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Vehicular traffic density is a key factor in determining the behaviour of radio overlapping and thus impacts performance of data and safety message communication in Vehicular Ad hoc Networks (VANETs). In this paper, we propose a novel density model for urban traffic systems and employ this model for the purpose of spatial-temporal analysis of radio overlapping. To model traffic density, we consider a signalized junction and road segments linked to that junction as basic building blocks of urban traffic systems. The density model enables us to derive a framework to explain trends and critical regions of radio overlapping corresponding to VANET scenarios targeted for urban transportation systems, which cannot be derived from uniform density models widely used in existing literature. We apply the derived radio overlapping model to study channel load associated with periodic beaconing, a fundamental mechanism for safety message communication in VANETs. This study also provides a generic analytical framework to investigate other performance aspects of data and safety message communication in VANETs. Our experimental results using the proposed realistic density model demonstrate the need for an adaptive mechanism to adjust transmission power and data rate to reduce channel loads associated with dense traffic conditions.