Stochastic Characteristics and Simulation of the Random Waypoint   Mobility Model
  Simulation results for Mobile Ad-Hoc Networks (MANETs) are fundamentally governed by the underlying Mobility Model. Thus it is imperative to find whether events functionally dependent on the mobility model 'converge' to well defined functions or constants. This shall ensure the long-run consistency among simulation performed by disparate parties. This paper reviews a work on the discrete Random Waypoint Mobility Model (RWMM), addressing its long run stochastic stability. It is proved that each model in the targeted discrete class of the RWMM satisfies Birkhoff's pointwise ergodic theorem [13], and hence time averaged functions on the mobility model surely converge. We also simulate the most common and general version of the RWMM to give insight into its working. 
A. Ahuja, K. Venkateswarlu and P. Venkata Krishna
cs.NI