The impact of source terms in the variational representation of traffic flow

Jorge A Laval (1) , Guillaume Costeseque (2) , Bargavarama Chilukuri (1)

1 School of Civil and Environmental Engineering [Atlanta]
2 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences

This paper revisits the variational theory of traffic flow, now under the presence of continuum lateral inflows and outflows to the freeway say Eulerian source terms. It is found that a VT solution can be easily exhibited only in Eulerian coordinates when source terms are exogenous meaning that they only depend on time and space, but not when they are a function of traffic conditions, as per a merge model. In discrete time, however, these dependencies become exogenous, which allowed us to propose improved numerical solution methods. In Lagrangian and vehicle number-space coordinates, VT solutions may not exist even if source terms are exogenous.

Mots clés: traffic flow; source terms; kinematic wave model

Domaines: Analyse numérique [math.NA]

Jorge A Laval, Guillaume Costeseque, Bargavarama Chilukuri. The impact of source terms in the variational representation of traffic flow. Transportation Research Part B: Methodological, 2016, ⟨10.1016/j.trb.2016.09.011⟩. ⟨hal-01281117v2⟩