François Baccelli

Stochastic Networks Calculus

The research described here bears on stochastic discrete event systems and more precisely on stochastic networks (see the more general web page on queueing theory) and Petri nets (see the following Petri net bibliography).
We concentrated on the development of an algebraic framework allowing for a mathematical represention of networks regardless of their dimension and the underlying stochastic assumptions. This formalism also allows one to define classes of networks (e.g. event graphs, free choice nets etc.) for which similar methods of analysis work. Based on this mathematical representation, one can then design controls or evaluate analytically performaces in new ways, quite different from the more classical Markovian approach. For more on this approach, see the Wiley book entitled Synchronization and Linearity, which we coauthored with G. Cohen, G. J. Olsder and J. P. Quadrat in 1992.

Concerning my own research, here are the main domains of current interest, which are also summarized in the slides of a lecture that I gave at the 10-th Applied Probability Conference in Ulm (Germany) in July 1999:

Our research group was partner of the European project Alapedes which was part of the TMR program; there was also a Spring school on this topic in Noirmoutier: Algèbres Max-Plus et applications en informatique et automatique which stressed the recent developments of the theory and several domains of application in manufacturing, in transportation systems, and in computer science.

Several types of appications have been and are being investigated:

A. Jean-Marie has a software prototype called ERS which allows one to manipulated some of these objects and many more.
Last revised: July, 2011.