Free Energy Approximations for CSMA networks

In this paper we study how to estimate the back-off rates in an idealized CSMA network consisting of $n$ links to achieve a given throughput vector using free energy approximations. More specifically, we introduce the class of region-based free energy approximations with clique belief and present a closed form expression for the back-off rates based on the zero gradient points of the free energy approximation (in terms of the conflict graph, target throughput vector and counting numbers). Next we introduce the size $k_{max}$ clique free energy approximation as a special case and derive an explicit expression for the counting numbers, as well as a recursion to compute the back-off rates. We subsequently show that the size $k_{max}$ clique approximation coincides with a Kikuchi free energy approximation and prove that it is exact on chordal conflict graphs when $k_{max} = n$. As a by-product these results provide us with an explicit expression of a fixed point of the inverse generalized belief propagation algorithm for CSMA networks. Using numerical experiments we compare the accuracy of the novel approximation method with existing methods

Physics-inspired methods for networking and communications

Advances in statistical physics relating to our understanding of large-scale complex systems have recently been successfully applied in the context of communication networks. Statistical mechanics methods can be used to decompose global system behavior into simple local interactions. Thus, large-scale problems can be solved or approximated in a distributed manner with iterative lightweight local messaging. This survey discusses how statistical physics methodology can provide efficient solutions to hard network problems that are intractable by classical methods. We highlight three typical examples in the realm of networking and communications. In each case we show how a fundamental idea of statistical physics helps solve the problem in an efficient manner. In particular, we discuss how to perform multicast scheduling with message passing methods, how to improve coding using the crystallization process, and how to compute optimal routing by representing routes as interacting polymers

Effect of network density and size on the short-term fairness performance of CSMA systems

As the penetration of wireless networks increase, number of neighboring networks contending for the limited unlicensed spectrum band increases. This interference between neighboring networks leads to large systems of locally interacting networks. We investigate whether the short-term fairness of this system of networks degrades with the system size and density if transmitters employ random spectrum access with carrier sensing (CSMA). Our results suggest that (a) short-term fair capacity, which is the throughput region that can be achieved within the acceptable limits of short-term fairness, reduces as the number of contending neighboring networks, i.e., degree of the conflict graph, increases for random regular conflict graphs where each vertex has the same number of neighbors, (b) short-term fair capacity weakly depends on the network size for a random regular conflict graph but a stronger dependence is observed for a grid deployment. We demonstrate the implications of this study on a city-wide Wi-Fi network deployment scenario by relating the short-term fairness to the density of deployment. We also present related results from the statistical physics literature on long-range correlations in large systems and point out the relation between these results and short-term fairness of CSMA systems. © 2012 Koseoglu et al; licensee Springer

Transition time asymptotics of queue-based activation protocols in random-access networks

We consider networks where each node represents a server with a queue. An active node deactivates at unit rate. An inactive node activates at a rate that depends on its queue length, provided none of its neighbors is active. For complete bipartite networks, in the limit as the queues become large, we compute the average transition time between the two states where one half of the network is active and the other half is inactive. We show that the law of the transition time divided by its mean exhibits a trichotomy, depending on the activation rate functions