Nowadays, one of the most major issues for electric vehicles (EVs) concerns their charging. In our previous research works in this field, we have proposed a predictive charging policy aiming to reduce waiting times of EVs within charging stations. In this paper we continue this effort by developing a formal model to describe and study the charging process behavior. Based on this model, the objective consists of serving a large number of charging demands with a minimum of time tacking into account many parameters of the system such as the location of EVs, their consumption and their real needs in terms of energy. Our developed model is described as states/transitions occurring sequence in a chronological order. It based on Petri net model in which each event execution requires the time amount. Managing charging demands is ensured by a collaborative platform based on communication technologies and geopositioning techniques. The behavior of this platform is represented and access control of registered EVs is also addressed. Some qualitative properties of charging system such as reachability, deadlock-free and synchronization are checked and validated using Petri net theory. Afterwards, we combine Petri nets with (Max, +) equations in order to express the analytic behavior of the process and, to analyze and validate some of its quantitative properties.