkeley %D 2008 %8 December 29 %@ UCB/EECS-2008-185 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-185.html %F Jiang:EECS-2008-185