Using localized random walks to model Delay-Tolerant Networks

Mobile wireless delay-tolerant networks (DTNs) are wireless networks that suffer from intermittent connectivity, but enjoy the benefit of mobile nodes that can store, carry, and forward packets or messages, bringing them closer to their destinations through a selective forwarding policy. The evaluation of DTN routing protocols has primarily relied on simulation because most theoretical mobility models are unable to represent the mobility patterns that such protocols seek to take advantage of. In this paper we present and analyze a mobility model that we call localized random walk. This model is simple enough that it can be incorporated into mathematical models, but is spatially localized, which unlike other common mobility models, will make it possible to showcase the properties of heuristic-based DTN routing protocols. We derive the stationary spatial distribution of the mobility model, approximate what we call its spatial cross section, approximate the properties of its interaction with nodes following other mobility models, and use it to model some relatively simple DTN scenarios.