TABLE OF CONTENTS We consider a mobile wireless network with n nodes moving within a unit square [2]. We assume that time is divided into slots of unit length. We assume the following i.i.d. mobility model proposed in [3]. At each time slot, the positions of each node are i.i.d. and uniformly distributed within the unit square. Between time slots, the distributions of the positions of the nodes are independent. Although the assumption on an i.i.d. mobility model is somewhat restrictive, its mathematical tractability allows us to gain important insights into the structure of the problem. We will comment on some extensions to the i.i.d. mobility model in the conclusion.
For simplicity, we assume the following traffic model similar to the models in [3, 4]. We assume that the number of nodes n is even and the nodes can be labeled in such a way that node 2 i - 1 communicates with node 2i, and node 2 i communicates with node 2i - 1 , i = l, 2, , n/2. The communication between any source-destination pairs can go through multiple other nodes as relays. That is, the source can either send a message directly to the destination; or, it can send the message to one or more relay nodes; the relay nodes can further forward the message to other relay nodes (possibly after moving to another position); and...
