Download Discrete Event Systems, Manufacturing Systems, and by P. E. Caines, Y. J. Wei (auth.), P. R. Kumar, P. P. Varaiya PDF

By P. E. Caines, Y. J. Wei (auth.), P. R. Kumar, P. P. Varaiya (eds.)

This IMA quantity in arithmetic and its purposes DISCRETE occasion structures, production platforms AND communique NETWORKS relies at the lawsuits of a workshop that used to be a vital part of the 1992-93 IMA software on "Control idea. " The learn of discrete occasion dynamical platforms (DEDS) has turn into swiftly well known between researchers in structures and regulate, in verbal exchange networks, in production, and in dispensed computing. This improvement has created difficulties for re­ searchers and power "consumers" of the study. the 1st challenge is the veritable Babel of languages, formalisms, and techniques, which makes it very tough to figure out the commonalities and differences one of the competing faculties of ways. the second one, similar, challenge arises from the several traditions, paradigms, values, and adventure that students convey to their research of DEDS, looking on whether or not they come from keep watch over, com­ munication, desktop technology, or mathematical common sense. for this reason, highbrow trade between students turns into compromised through unexplicated assumptions. the aim of the Workshop used to be to advertise alternate between students representing the various significant "schools" of proposal in DEDS with the desire that (1) better readability could be accomplished thereby, and (2) cross-fertilization will bring about extra fruitful questions. We thank P. R. Kumar and P. P. Varaiya for organizing the workshop and modifying the court cases. We additionally take this chance to thank the nationwide technological know-how origin and the military examine workplace, whose monetary help made the workshop attainable. A vner Friedman Willard Miller, Jr.

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Discrete Event Systems, Manufacturing Systems, and Communication Networks

This IMA quantity in arithmetic and its functions DISCRETE occasion structures, production platforms AND communique NETWORKS relies at the court cases of a workshop that was once an essential component of the 1992-93 IMA application on "Control conception. " The examine of discrete occasion dynamical platforms (DEDS) has turn into speedily well known between researchers in structures and keep watch over, in conversation networks, in production, and in disbursed computing.

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Extra resources for Discrete Event Systems, Manufacturing Systems, and Communication Networks

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We now return to our optimization algorithm driven by IPA estimates, and consider the issue of convergence of the algorithm. We first address the case where updating takes place after every busy period of the queue. Convergence results for this case were first reported in [11], [6]. Interestingly, the convergence of algorithms with other update times are intimately related to convergence in this case (see [9]). Recall that S( k) is the index of the last customer in the kth busy period, and S(k) = E7=1 N(j), where N(k) is the number of customers served in the kth busy period.

By the definition, each of Li 's is either a member of MEk or a formula deduced from its predecessors in the sequence. 3, So L; itself is a Ek-line. In this case, we leave this line unchanged. Hence if there is no L; containing the element of K(MEk-1), we let pI = P. e. {LL···,L;}. Now replace Li in P by Pi to get the new proof sequence for F: Notice that Li appears in the last line of Pi, so if Li is used to deduce other formula Lj, j > i, it can still be invoked after Pi has been inserted. MARKOVIAN FRAGMENTS OF COCO LOG THEORIES 27 Repeat this procedure until all K(MEk_d-lines have been replaced by their corresponding MEk_l-proof sequences.

2. (Decidable Theoremhood)[CW90,W91] For any k 2: 0, the logical theory MTh(on generated by ML,k for M together with the observed input-output sequence o~ is decidable. 3. ([CW90,W91]) For any k 2: 0, the axiom system for M together with the observed input-output sequence o~, ML,k is consistent. o We do not have a Nesting Property for a Markovian fragment system since there exist some members of ML,( on that are not theorems of ML,(o~+l). For example, K(ML,k-d ct. MTh(o~+l). 5. Main theorem. In the notation we have established, we shall present conditions under which for a formula F £ W F F(Lk') and hence that the trajectories of two identical systems in identical initial states controlled by complete and Markovian COCO LOG theories should be identical.

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