A probabilistic model for message propagation in two-dimensional vehicular ad-hoc networks

Vehicular ad-hoc networks (VANET) promise to enhance the road safety and travel comfort significantly in both highway and city scenarios. Message propagation, either for emergency or pleasure purposes, constitutes a major category of VANET applications, and is particularly challenging in infrastructure-less vehicle-to-vehicle communication scenarios. In this paper, we study the connectivity property of message propagation in two-dimensional VANET. We first derive the exact expression for the average size of the connected components in the one-dimensional case, i.e., messages propagating along a main street, and give a close approximation to the size distribution. We further derive the connectivity of message propagation in the two-dimensional ladder case, i.e., covering the main and two side streets, and formulate the problem for the two-dimensional lattice case to cover all the blocks in a district. Extensive simulation has been conducted to verify the analytical model and provide further insights in message propagation with and without geographic constraints, respectively. The simulation results show the efficacy of the model and the tradeoff between these two message forwarding strategies, and provide guidelines for future network planning and protocol development.