Achieving target throughputs in random-access networks

Authors:
P. M. van de Ven;A. J. E. M. Janssen;J. S. H. van Leeuwaarden;S. C. Borst
Affiliations:
Department of Mathematics & Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands and EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Department of Mathematics & Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands and EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Department of Mathematics & Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands and Bell Laboratories, Alcatel-Lucent, P.O. Box 636, Murray Hill, ...
Venue:
Performance Evaluation
Year:
2011

Citing 9
Cited 1

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Abstract

Random-access algorithms such as CSMA provide a popular mechanism for distributed medium access control in large-scale wireless networks. In recent years, tractable stochastic models have been shown to yield accurate throughput estimates for CSMA networks. We consider a saturated random-access network on a general conflict graph, and prove that for every feasible combination of throughputs, there exists a unique vector of back-off rates that achieves this throughput vector. This result entails proving global invertibility of the non-linear function that describes the throughputs of all nodes in the network. We present several numerical procedures for calculating this inverse, based on fixed-point iteration and Newton's method. Finally, we provide closed-form results for several special conflict graphs using the theory of Markov random fields.