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# 06. More about GSPN Models - CS4 Modelling and Simulation...

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CS4 Modelling and Simulation LN-6 6 More about GSPN Models In this note we will consider two simple systems modelled by GSPN and in the course of doing so examine more closely the dynamics of these models with respect to timed and immediate transitions. At the end of the note we will summarise some of the key features of the SPNP modelling tool and describe how it may be used to generate and solve GSPN models. 6.1 System Dynamics Recall that in an untimed Petri net the firing of a transition corresponded to an event in the system. In GSPN we recognised that these events might arise in two different ways: it may be induced by the completion of some activity; these activities can be further divided into two categories: those which take significant time to complete. those whose duration is negligible compared with other actions in the system, often called control actions . it may result from the verification of some logical condition of the system. Timed transitions represent actions which take some time to be completed. Immediate transitions represent logical events and control actions. For timed transitions, when they become enabled, i.e. all the input places of the transi- tion become marked with the necessary number of tokens, we imagine the corresponding activity starting in the system. This activity will continue until it is completed or inter- rupted. We assume that each transition has a timer or local clock associated with it: when the transition is enabled the timer is set to a value. Since we are using a random variable to represent activity durations, this value is sampled 1 from the exponential distribution with the appropriate rate parameter. While the transition is enabled we assume that the timer decrements at a constant speed. When the timer reaches zero the transition fires. For immediate transitions, the firing of the transition takes no time and is assumed to occur instantaneously. We also assume that enabled immediate transitions always have priority over any enabled timed transitions, so we fire all possible immediate transitions first. If only one immediate transition is enabled, it fires, and the new marking is produced. If several immediate transitions are enabled, some mechanism is necessary to identify which transition will fire. In fact the choice of transition to be fired is only important in cases where there is conﬂict between the enabled transitions, i.e. the firing of one will disable another. If the enabled immediate transitions are concurrent, they can be fired in any order. When enabled immediate transitions are in conﬂict GSPNs associate weights , or relative probabilities, with each transition. We can think of a distribution being sampled to determine which transition actually fires in each case.

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06. More about GSPN Models - CS4 Modelling and Simulation...

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