Combining stochastic geometry and statistical mechanics for the analysis and design of mesh networks

We consider a two-dimensional mesh network comprising several source-destination pairs, each communicating wirelessly in a multihop fashion. First, we introduce a novel transmission policy for multihop networks according to which all the buffering in the network is performed at source nodes while relays just have unit-sized buffers. We demonstrate that incorporating this buffering scheme in conjunction with minor amendments to the medium access control (MAC) layer yields several benefits such as keeping packet delays small and helping regulate the traffic flow in a completely distributed fashion. Second, we employ a novel combination of tools from stochastic geometry and statistical mechanics to characterize the throughput and end-to-end delay performances of multihop wireless networks for two different channel access mechanisms, Carrier Sense Multiple Access (CSMA) and ALOHA. Our study also offers valuable insights from a system design stand-point such as determining the optimum density of transmitters or the optimal number of hops along a flow that maximizes the system’s throughput performance. We corroborate our theoretical analyses via simulations.