A mathematical model of traffic flow on a network of unidirectional roads
SIAM Journal on Mathematical Analysis
A limited memory algorithm for bound constrained optimization
SIAM Journal on Scientific Computing
Resurrection of “second order” models of traffic flow
SIAM Journal on Applied Mathematics
Kinetic derivation of macroscopic anticipation models for vehicular traffic
SIAM Journal on Applied Mathematics
Trust-region methods
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
PoolView: stream privacy for grassroots participatory sensing
Proceedings of the 6th ACM conference on Embedded network sensor systems
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We are interested in models for vehicular traffic flow based on partial differential equations and their extensions to networks of roads. In this paper, we simplify a fluidodynamic traffic model and derive a new traffic flow model based on ordinary differential equations (ODEs). This is obtained by spatial discretization of an averaged density evolution and a suitable approximation of the coupling conditions at junctions of the network. We show that the new model inherits similar features of the full model, e.g., traffic jam propagation. We consider optimal control problems controlled by the ODE model and derive the optimality system. We present numerical results on the simulation and optimization of traffic flow in sample networks.