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Figure 3.3 A snapshot of Uppaal model checker3.3. Modeling production systems with patterns of timed automataFor modeling a production system the timed automata (TA) based formalism isused. It is appropriate for systems that can be modeled as a collection of nondeterministicprocesses with finite control structure and real-valued clocks (i.e.timed automata), communicating through channels and (or) shared data structures.Typical application areas include real-time controllers, communication protocols,and other components in which timing aspects are critical. Suitable computingengine for TA based MC is UppAal (www.uppaal.com).To solve a production system model the pattern-based modeling and parametricmodel checking method can be used. For different tasks various specialized viewsof a root model M 0 are constructed and analyzed. The model M 0 consists of aparallel composition (denoted by ||) of UppAal automata that are constructed usingbasic model patterns T r and T m r, i.e., M 0 ≡ (|| i T i) || (|| j T m j).• Pattern T r – “recipe”– is an automaton that models a technological process,i.e., the precedence relation of technological operations that are necessaryto manufacture a certain type of product (Fig 3.4a).• Pattern T m is an automaton for modeling machining units performingtechnological operations (Fig 3.4b).Here we distinguish between the concepts pattern and template that seeminglyhave a similar meaning. Since template has fixed semantics in UppAal denoting aclass of automata that can be instantiated by giving explicit values to its parameters,we use a more general notion – pattern – denoting typical fragments of automatathat occur repeatedly in the model. Both patterns are sequential and the operationsof pattern T r and their performing by MU represented in T m are synchronized via37