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 a significant impact on the network's coverage, maximum throughput, and achievable throughput-delay tradeoffs. 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 entrance to a set of states. 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 one-dimensional lattices. We also derive first entrance time distributions for these walks. We find that a correlated random walk (i) 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; (ii) has a smaller first entrance time to small sets of states than the random waypoint and random walk models and (iii) leads to uniform distribution of nodes (except at the boundaries) in steady state.