Study of Connectivity in a Vehicular Ad Hoc Network with Random Node Speed Distribution

In this paper we study connectivity in a 1D Vehicular Ad hoc Networks (VANETs) formed by vehicles with random speeds. Vehicles enter the highway in a time interval of length t following a Poisson distribution with speeds chosen according to fv(v). We propose an analytical model to study the connectivity among vehicles in a highway segment of length L. Based on the model; we derive a simple closed-form expression for probability of connectivity in an n-node VANET with the assistance of range distribution of order statistics. We also obtain expressions for some fundamental metrics of connectivity such as expected cluster length and cluster size. The impact of transmission range and network density on the connectivity metrics is studied as well. We also find the critical transmission range to reach a certain connectivity level in the network, it can be used to determine the right technology which supports the given connectivity level. Finally, the correctness and accuracy of analytical results are evaluated through simulation study.