We analyze the connectivity of simulation ad hoc networks, which use random mobility models. Based on the theorem of minimum degree, the study of connectivity probability is converted into an analysis of the probability of minimum node degree. Detailed numerical analyses are performed for three mobility models: random waypoint model, random direction model, and random walk model. For each model, the connectivity probability is calculated and its relations with the communication range r and the node number n are illustrated. Results of the analyses show that with the same network settings, the connectivity performance decreases in the following order: random walk model, random direction model, and random waypoint model. This is because of the non-uniform node distribution in the last two models. Our work can be used by researchers to choose, modify, or apply a reasonable mobility model for network simulations.

The asymptotic properties of node distribution and speed distribution in random direction model were analyzed, respectively, by the tools of geometric probability and palm calculus. The probability density function for node distribution in circular regions was obtained which indicated that mobile nodes tended to disperse as simulation advancing. The speed decay phenomenon was confirmed in this model. Moreover, the hypostasis of speed decay was proved to be the correlation between speed and duration within any movement period.