A GSMP formalism for discrete event systems

Article Abstract:

The lack of a comprehensive framework for describing and analyzing discrete event systems hinders the study of such systems; an attempt is made to develop such a system. A specific type of stochastic process called a generalized semi-Markov process (GSMP) is defined that captures the required dynamical structure of a discrete event system. The GSMP framework is seen both as a precise 'language' for describing discrete event system and as a mathematical setting that can be used to analyze discrete event processes. An abstract description of a discrete event system is given, a GSMP is specified as a particular type of event-driven stochastic process, the GSMP framework is specialized further to generate the class of time-homogeneous GSMPs, and a flavor is given of the computational enhancements to discrete event simulations possible through use of the GSMP framework.

Dynamic Systems, Markov Process

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Sample path properties of timed discrete event systems

Article Abstract:

Discrete event system (DES) models are used to describe processes determined by the occurrences of discrete events, such as the arrival of a message in a network or the failure of a processor in a computer system. Most of the traditional mathematical tools used to analyze the presence of uncertainty are of little help in solving many practical problems. DES modeling emphasizes two areas: deterministic analysis issues and such problems as system performance. The two areas are distinguished by timing: the first known, the second unknown. The problem of creating a perturbed sample path, given a parameter perturbation, from information in a nominal sample path is considered. Two conditions that have to be satisfied for this to be feasible are observability and constructability. How both of these conditions are met in the technique developed is described.

Uncertainty, Simulation, Mathematics of Computing, Models of Computation

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