Spatial Stochastic Vehicle Traffic Modeling for VANETs

Connectivity is a fundamental requirement for vehicular ad hoc networks (VANETs) to secure reliable information dissemination. Connectivity is not guaranteed in the case of traffic sparsity and low market penetration of networked vehicles. Therefore, it is essential to examine the connectivity condition before deploying VANETs. The probabilistic distribution of inter-vehicle spacing plays a crucial role in the study of connectivity. It is quite often in previous studies to assume a priori distribution. This paper has studied this issue analytically and proved a general result as follows. A Poisson vehicle flow of volume {\lambda } enters a road stretch over the period [0, \infty ) , with the speed of each vehicle sampled from a common probability distribution of the density function {f}_{V} {(v)} ; then, in the steady state, the number of vehicles within any road section [ {x}_{1}{,}~{x}_{2} ] at any time instant {t>0} is Poisson distributed with the parameter \lambda ({x}_{2}\,\, {-} \,\, {x}_{1})\int _{0}^{\infty } {\frac {1}{v}{f}_{V}{(v)dv}} . This theoretical result is also confirmed with extensive simulation studies.