Displaying similar documents to “Nonlinear Markov processes in big networks”

A Markov chain model for traffic equilibrium problems

Giandomenico Mastroeni (2010)

RAIRO - Operations Research

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We consider a stochastic approach in order to define an equilibrium model for a traffic-network problem. In particular, we assume a Markovian behaviour of the users in their movements throughout the zones of the traffic area. This assumption turns out to be effective at least in the context of urban traffic, where, in general, the users tend to travel by choosing the path they find more convenient and not necessarily depending on the already travelled part. The developed model...

Fast simulation for Road Traffic Network

Roberta Jungblut-Hessel, Brigitte Plateau, William J. Stewart, Bernard Ycart (2010)

RAIRO - Operations Research

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In this paper we present a method to perform fast simulation of large Markovian systems. This method is based on the use of three concepts: Markov chain uniformization, event-driven dynamics, and modularity. An application of urban traffic simulation is presented to illustrate the performance of our approach.

Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

Dan Goreac (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied...