The nets with places and transitions and without time are also called PT-nets (place/transition-nets). There exist a large number of different implementations of Petri Net extensions, for a sample see http://www.ee.umanitoba.ca/tech.archive/pnex1.html (pnex1.html - pnex7.html). We will here present another time extension, DSPN, and a class of extensions with individualized tokens.
DSPNs are Petri Nets with time implemented in a different way from what has been presented here. In these there are three types of transitions: immediate transitions represented as thin black rectangles, deterministic transitions represented as thicker black rectangles, and exponential transitions represented as thicker white boxes and the time drawn from the negative exponential distribution. The immediate transitions may be given priorities. Inhibitor arcs may be used. Firing a transition with time differs from the model presented here in that the tokens remain in their input places for the firing time. We will not treat DSPNs in detail. Below is the DSPN model corresponding to the simple crossing shown in Figure W3. For the exponential transitions the intensity is given, the mean time between transitions is thus 6.6666... for Ngen and 0.5 for Ncrs2. Ncrs0 is an immediate transition.
Figure DSPN. DSPN model equivalent to W3