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Optimization of Stochastic Discrete Event Dynamic Systems: A Survey of Some Recent Results

  • Alexei A. Gaivoronski
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 374)

Abstract

Models of discrete event dynamic systems (DEDS) include finite state machines [24], Petri nets [35], finitely recursive processes [26], communicating sequential processes [18], queuing models [41] among others. They become increasingly popular due to important applications in manufacturing systems, communication networks, computer systems. We would consider here a system which evolution or sample path consists of the sequence
$$y\left( {x,\omega} \right) = \left\{ {\left( {{t_0},{z_0}} \right),\left( {{t_1},{z_1}} \right),...,\left( {{t_s},{z_s}} \right)} \right\},{t_i} = {t_i}\left( {x,\omega} \right),{z_i} = {z_i}\left( {x,\omega} \right)$$
where zi(x,ω)) ∈ W is the state of the system during the time interval \({t_i}\left( {x,\omega} \right) \le t < {t_{i + 1}}\left( {x,\omega} \right)\), x∈X⊆Rn is the set of control parameters and ω∈Ω is an element of some probability space (Ω, 𝔹, ℙ). Particular rules which govern transitions between states at time moments ti. can be specified in the framework of one of the models mentioned above. For describing the time behavior the generalized semi- Markov processes proved to be useful [47].

Keywords

Discrete Event Sample Path Perturbation Analysis Evolution Step Discrete Event System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Alexei A. Gaivoronski
    • 1
  1. 1.V.Glushkov Institute of CyberneticsKievUSSR

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