An extension of the Colombo phase transition model is proposed. The congestion described by a two-dimensional zone defined around standard fundamental diagram. General criteria for building such set-valued diagram are enumerated and instantiated on several fluxes with different concavity properties. solution to Riemann problem in presence transitions obtained through design solver, which enables construction Cauchy using wavefront tracking. free-flow Newell–Daganzo diagram, allows more...

We present a Lax--Friedrichs-type algorithm to numerically integrate class of nonlocal and nonlinear systems conservation laws in several space dimensions. The convergence the approximate solutions is proved, also providing existence solution slightly more general setting than other results current literature. An application crowd dynamics model considered.

The control of traffic flow can be related to different applications. In this work, a method manage variable speed limits combined with coordinated ramp metering within the framework Lighthill–Whitham–Richards (LWR) network model is introduced. Following 'first-discretize-then-optimize' approach, first order optimality system derived and switch speeds at certain fixed points in time explained, together boundary for metering. Sequential quadratic programming methods are used solve problem...

We investigate the possibility of properly controlling a given vehicle to improve overall traffic flow. The system is described by micro-macro model taking into account interactions with surrounding traffic. state an optimal control problem using maximal speed coordinated as variable. More precisely, we use MPC (Model Predictive Control) approach get fuel consumption reduction when congested due presence fixed downstream bottleneck on highway. In addition show that application also improves...

We prove the well-posedness of entropy weak solutions for a class scalar conservation laws with non-local flux arising in traffic modeling. approximate problem by Lax-Friedrichs scheme and we provide L ∞ BV estimates sequence solutions. Stability respect to initial data is obtained from condition through doubling variable technique. The limit model as kernel support tends infinity also studied.

Several realistic situations in vehicular traffic that give rise to queues can be modeled through conservation laws with boundary and unilateral constraints on the flux. This paper provides a rigorous analytical framework for these descriptions, comprising stability respect initial data, inflow constraint. We present rigorously state optimal management problems prove existence of corresponding controls. Specific cases are dealt detail ad hoc numerical integrations. These here obtained...

We prove the existence for small times of weak solutions a class non-local systems in one space dimension, arising traffic modeling. approximate problem by Godunov type numerical scheme and we provide uniform ${{\mathbf{L}}^\infty } $ BV estimates sequence solutions, locally time. finally present some simulations illustrating behavior different classes vehicles analyze two cost functionals measuring dependence congestion on composition.

We introduce a Follow-the-Leader approximation of nonlocal generalized Aw--Rascle--Zhang (GARZ) model for traffic flow. prove the convergence to weak solutions corresponding macroscopic equations deriving $L^\infty$ and BV estimates. also provide numerical simulations illustrating micro-macro we numerically investigate local limit both microscopic models.

We extend the results on conservation laws with local flux constraint obtained in [2, 12] to general (non-concave) functions and non-classical solutions arising pedestrian flow modeling [15]. first provide a well-posedness result based wave-front tracking approximations Kružhkov doubling of variable technique for law constrained flux. This provides sound basis dealing accounting panic states model introduced by Colombo Rosini In particular, constraints are used here presence doors obstacles....

This paper focuses on the numerical approximation of solutions nonlocal conservation laws in one space dimension. These equations are motivated by two distinct applications, namely, a traffic flow model which mean velocity depends weighted downstream density, and sedimentation where either solid phase or solid-fluid relative concentration neighborhood. In both models, is function convolution product between unknown kernel with compact support. It turns out that such may exhibit oscillations...