A mobile ad hoc network is a collection of wireless nodes, all of which may be mobile, that dynamically create a wireless network amongst them without using any infrastructure. Ad hoc wireless networks come into being solely by peer-to-peer interactions among their constituent mobile nodes, and it is only such interactions that are used to provide the necessary control and administrative functions supporting such networks. Mobile hosts are no longer just end systems; each node must be able to function as a router as well to relay packets generated by other nodes. As the nodes move in and out of range with respect to other nodes, including those that are operating as routers, the resulting topology changes must somehow be communicated to all other nodes as appropriate. In accommodating the communication needs of the user applications, the limited bandwidth of wireless channels and their generally hostile transmission characteristics impose additional constraints on how much administrative and control information may be exchanged, and how often. Ensuring effective routing is one of the greatest challenges for ad hoc networking. As a practice, ad hoc routing protocols make routing decisions based on individual node mobility even for applications such as disaster recovery, battlefield combat, conference room interactions, and collaborative computing etc. that are shown to follow a pattern. In this thesis we propose an algorithm that performs routing based on underlying mobility patterns. A mobility pattern aware routing algorithm is shown to have several distinct advantages such as: a more precise view of the entire network topology as the nodes move; a more precise view of the location of the individual nodes; ability to predict with reasonably accuracy the future locations of nodes; ability to switch over to an alternate route before a link is disrupted due to node movements. / Master of Science

<p>This thesis studies non-nearest-neighbor random walks in random environments (RWRE) on the integers and on the d-dimensional integer lattic that are drawn in an i.i.d. way according to a Dirichlet distribution. We complete a characterization of recurrence and transience in a given direction for random walks in Dirichlet environments (RWDE) by proving directional recurrence in the case where the Dirichlet parameters are balanced and the annealed drift is zero. As a step toward this, we prove a 0-1 law for directional transience of i.i.d. RWRE on the 2-dimensional integer lattice with bounded jumps. Such a 0-1 law was proven by Zerner and Merkl for nearest-neighbor RWRE in 2001, and Zerner gave a simpler proof in 2007. We modify the latter argument to allow for bounded jumps. We then characterize ballisticity, or nonzero liiting velocity, of transienct RWDE on the integers. It turns out that ballisticity is controlled by two parameters, kappa0 and kappa1. The parameter kappa0, which controls finite traps, is known to characterize ballisticity for nearest-neighbor RWDE on the d-dimensional integer lattice for dimension d at least 3, where transient walks are ballistic if and only if kappa0 is greater than 1. The parameter kappa1, which controls large-scale backtracking, is known to characterize ballisticity for nearest-neighbor RWDE on the one-dimensional integer lattice, where transient walks are ballistic if and only if the absolute value of kappa1 is greater than 1. We show that in our model, transient walks are ballistic if and only if both parameters are greater than 1. Our characterization is thus a mixture of known characterizations of ballisticity for nearest-neighbor one-dimensional and higher-dimensional cases. We also prove more detailed theorems that help us better understand the phenomena affecting ballisticity.</p>