For the performance analysis of multihop wireless networks, the key issues are energy consumption, end-to-end reliability, delay and throughput. In the research of wireless multihop networks, the “disk models’ that are often employed assume that the radius for a successful transmission of a packet has a fixed and deterministic value, irrespective of the condition of the wireless channel. Taking into account the stochastic nature of the fading channel, the Rayleigh fading link model includes fading as a random variation in the path loss. As a result, all properties of the network become random variables, in particular the signal-to-noise-and-interference ratio (SINR) that determines the success of a transmission.
This thesis explores the performance of one- and two-dimensional networks with equidistant nodes and uniformly randomly placed nodes. For regular two-dimensional networks, three topologies are studied based on a uniform traffic model and a simple random MAC scheme. Square networks are explored in more detail for their load distribution. By comparing the energy consumption and the achievable throughput for random and regular networks, we demonstrate that random distributions incur substantially higher energy expenditures at a lower achievable throughput.
For sensor networks with a slotted ALOHA MAC protocol in Rayleigh fading channels, we present closed-form expressions of the average link throughput, and we compare networks with three regular topologies in terms of throughput, transmit efficiency, and transport capacity. For random networks with nodes distributed according to a two-dimensional Poisson point process, the average throughput is analytically characterized and numerically evaluated.
Uniformly random or Poisson distributions are widely accepted models for the location of the nodes in wireless sensor networks if nodes are deployed in large quantities and there is little control over where they are dropped. On the other hand, by placing nodes in regular topologies, we expect benefits both in coverage and efficiency of communication. We describe and analyze quasi-regular networks, which only use nodes as sentries and relays that are approximately evenly spaced, thereby emulating a regular grid topology. It is shown that quasi-regular networks have a significant energy and lifetime advantage compared with purely random networks.