Realistic Boundary Conditions for Ad Hoc Network Node Mobility Models and a New Approach to the Random Waypoint Model

AbstractIn this paper, we examine the cause of the border effect observed in many mobility models used toconstruct simulations of ad hoc networking protocol performance. We specify conditions under whicha node mobility model must produce spatial mobile node distribution functions that obey the diffusionequation. In particular demonstrate that these conditions are satisfied by the random direction (RD)model. We show that it is possible to construct mobility models that attain uniform steady-state dis-tributions without resorting to reflection or “wrapping” of nodes at the border of a test region. Finally,we show that the random waypoint (RWP) model may be reproduced by the application of a “volumerule” to an RD model. This volume rule violates the assumptions that lead to the diffusion equation. Wesuggest a generalization of the RWP model that can provide more uniform mobile node distributions. 1 Introduction At present, most wireless devices rely upon fixed infrastructure to connect to one another and the outsideworld. Fixed installations are necessary due to the need for power to operate them, access to a larger wirednetwork, and for centralized processing to coordinate relatively unsophisticated devices. As the numberand sophistication of portable wireless network devices increases, it becomes useful to consider replacingthis centralized network architecture with one that is generated spontaneously among local network nodes,or an ad hoc network. Ad hoc networking promises to liberate wireless devices from dependence on fixedinfrastructure by allowing devices to communicate to one another via a dynamically generated network,where peers pass data to and through one another rather than to a fixed central node. In order to achievethis, network protocols (NPs) must be developed that allow independent nodes to agree upon a networktopology, and that can then keep pace with changes to the network as nodes move in and out of range ofone another.In recent years, there has been much interest in designing models for simulating the operation of arbitraryad hoc networking protocols for networks with mobile nodes. Such simulations are typically defined by:1. The network protocol to be tested, or a specified property of the mobile node ensemble to be studied,such as internode distances, the existence of spanning trees subject to relevant constraints, etc.2. A fixed test volume of d-dimensional space (often with d = 2) in which mobile nodes move about.3. A mobility model that specifies the behavior and motion of mobile nodes as they move about thevolume, which may include rules describing the conditions under which mobile nodes may exit the testvolume (and hence the simulation) or be introduced into it.1