Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets

We analyze a timed Petri net model of an emergency call center which processes calls with different levels of priority. The counter variables of the Petri net represent the cumulated number of events as a function of time. We show that these variables are determined by a piecewise linear dynamical system. We also prove that computing the stationary regimes of the associated fluid dynamics reduces to solving a polynomial system over a tropical (min-plus) semifield of germs. This leads to explicit formul{\ae} expressing the throughput of the fluid system as a piecewise linear function of the resources, revealing the existence of different congestion phases. Numerical experiments show that the analysis of the fluid dynamics yields a good approximation of the real throughput.Comment: 21 pages, 4 figures. A shorter version can be found in the proceedings of the conference FORMATS 201

Texture and dislocation structures observation in a dual-phase steel under strain-path changes at large deformation

International audienc

Characterization of the strain-induced plastic anisotropy of rolled sheets by using sequences of simple shear and uniaxial tensile tests

International audienceThe characterization of the plastic behaviour of rolled metal sheets at large strains is a critical ingredient of any finite element analyse software aimed at predicting stress and strain distributions and the eventual occurrence of defects in sheet metal forming. On the other hand, due to the reduced thickness of such rolled sheets, the experimental techniques available for their characterization are scarce. Recently, however, the development of reliable simple shear tests has brought a real breakthrough in this area. The present paper shows how two-stage non-proportional loadings involving sequences of simple shear and/or uniaxial tensile deformations can be adequately used to investigate the isotropic, kinematic and distortional hardening of rolled metal sheets at moderate and finite strains. The experimental techniques and their optimization are analysed and several examples concerning currently used structural materials are provided

The Effect of Strain Path Change on Texture Evolution at Finite Strain of Multiphase Steel: Numerical and Experimental Investigations

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Time Petri Nets with Dynamic Firing Dates: Semantics and Applications

International audienceWe define an extension of time Petri nets such that the time at which a transition can fire, also called its firing date, may be dynamically updated. Our extension provides two mechanisms for updating the timing constraints of a net. First, we propose to change the static time interval of a transition each time it is newly enabled; in this case the new time interval is given as a function of the current marking. Next, we allow to update the firing date of a transition when it is persistent, that is when a concurrent transition fires. We show how to carry the widely used state class abstraction to this new kind of time Petri nets and define a class of nets for which the abstraction is exact. We show the usefulness of our approach with two applications: first for scheduling preemptive task, as a poor man's substitute for stopwatch, then to model hybrid systems with non trivial continuous behavior