A class of perturbed Cell-Transmission models to account for traffic variability

Sebastien Blandin (1) , Dan Work (1) , Paola Goatin (2, 3) , Benedetto Piccoli (4) , Alexandre Bayen (1)

1 CEE - Department of Civil and Environmental Engineering [Berkeley]
2 IMATH - Institut de Mathématiques de Toulon - EA 2134
3 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
4 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"

We introduce a general class of traffic models derived as perturbations of cell-transmission type models. These models use different dynamics in free-flow and in congestion phases. They can be viewed as extensions to cell transmission type models by considering the velocity to be a function not only of the density but also of a second state variable describing perturbations. We present the models in their discretized form under a new formulation similar to the classical supply demand formulation used by the seminal Cell-Transmission Model. We then show their equivalence to hydrodynamic models. We detail the proper- ties of these so-called perturbed cell-transmission models and illustrate their modeling capabilities on a simple benchmark case. It is shown that they en- compass several well-known phenomena not captured by classical models, such as forward moving disturbances occurring inside congestion phases. An imple- mentation method is outlined which enables to extend the implementation of a cell transmission model to a perturbed cell transmission model.

Domaines: Equations aux dérivées partielles [math.AP]

Sebastien Blandin, Dan Work, Paola Goatin, Benedetto Piccoli, Alexandre Bayen. A class of perturbed Cell-Transmission models to account for traffic variability. Transportation Research Board 89th Annual Meeting, Jan 2010, Washington, DC, United States. ⟨hal-00536740⟩