The Minimum Cycle Time And Applications Of Weight Timed Event Graphs Without The Ring In Dioids

Many control problems in the computer network, the digital circuit and the automa-tion manufacturing industry can be abstracted as the input-output behavior of a timed event graphs(TEGs). The TEGs is based on the max-plus algebraic system.Max-plus algebra is an algebraic structure, which is obtained by replacing the operations addition and multiplication in general algebraic structure with the operations maximum and addi-tion.With the deepening of the study of maximal plus algebra, the TEGs has been greatly developed.In particular, the TEGs in a dioid called O solves a lot of control problems. Dioid O is defined on the set of additive operators, and its internal operation is to take the minimum and multiplication.In this paper, we mainly study the periodicity of the operator of the no self loop timed event graphs in dioid.A subclass of timed Petri nets that we call no self loop timed event graphs will be first defined, which can describe batch constitution (several successive input events are necessary to release one output event) and duplication (one input event release several output events). These behaviors are described by the form power series of four elementary operators γv,δτ,βb,, and μm on a dioid O by addition and multiplication operations(sum, product). Using the algebraic method, to study control problem of no self loop weighted timed event graph. The optimal index set required for almost no accumulation of the end of a cycle, The final calculated by the optimal control function of H= βbγvμm can achieve the optimal index. Finally an example of the optimal control and its conclusions are explained.