Modeling of priority queueing service in discrete event systems using hybrid Petri nets

We propose a hybrid Petri net (HPN) that extends the framework of the original colored generalized stochastic Petri net by hiding queues in special places. The hybrid Petri net contains ordinary tokens and control tokens. Both ordinary tokens and control tokens can be exogenous, or can be obtained by a Markovian movement of a token from one place to another place after firing of transition. A control token forces an ordinary token to move instantaneously to another place according to a Markovian routing rule. We show that this new class of Petri net has product form stationary solution, and establish the non-linear token flow equations that govern it. The stability of the hybrid Petri net is discussed in this new context