In: Hai Jin, Guang R. Gao, Zhiwei Xu, et al. (Eds.): Lecture Notes in Computer Science, Vol. 3222: Network and Parallel Computing: IFIP International Conference, NPC 2004, Wuhan, China, October 18-20, 2004, pages 333-340. Springer-Verlag, 2004.
Abstract: Continuous Event Graphs (CEGs), a subclass of Continuous Petri Nets, are defined as the limiting cases of timed event graphs and Timed Event Multigraphs. A set of dioid algebraic linear equations will be inferred as a novel method of analyzing a special class of CEG, if treated the cumulated token consumed by transitions as state-variables, endowed the monotone nondecreasing functions pointwise minimum as addition, and endowed the lower-semicontinuous mappings, from the collection of monotone nondecreasing functions to itself, the pointwise minimum as addition and composition of mappings as multiplication. As a new modeling approach, it clearly illustrate characteristic of continuous events. Based on the algebraic model, an example of optimal Control is demonstrated.