Spatial Stochastic Vehicle Traffic Modeling for VANETs

Abstract

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 intervehicle 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 λ enters a road stretch over the period [0, ∞), with the speed of each vehicle sampled from a common probability distribution of the density function fV (v); then, in the steady state, the number of vehicles within any road section [x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ] at any time instant t > 0 is Poisson distributed with the parameter λ(x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ) f <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> 1/V f(v)dv. This theoretical result is also con1 0 firmed with extensive simulation studies.