Statistical Mechanics for Wireless Systems: Application of Exclusion Processes to the Modeling and Analysis of Multihop Networks

This thesis focuses on the modeling and analysis of wireless multihop networks, employing a combination of ideas from a well-known tool in stochastic geometry, namely the Poisson shot noise theory and an unfamiliar concept in statistical mechanics, namely the totally asymmetric simple exclusion process (TASEP). <p>We begin our study by considering the simplest wireless multihop network topology - the line network, where the source, destination and all the relays are located in a collinear fashion. First, we propose a simple buffering and transmission scheme for wireless line networks which not only guarantees packet delivery but also helps keep packet delays small whilst regulating the flow of packets in a completely decentralized fashion. Second, we characterize the end-to-end delay distribution and achievable throughput of the wireless multihop line network for two different channel access schemes, randomized-TDMA and ALOHA. Additionally, we use our results to provide some useful design insights in long line networks. </p><p>Next, we consider a more intricate network topology comprising an infinite number of source-destination flows and analyze design-level issues such as determining the optimum density of transmitters or the optimal number of hops along a flow that maximizes the throughput performance of the network. We also consider several other complex topologies comprising intersecting flows and propose the partial mean-field approximation (PMFA), an elegant technique that helps tightly approximate the throughput (and end-to-end delay) of such systems. We then demonstrate via a simple toy example that the PMFA procedure is quite general in that it may be used to accurately evaluate the performance of multihop networks with arbitrary topologies. </p><p>Finally, we identify that when reliable delivery of packets is not very critical, a viable solution towards balancing end-to-end delay and reliability in multihop networks is to have the nodes forcibly drop a small fraction of packets. Based on this principle, we present an analytical framework that helps quantify the throughput-delay-reliability performances of the ALOHA multihop network. We find that while in the noise-limited regime, dropping a small fraction of packets in the network leads to a smaller end-to-end delay at the cost of reduced throughput, in the interference-limited scenario, dropping a few packets in the network can sometimes help mitigate the interference in the network leading to an increased throughput. </p><p>We intend to promote TASEPs as a powerful tool to analyze the performance of multihop networks and hope that this introductory work instigates interest in solving other relevant wireless networking problems employing ideas from statistical mechanics.</p>