Qualitative Analysis of Periodic Schedules for Deterministically Timed Petri Net Systems (Special Section on Discrete Mathematics and Its Applications)

概要

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Periodic schedules are seldom treated in the theory but abound in practice (air flight schedule, train schedule, manufacturing schedule, etc). This paper introduces a Petri Net based perspective to periodic schedules. These are classified, according to the time interpretation into single-server and multiple-server semantics and, according to transitions firing periodicity constraints, into strict and general periodic schedules. Using a net transformation rule, the computation of the general schedule class can be done through techniques for the strict subclass. Introducing truncation error terms ε for the floor functions, a necessary and sufficient condition for the feasibility of a strict periodic schedule is given in terms of a large size system of nonlinear inequalities containing ε terms. Moreover averaging this condition on subperiods allows to get a small size linear system of inequalities as necessary conditions for speeding up iterative computation processes. This paper aims to present qualitative analysis of periodic schedules for deterministically timed Petri net systems, as a precursor to quantitative analysis that requires large-scale computational experiments and hence will be dealt in later work.
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1993-04-25