A Class of Perturbed Cell-Transmission Models to Account for Traffic Variability

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.