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|We study uid analogues of a subclass of Petri nets, called Fluid Timed Event Graphs with Multipliers, which are a timed extension of weighted T-Systems studied in the Petri Net literature. These event graphs can be studied naturally, with a new algebra, analogous to the min-plus algebra, but de ned on piecewise linear concave increasing functions, endowed… (More)

In general semimodules, we say that the image of a linear operator B and the kernel of a linear operator C are direct factors if every equivalence class modulo C crosses the image of B at a unique point. For linear maps represented by matrices over certain idempotent semifields such as the (max,+)-semiring, we give necessary and sufficient conditions for an… (More)

We show that Continuous Timed Petri Nets (CTPN) can be modeled by generalized polynomial recurrent equations in the (min,+) semiring. We establish a correspondence between CTPN and Markov decision processes. We survey the basic system theoretical results available: behavioral (inputoutput) properties, algebraic representations, asymptotic regime. A… (More)

The Traffic Assignment problem consists in determining the routes used by sets of network users taking into account the link congestions. In deterministic modelling, Wardrop Equilibriums are computed. They can be reduced to huge nonlinear multiflow problems in the simplest cases. In stochastic modelling, Logit Assignments are used. They can be obtained,… (More)

- Grigori L. Litvinov, Pierre Del Moral, +23 authors J . - P . Quadrat
- 2006

To Anatoly Vershik with admiration and gratitude This paper is a brief introduction, practically without exact theorems and proofs, to the Maslov dequantization and idempotent and tropical mathematics. Our list of references is not complete (not at all). Additional references can be found, e.g., in the electronic archive http://arXiv.org and in [9, 17, 21,… (More)

- Mengzhen Kang, P . - H . Cournède, J . - P . Quadrat, Philippe de Reffye
- 2006 Second International Symposium on Plant…
- 2006

The article describes a stochastic formal language adapted to the botanical concepts underlying the GreenLab organogenesis model. It is based on stochastic L-systems (parallel rewriting grammars) and on multi-type branching processes: stochastic processes control bud productions and at each growth cycle, each new growth unit is the result of a random… (More)

- G. Cohen, Stéphane Gaubert, J . - P . Quadrat, Peter Kokotovic
- 2004

In maxplus algebra, linear projectors on an image of a morphism B parallel to the kernel of another morphism C can be built under transversality conditions of the two morphisms. The existence of a transverse to an image or a kernel of a morphism is obtained under some regularity conditions. We show that those regularity and transversality conditions can be… (More)

- MASLOVSEMIRINGSP . LOTITO, J . - P . Quadrat, E . MANCINELLIAbstra
- 2009

We show that car traffic on a town can be modeled using a Petri net extension where arcs have negative weights. The corresponding minplus dynamics is not linear but homogeneous of degree one. Possibly depending on the initial condition, homogeneous of degree 1 minplus systems may be periodic or have a chaotic behavior (to which corresponds a constant… (More)

We study here the min-plus analogues of Jacksonnetworks of queues and show that the corresponding geodesic problems on Zm can be reduced to minimal cost flow problems on complete graphs having m nodes. In some particular cases, these flow problems can be solved explicitly giving formulae analogue, in the min-plus algebra, to the standard product forms. Nous… (More)