Computing the Steady-State Distribution of G-networks with Synchronized Partial Flushing

Analysis of stochastic Petri nets with signals

“…Moreover, observe that, in addition, the customer deletion policy at Q 2 and Q 3 is different from what is proposed in, for instance in [12,29]. In fact, in these papers the signal would first arrive at Q 2 (Q 3 ) and, if this were not empty, would go to Q 3 (Q 2 ).…”

“…12 for passive action t 12 in process P 2 ). The sets of outgoing, incoming, active and passive actions in each joint state are denoted according to the following notation (wherein k = 1, 2): P k : the set of passive action types in the process P k -each must be passive at all its instances in P k ;…”

“…According to the deletion policy of the model of Figure 13, the signal arriving at Q 2 and Q 3 vanishes. Conversely, if we assume the simultaneous deletion policy described in [12,29] with Q 2 reached before Q 3 , then the signal deletes one customer from Q 2 before vanishing on arrival at Q 3 . This different behaviour, combined with the synchronised positive customer arrivals at Q 2 and Q 3 , lead to different productform conditions and expressions.…”

Product-Form in G-Networks

“…The PITS can have a cyclic topology and hence it may reproduce sophisticated behaviors such as the partial flushing [13,16,17] previously proposed in the G-network theory.…”

“…We consider a G-network of the class studied in [13] as depicted in Figure 6. In this example a positive customer leaving Q 1 can join Q 2 with probability q as a standard positive customer, while with probability 1 − q it affects Q 2 as a signal.…”