Analysis Techniques For Man-Machine Systems Design

NATO UNCLASSIFIED- 35 - AC/243(Panel-8)TR/7Volume 22.6 PETRI NETSWhat the technique doesA Petri net is a graphical and mathematical modelling tool for describing and studying information processingsystems in which concurrent, asynchronous, distributed, non-deterministic and/or stochastic processes can occur (seeMurata, 1989 and Peterson. 1981). Recently, there has been a growing interest in applying them during therequirement development phase (Davis, 1990).Petri nets are graphs where two types of nodes - places (circles) and transitions (bars) - are interconnected bydirected arcs. For each transition, the directed arcs connect input places to transitions, and transitions to output places.An example of a Petri net is shown in Figure 2.9.communication order is processing operator 1 communication order is contirmaorder arrives waiting starts is active is terminated complete cm ndsystem is idle,waiting for orderscommunication order is order operator 2 communication order is confaorder arrives waiting processing is active is terminated complete seo mastartscommandFigure 2.9:A Petri net model of a communication system: initial conditionThe simple Petri net view of a system concentrates on two primitive concepts (Peterson, 1981):* Events: these are the results of actions which take place in the system. Their occurrence is controlled by thestate of the system which can be described as a set of conditions. Events are modelled as transitions (bars).* Conditions: certain (pre)conditions must hold for an event to occur, and the occurrence of an event may causeone or more new (post)conditions. Conditions are modeled as places (circles).An event in the example (Figure 2.9) is "order processing starts." The relevant preconditions are "an order is waiting"and "system is idle." The post-condition would be that "operator 2 is active" and "system is not idle." (Otherinterpretations of transitions and places are given in Table 2.4 (Murata, 1989)). In the given example, there can be aconflict between the two operators. In fact, only one operator can use the communication system at a time.A place can contain tokens (illustrated as dots within the circle). A Petri net is executed by defining a distribution oftokens to the places of the net (a marking) and then firing the transitions. When a Petri net model is executed thedistribution of tokens among the places is changed as illustrated in Figure 2.10. A token is transferred through atransition if all the connected places contain one or more tokens. Timed Petri nets are possible. In that case an eventduration time is associated with each transition. The values can be constant, or computed as functions of the values oftokens at the input places, or sampled from distributions.NATO UNCLASSIFIED