In Vehicular Ad hoc NETworks (VANETs) the vehicles moving along roads communicate with each other through ad hoc wireless devices. VANETs have attracted a great deal of attention in the research community in recent years, with the main focus being on their support of safety applications. Time Division Multiple Access (TDMA)-based protocols are advantageous in many aspects of VANETs. They can cope with the hidden-terminal problem, and guarantee a strict Quality-of-Service (QoS) to satisfy real-time applications. However, the initial assignment of time-slots to the vehicles can suffer from the access collision problem, which can frequently occur between vehicles trying to access the same time slots. Moreover, a low latency access is not usually possible. That is why we have developed an Active Signaling system (AS-DTMAC : Active Signaling Decentralized Tdma MAC protocol) which operates above the existing DTMAC protocol : a Medium Access Control (MAC) protocol specially devoted to VANETs. AS-DTMAC can drastically reduce the number of access collisions and also offer low latency access. The aim of this article is to provide a complete mathematical analysis of the performance of this scheme, to show its high performances and to validate these results using simulations.