By Ib M. Skovgaard

ISBN-10: 094060020X

ISBN-13: 9780940600201

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**Example text**

T). The derivative of firing vector represents the flow of the t i m e d model f ( T ) -&(T). D e p e n d i n g on how the flow of the t r a n s i t i o n is defined m a n y firing semantics are possible; the most used in literature are finite servers semantics (or constant speed) and infinite server semantics (or variable speed) (Recalde and Silva, 2001) (David and Alla, 2004). A t r a n s i t i o n tj c T is enabled at m iff Vpi c "tj, mi > 0, and its enabling degree is enab(tj,m)-- min { mi }.

In a dt-contPN, this is not always true. Let us consider the net in Fig. 5. Assume transition t2 is stopped ( w 2 ( O ) = 0), then m3(1) = m a ( O ) - 0 . W 1 ( 0 ) - - 0 . 1 -- 0 . 5 • W 1 ( 0 ) . B u t W 1 ( 0 ) is upper b o u n d e d by A1. m3(0) - 5 . 0 . 5. If the m a x i m u m value is chosen, then m3(1) will be negative!! 5. R E A C H A B I L I T Y " E Q U I V A L E N C E " B E T W E E N S A M P L E D AND C O N T I N U O U S MODELS This can be avoided if the sampling period is small enough.

R , called the fundamental equation. which is T h e basic difference between discrete and continuous P N is t h a t the c o m p o n e n t s of t h e markings and firing count vectors are not restricted to take value in the set of n a t u r a l n u m b e r s but in the non-negative reals. The set of markings t h a t are reachable with a finite firing sequence for a given system IN', m o ) is denoted as R S un (A[, mo). In classical Systems and Signal Theory, it is wellknown t h a t the Sampling theorem (frequently known as the N y q u i s t - S h a n n o n sampling theorein) provides an u p p e r b o u n d for the sampling period of limited b a n d w i d t h signals in order " n o t to loose information".

### Analytic statistical models by Ib M. Skovgaard

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