Sound mobility models

Simulation has become an indispensable tool in the construction and evaluation of mobile systems. By using mobility models that describe constituent movement, one can explore large systems, producing repeatable results for comparison between alternatives. Unfortunately, the vast majority of mobility models---including all those in which nodal speed and distance or destination are chosen independently---suffer from decay; average speed decreases until converging to some long-term average. Such decay provides an unsound basis for simulation studies that collect results averaged over time, complicating the experimental process.This paper shows via analysis that such decay is inevitable in a wide variety of mobility models, including the most common in use today. We derive a general framework for describing this decay, and apply it to a number of practical cases. Furthermore, this framework allows us to transform any given mobility model into a stationary one: choose initial speeds from the steady-state distribution, and subsequent speeds from the original. This transformation provides sound models for simulation, eliminating variations in average nodal speed.