# BS EN 62551:2012 pdf download

BS EN 62551:2012 pdf download.Analysis techniques for dependability —— Petri net techniques.

4 General description of Petri nets

4.1 Untimed low-level Petri nets

Petri nets (PNs) are graphs in which active and passive nodes are differentiated. The passive elements are called places; they model local states or conditions for example, and are marked with tokens lithe local state is fulfilled. The active elements are called transitions. They model the possible changes from one state to another (e.g. the potential events that may occur). Places and transitions may be called nodes. The causal relations between the phenomena represented by places and transitions are explicitly described through various kinds of directed arcs that connect these nodes (see the basic symbols of a Petri net in Table 1 and Clause A.1 for an introduction to PNs). Inhibitor arcs can only connect preset places with transitions in their postset (see A.1.2).

A transition is enabled. ii all its preset places that are connected with it by normal arcs or test arcs are marked with a sufficient number of tokens and if all its preset places that are connected with it by inhibitor arcs are unmarked. The number of tokens that are sufficient for the enabling of a transition is annotated to the arc. In general, this annotation can be marking dependent (see (3j). See 4.4 for commonly used generalizations of these concepts.

If a transition is enabled, it may fire. I.e. it may change the marking of the moe. The firing of a transition only changes the marking of places that are connected with it by normal arcs:

firing leads to absorbing tokens from corresponding places in its preset and to the production of tokens In its postset. The number of tokens that Is absorbed and produced is specified by the arc label. If no arc label is given, the number is one.

That means that the places, transitions and arcs form the static elements and relations of a system, whereas the tokens may be produced or may vanish according to the states of tne modelled system.

The reachability graph of a PN consists of all the global markings that can be reached from an initial marking through an arbitrary sequence of transition firings. In this graph, a node represents an individual global marking and each arc represents the firing of a transition that transforms one global marking to another.

PNs may be non graphically represented by incidence matrices. If T is the set of transitions and P is the set of places, then the incidence matrix is of dimension IPIlT1. For every transition, the changing of the global marking due to firing is specified in a corresponding column.

42 Timed low-level Petri nets

In timed PN, both untimed as well as timed transitions may be used. In order to fire, a timed transition shall be enabled for a specific time duration. This duration may be deterministic or stochashc, depending on the transition-specific distribution function (cumulative distribution function — COF) and the corresponding parameters. If two or more transitions are enabled at the same time, then the firing of transitions Is determined by a further specification of the transition, I.e. the preselection policy’ or the ‘race policy’. In addition, choices about execution policy and memory policy, aside from the firing time distributions, shall be specified ((3J). After this duration has elapsed, the transition is allowed to fire. Table 2 shows the commonly used transitions in timed PNs.

Corresponding to the specific type of a timed transition, It may be attributed by a time parameter that specifies the fixed firing duration (transitions with deterministic firing time), the constant firing rate (transitions with exponential or geometric distributed tiring times) or the probability distribution with its parameters (transitions with arbitrary distributed firing times). Note that untimed transitions are a particular case of fixed firing duration transitions with a deterministic delay of zero.