Efficient Distributed Medium Access

Consider a wireless network of n nodes represented by a graph G = (V,E) where anedge (i, j) ∈ E models the fact that transmissions of i and j interfere with each other, i.e.simultaneous transmissions of i and j become unsuccessful. Hence it is required that ateach time instance a set of non-interfering nodes (corresponding to an independent set in G)access the wireless medium. To utilize wireless resources efficiently, it is required to arbitratethe access of medium among interfering nodes properly. Moreover, to be of practical use,such a mechanism is required to be totally distributed as well as simple.As the main result of this paper, we provide such a medium access algorithm. It israndomized, totally distributed and simple: each node attempts to access medium at eachtime with probability that is a function of its local information. We establish efficiency of thealgorithm by showing that the corresponding network Markov chain is positive recurrent aslong as the demand imposed on the network can be supported by the wireless network (usingany algorithm). In that sense, the proposed algorithm is optimal in terms of utilizing wirelessresources. The algorithm is oblivious to the network graph structure, in contrast with the so-called polynomial back-off algorithm by Hastad-Leighton-Rogoff (STOC ’87, SICOMP ’96)that is established to be optimal for the complete graph and bipartite graphs (by Goldberg-MacKenzie (SODA ’96, JCSS ’99)). Work of D. Shah and J. Shin supported in parts by the AFOSR complex networks grant and DARPAITMANET grant. Research of P. Tetali supported in part by NSF grant CCF-0910584.Laboratory for Information and Decision Systems and Department of Electrical Engineering and ComputerScience at Massachusetts Institute of Technology. Email: [email protected] and Randomness Center at Georgia Institute of Technology. Email: [email protected] of Mathematics and School of Computer Science at Georgia Institute of Technology. Email:[email protected].