By P. E. Caines, Y. J. Wei (auth.), P. R. Kumar, P. P. Varaiya (eds.)
This IMA quantity in arithmetic and its functions DISCRETE occasion structures, production structures AND verbal exchange NETWORKS is predicated at the complaints of a workshop that used to be a vital part of the 1992-93 IMA application on "Control conception. " The examine of discrete occasion dynamical structures (DEDS) has develop into swiftly renowned between researchers in platforms and keep watch over, in communique networks, in production, and in dispensed computing. This improvement has created difficulties for re searchers and capability "consumers" of the study. the 1st challenge is the veritable Babel of languages, formalisms, and methods, which makes it very tricky to figure out the commonalities and differences one of the competing colleges of techniques. the second one, similar, challenge arises from the various traditions, paradigms, values, and adventure that students deliver to their learn of DEDS, looking on whether or not they come from keep an eye on, com munication, machine technology, or mathematical common sense. accordingly, highbrow alternate between students turns into compromised by means of unexplicated assumptions. the aim of the Workshop used to be to advertise trade between students representing a few of the significant "schools" of inspiration in DEDS with the wish that (1) better readability could be accomplished thereby, and (2) cross-fertilization will result in extra fruitful questions. We thank P. R. Kumar and P. P. Varaiya for organizing the workshop and modifying the complaints. We additionally take this chance to thank the nationwide technology beginning and the military learn workplace, whose monetary aid made the workshop attainable. A vner Friedman Willard Miller, Jr.
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Additional info for Discrete Event Systems, Manufacturing Systems, and Communication Networks
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We then serve the customers using the updated parameter value, until the next time we update the value again, which is after the r(2)th customer leaves. The procedure is repeated, generating a sequence of control parameters B(I), B(2), . The updates of the control parameter are performed after customers r(I), r(2), .... , the mth update is performed just after the r(m)th customer departs from the system. 1)). For the parameter updates, we use a stochastic approximation algorithm , . Specifically, let B(n) be the value of the control parameter used in the service time of the nth customer.
The technique of IPA can be used to estimate the derivative of J from observations of the sample path of the queue. We use the estimate of the derivative of J to recursively update the value of the control parameter (on-line) so that J is minimized asymptotically. 12)). We are interested in the convergence properties of such an algorithm. In , Wardi analyzes the convergence of an algorithm for minimizing J(O) = f(W(O)), where W(O) is the steady-state mean waiting time, and f is a smooth function.