Phase Transition Model for Traffic at a Junction

Abstract

Consider a junction with n incoming and m outgoing roads. Along each road, the flow of traffic is described through the continuum model displaying phase transitions introduced in [5]. This note provides a Riemann solver for the resulting Riemann problem at the junction.2000 Mathematics Subject Classification: 35L65, 90B10.

Microscopic Selection of Solutions to Scalar Conservation Laws with Discontinuous Flux in the Context of Vehicular Traffic

“…By comparing (16) and (20) it is clear that the trajectories corresponding to the microscopic (15) and macroscopic (17) descriptions do not coincide. Indeed, according to the microscopic description each car start to move at time t = 0 + with strictly positive speed.…”

“…There is a number of works on trafic modeling where the jump admissibility criterion is taken according to the principle of flow maximization: we refer, for instance, to [18,20,26,40,45]. It also appeared in modeling of flows in porous media [1,5,19,38], the resulting solution being referred to as the "optimal entropy solution" and justified via the vanishing capillarity approach in specific flux configurations.…”

“…However Kruzhkov solutions are not always physically reasonable [43]. This is evident, for instance, when dealing with traffic flows through crossroads [20,25,26,35] or point-wise bottlenecks [21]. However, we stick to the notion of Kruzhkov admissibility away from the flux discontinuity location x = 0.…”

A macroscopic traffic model with phase transitions and local point constraints on the flow

“…From the analytical point of view, in [21] this model is proved to be globally well posed for any initial datum with bounded total variation; in [13,14] a new version of Godunov scheme is proposed in order to compute numerically its solutions. In [16,20,33] this model has been generalized to the case of a network.…”