In this article, we investigate the network transition between non-saturation and saturation regimes for a Vehicular Ad hoc Network (VANET) which is composed of mobile nodes. We combine vehicular traffic theory, queuing model, and Markov chain to evaluate the performance of the network under spatial or networking saturation for multiple data classes over control channel and service channel. Our results indicate that the vehicle density growth can result in saturation of wireless medium around the roadside unit (RSU), further resulting in buffer overflows at on board units (OBUs). We also investigate the network saturation points for different transmission ranges of a RSU. Our results show that RSU's transmission coverage has to be chosen with respect to data patterns of OBUs, minimal distance between vehicles, and number of lanes in order to avoid network saturation condition.