Abstract
A discrete event system (DES) is a dynamical system whose evolution in time develops as the result of the occurrence of physical events at possibly irregular time intervals. Although many DES's operation is asynchronous, others have dynamics which depend on a clock or some other complex timing schedule. Here we provide a formal representation of the advancement of time for logical DES via interpretations of time. We show that the interpretations of time along with a timing structure provide a framework to study principles of the advancement of time for hierarchical DES (HDES). In particular, it is shown that for a wide class of HDES the event rate is higher for DES at the lower levels of the hierarchy than at the higher levels of the hierarchy. Relationships between event rate and event aggregation are shown. We define a measure for event aggregation and show that there exists an inverse relationship between the amount of event aggregation and the event rate at any two successive levels in a class of HDES. Next, we study how to design the timing structure to ensure that there will be a decrease in the event rate (by some constant factor) between any two levels of a wide class of HDES. It is shown that if the communications between the various DES in the HDES satisfy a certain admissibility condition then there will be a decrease in the event rate. These results for HDES constitute the main results of this paper, since they provide the first mathematical characterization of the relationship between event aggregation and event rates of the HDES and show how to design the interconnections in a HDES to achieve event rate reduction. Several examples are provided to illustrate the results.
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The authors gratefully acknowledge the partial support of the Jet Propulsion Laboratory. Please address all correspondence to K. Passino (email: passino@eagle.eng.ohio-state.edu).
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Passino, K.M., Antsaklis, P.J. Event rates and aggregation in hierarchical discrete event systems. Discrete Event Dyn Syst 1, 271–287 (1992). https://doi.org/10.1007/BF01796825
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DOI: https://doi.org/10.1007/BF01796825