Abstract
We propose a new approach to the modeling and analysis of cycle times in interval P-time event graphs based on dual linear representations in the (max,+) and (min,+) semirings. We start with first order inequalities in the (max,+)-algebra for execution times of transitions based on the simplification at the event graph level. Then we show that the state vector is bounded by a (max,+)-algebraic inequality from below and by a (min,+)-algebraic inequality from above, where both lower and upper bounds are sharpened compared to the previous appproaches. New conditions are then derived for the existence of periodic behaviors. The results are illustrated by two examples, the second one is a model of a manufacturing system from the electroplating industry.
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