In order to analyze whether timing requirements of a real-time application are met, we propose an extension of the T-time {Petri} net model which takes into account the scheduling of the software tasks distributed over a multi-processor hardware architecture. The paper is concerned with static priority pre-emptive based scheduling. This extension consists in mapping into the {Petri} net model the way the different schedulers of the system activate or suspend the tasks. This relies on the introduction of two new attributes for the places (allocation and priority). First we give the formal semantics of this extended model as a timed transition system (TTS). Then we propose a method for its analysis consisting in the computation of the state class graph. Thus the verification of timing properties can be conducted (possibly together with an observator) and comes to analyze the such obtained state class graph