Traffic load in a dense wireless multihop network

In wireless multihop networks each node acts as a relay for the other nodes. Consequently, the distribution of the traffic load has a strong spatial dependence. We consider a dense multihop network where the routes are approximately straight line segments. To this end we introduce the so-called line segment traversing process which defines the movement of points in a given region. In particular, the points move along the line segments with a spatial velocity which depends on the current location of the point. We use this process to model the movement of packets and utilise its properties to study the relayed traffic load which corresponds to the traffic load experienced by a node in a given location, and to study the queueing delays as a function of the location using the spatial velocity of the line segment process. The efficiency of a wireless multihop network depends significantly on the used MAC protocol, which then has an impact on queueing delays in a congested network. Our model can be adapted to any given MAC protocol by a proper choice of the spatial velocity. Additionally, from the model we also obtain an expression for the mean one-way delay in the network, which is itself an important performance measure of the network. Finally, we use ns2-simulations to validate some of the key ideas, along with several numerical examples illustrating the effects of MAC protocols on the mean end-to-end delay and power (ratio of throughtput to mean delay).