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Mathematical methods for stochastic discrete event systems

Ziel



A large class of stochastic discrete event systems such as queuing network and stochastic Petri networks are amenable to a state representation of the form X(n + l) = f(X(n), Y(n)), n = 0,1,... where the function f and the random sequence {Y(n)} are given. The behavior of the sequence {X(n)} will be the subject of study. The sequence {Y(n)} can be considered as a driving sequence including some input and controlling parameters. Sequence X(n) will be referred to as Stochastic Recursive Sequences (SRS). For example, in queuing networks {Y(n)} means the sequence of inter-arrival and service times and of routing policies, and {X(n)} may be either queue-length and/or waiting-time processes.

The aim of this project is the development of general mathematical methods for the analysis and control of various classes of stochastic discrete event systems such as queueing networks, Petri networks, generalized semi-Markov processes etc., as well as the applications of these results to various models arising in communication systems or computer architectures. The partners have strong and complementary records both in the mathematical part of the project (point processes: Braunschweig, Paris; stochastic recurrence sequences: Novosibirsk, Paris; asymptotic theory: Moscow, Novosibirsk, Cambridge; analytical theory: Amsterdam, Braunschweig, Moscow, etc.) and in the applications (production of performance evaluation software and involvement in industrial projects: Amsterdam, Cambridge, Paris).

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Institut National de la Recherche en
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Siège de Sophia-Antipolis Route des Lucioles 1004
06902 Sophia Antipolis
Frankreich

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