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).

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.

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.

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.

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.