Hop count, i.e., the number of wireless hops a packet has to go through to reach the destination, is a fundamental metric in multi-hop wireless ad-hoc networks. Network performance, such as throughput, end-to-end delay, energy consumption, and so on, depends critically on hop count. Previous work on modeling hop count is limited in making unrealistic simplifying assumptions either at the physical or network, or both layers of the communication protocol stack. A key contribution of this thesis is to present an analytical model to derive the probability distribution of hop count under realistic assumptions at both physical and network layers. Specifically, the model considers a log-normal shadowing radio propagation capable of accommodating the random signal fading observed in most wireless communication environments, and the widely used geographic routing at the network layer. Validation of the model is achieved by a comprehensive set of simulation experiments including a trace driven simulation of a real-word vehicular ad-hoc network. The model reveals that the presence of randomness in radio propagation reduces the required number of hops to reach a given destination significantly. To demonstrate the utility of the proposed hop count model, the thesis proposes three new applications which address some of the key challenges in multi-hop wireless networks. The first application derives the per-node packet forwarding load in multi-hop wireless sensor networks and reveals that the nodes in the vicinity of the base station has a significantly less forwarding load than previously thought under simplifying radio propagation and routing assumptions. The second application demonstrates that using hop count as a measure of distance traveled by a data packet, geocasting can be achieved in multi-hop wireless networks in situations when some of the network nodes do not have access to reliable location information. Finally, the proposed hop count model is used to evaluate the performance of the third application which demonstrates that the overhead of geographic routing can be reduced significantly by embracing a position update philosophy which adapts to the mobility and communication patterns of the underlying ad-hoc network.

Hop count, i.e., the number of wireless hops a packet has to go through to reach the destination, is a fundamental metric in multi-hop wireless ad-hoc networks. Network performance, such as throughput, end-to-end delay, energy consumption, and so on, depends critically on hop count. Previous work on modeling hop count is limited in making unrealistic simplifying assumptions either at the physical or network, or both layers of the communication protocol stack. A key contribution of this thesis is to present an analytical model to derive the probability distribution of hop count under realistic assumptions at both physical and network layers. Specifically, the model considers a log-normal shadowing radio propagation capable of accommodating the random signal fading observed in most wireless communication environments, and the widely used geographic routing at the network layer. Validation of the model is achieved by a comprehensive set of simulation experiments including a trace driven simulation of a real-word vehicular ad-hoc network. The model reveals that the presence of randomness in radio propagation reduces the required number of hops to reach a given destination significantly. To demonstrate the utility of the proposed hop count model, the thesis proposes three new applications which address some of the key challenges in multi-hop wireless networks. The first application derives the per-node packet forwarding load in multi-hop wireless sensor networks and reveals that the nodes in the vicinity of the base station has a significantly less forwarding load than previously thought under simplifying radio propagation and routing assumptions. The second application demonstrates that using hop count as a measure of distance traveled by a data packet, geocasting can be achieved in multi-hop wireless networks in situations when some of the network nodes do not have access to reliable location information. Finally, the proposed hop count model is used to evaluate the performance of the third application which demonstrates that the overhead of geographic routing can be reduced significantly by embracing a position update philosophy which adapts to the mobility and communication patterns of the underlying ad-hoc network.