Stochastic Properties of Mobility Models in Mobile Ad Hoc Networks

The stochastic model assumed to govern the mobility of nodes in a mobile ad hoc network has been shown to significantly affect the network´s coverage, maximum throughput, and achievable throughput-delay trade-offs. In this paper, we compare several mobility models, including the random walk, random waypoint, and Manhattan models on the basis of the number of states visited in a fixed time, the time to visit every state in a region, and the effect of the number of wandering nodes on the time to first enter a set of states. These metrics for a mobility model are useful for assessing the achievable event detection rates in surveillance applications where wireless-sensor-equipped vehicles are used to detect events of interest in a city. We also consider mobility models based on Correlated Random Walks, which can account for time dependency, geographical restrictions, and nonzero drift. We demonstrate that these models are analytically tractable by using a matrix-analytic approach to derive new, closed-form results in both the time and transform-domains for the probability that a node is at any location at any time for both semi-infinite and finite 1D lattices. We also derive first entrance time distributions for these walks. We find that a correlated random walk 1) covers more ground in a given amount of time and takes a smaller amount of time to cover an area completely than a random walk with the same average transition rate, 2) has a smaller first entrance time to small sets of states than the random waypoint and random walk models, and 3) leads to a uniform distribution of nodes (except at the boundaries) in steady state.