Roger Filliger

Mesoscopic derivation of a fundamental diagram of one-lane traffic

Keywords: Strategie de Production ; Nonlinear Boltzmann-equation ; Burgers-equation ; Fluid-dynamical theories of vehicular traffic Reference LPM-ARTICLE-2002-003View record in Web of Science Record created on 2006-06-22, modified on 2016-08-08

Cooperative flow dynamics in production lines with buffer level dependent production rates

We study, in the fluid flow framework, the cooperative dynamics of a buffered production line in which the production rate of each work-cell does depend on the content of its adjacent buffers. Such state dependent fluid queueing networks are typical for people based manufacturing systems where human operators adapt their working rates to the observed environment. We unveil a close analogy between the flows delivered by such manufacturing lines and cars in highway traffic where the driving speed is naturally adapted to the actual headway. This close analogy is thoroughly explored. In particular, by investigating the dynamic response of small perturbations around free flow stationary regimes, we can draw a “phase diagram”. This diagram exhibits two different flow patterns, namely the free and jamming production regimes. The transitions between these regimes are tuned by the production control parameters (i.e. the buffer capacities, the reaction sensitivity, the control sampling time, ...). We finally extract a dimensionless dynamic parameter directly relevant for design purposes.

Local versus nonlocal barycentric interactions in 1D agent dynamics

The mean-field dynamics of a collection of stochastic agents evolving under local and nonlocal interactions in one dimension is studied via analytically solvable models. The nonlocal interactions between agents result from (a) a finite extension of the agents interaction range and (b) a barycentric modulation of the interaction strength. Our modeling framework is based on a discrete two-velocity Boltzmann dynamics which can be analytically discussed. Depending on the span and the modulation of the interaction range, we analytically observe a transition from a purely diffusive regime without definite pattern to a flocking evolution represented by a solitary wave traveling with constant velocity.

Hyperbolic angular statistics for globally coupled phase oscillators

We analytically discuss a multiplicative noise generalization of the Kuramoto-Sakaguchi dynamics for an assembly of globally coupled phase oscillators. In the mean-field limit, the resulting class of invariant measures coincides with a generalized, two-parameter family of angular von Mises probability distributions which is governed by the exit law from the unit disc of a hyperbolic drifted Brownian motion. Our dynamics offers a simple yet analytically tractable generalization of Kuramoto-Sakaguchi dynamics with two control parameters. We derive an exact and very compact relation between the two control parameters at the onset of phase oscillators synchronization.

Noise induced temporal patterns in populations of globally coupled oscillators

The population dynamics of an assembly of globally coupled homogeneous phase oscillators is studied in presence of non-Gaussian fluctuations. The variance of the underlying stochastic process grows as t + beta2t2 (beta being a constant) and therefore exhibits a super-diffusive behavior. The cooperative evolution of the oscillators is represented by an order parameter which, due to the ballistic beta2t2 contribution, obeys to a surprisingly complex bifurcation diagram. The specific class of super-diffusive noise sources can be represented as a random superposition of two Brownian motions with opposite drift and this allows to derive exact analytic results. We observe that besides the existence of the well known incoherent to coherent phase transition already present for Gaussian noise, entirely new and purely noise induced temporal patterns of the order parameter are realized. Hence, the ballistic contributions of the fluctuating environment does structurally modify the bifurcation diagram obtained for Gaussian noise. To illustrate potential implications of the developed class of models, we explore the dynamic behavior of a swarm formed by a planar society of particles with coupled oscillator dynamics. For this collective dynamics, we discuss how noise-induced periodic orbits of the swarms barycenter may emerge.

Optimal threshold control for failure-prone tandem production systems

We consider the flow dynamics of a tandem production system formed by two failure-prone machines separated by a buffer stock. The production rates of the machines are regulated by a feedback mechanism which solves an associated optimal control problem with an average cost criterion. The cost structure penalizes both the entrance into and the sojourn on the buffer boundaries. The generic structure of the optimal control involves four buffer content thresholds. When the buffer content crosses these thresholds, the production rates are tuned to reduce the tendency to enter into the buffer boundaries. Using the fluid modelling framework, we obtain analytical results for the stationary buffer level distribution in the case where an operating machine can produce with, either a “nominal” or a “reduced” rate. In the stationary regime, the optimal positions of the buffer thresholds, the throughput and the average buffer content are presented.

On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications

We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-m distribution. We show that the associated Master equation can be written as a spatial mth order partial differential equation without integral term. This differential form is valid for state-dependent Poisson rates and we use it to characterize, via a mean-field approach, the collective dynamics of a large population of pure jump processes interacting via their Poisson rates. We explicitly show that for an appropriate class of interactions, the speed of a tight collective traveling wave behavior can be triggered by the jump size parameter m. As a second application we consider an exceptional class of stochastic differential equations with nonlinear drift, Poisson shot noise and an additional White Gaussian Noise term, for which explicit solutions to the associated Master equation are derived.

Local versus nonlocal barycenttic interactions in 1 D agent dynamics

The mean-field dynamics of a collection of stochastic agents evolving under local and nonlocal interactions in one dimension is studied via analytically solvable models. The nonlocal interactions between agents result from (a) a finite extension of the agents interaction range and (b) a barycentric modulation of the interaction strength. Our modeling framework is based on a discrete two-velocity Boltzmann dynamics which can be analytically discussed. Depending on the span and the modulation of the interaction range, we analytically observe a transition from a purely diffusive regime without definite pattern to a flocking evolution represented by a solitary wave traveling with constant velocity.