We study local calcium dynamics leading to a vesicle fusion in a stochastic, and spatially explicit, biophysical model of the CA3-CA1 presynaptic bouton. The kinetic model for vesicle release has two calcium sensors, a sensor for fast synchronous release that lasts a few tens of milliseconds and a separate sensor for slow asynchronous release that lasts a few hundred milliseconds. A wide range of data can be accounted for consistently only when a refractory period lasting a few milliseconds between releases is included. The inclusion of a second sensor for asynchronous release with a slow unbinding site, and thereby a long memory, affects short-term plasticity by facilitating release. Our simulations also reveal a third time scale of vesicle release that is correlated with the stimulus and is distinct from the fast and the slow releases. In these detailed Monte Carlo simulations all three time scales of vesicle release are insensitive to the spatial details of the synaptic ultrastructure. Furthermore, our simulations allow us to identify features of synaptic transmission that are universal and those that are modulated by structure.