A Statistical Mechanics-Based Framework to Analyze Ad Hoc Networks with Random Access

Characterizing the performance of ad hoc networks is one of the most intricate open challenges; conventional ideas based on information-theoretic techniques and inequalities have not yet been able to successfully tackle this problem in its generality. Motivated thus, we promote the totally asymmetric simple exclusion process (TASEP), a particle flow model in statistical mechanics, as a useful analytical tool to study ad hoc networks with random access. Employing the TASEP framework, we first investigate the average end-to-end delay and throughput performance of a linear multihop flow of packets. Additionally, we analytically derive the distribution of delays incurred by packets at each node, as well as the joint distributions of the delays across adjacent hops along the flow. We then consider more complex wireless network models comprising intersecting flows, and propose the partial mean-field approximation (PMFA), a method that helps tightly approximate the throughput performance of the system. We finally demonstrate via a simple example that the PMFA procedure is quite general in that it may be used to accurately evaluate the performance of ad hoc networks with arbitrary topologies.