The theory of conservation laws was applied to vehicular traffic modeling. For traffic at junctions the following two rules were used to define a unique solution:
(A) fluxes distribute on outgoing roads according to fixed coefficients;
(B) the through flux is maximized (respecting rule (A)).
The first rule expresses driver preferences, while the second one is an ”entropy” type condition.
A number of different transportation problems were considered as:
a) Traffic monitoring and GPS data (Rec. papers: 2, Other papers: 1,2).
b) DTA (Rec. paper: 1).
c) Traffic signals (Rec. papers: 4, Other papers: 5).
d) Moving bottlenecks (Rec. papers: 7).
NEW: Research on Autonomous Vehicles, see 1. of recent papers.
Books and surveys:
- Bressan, S. Canic, M. Garavello, M. Herty, B. Piccoli: Flows on networks: recent results and perspectives, European Mathematical Society Survey, 1 (2014), 47-111. Survey
- Garavello, B. Piccoli: Traffic flow on networks, Applied Math Series vol. 1, American Institute of Mathematical Sciences, Springfield, 2006. link
- Stern et al. Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments, Transportation Research C, link, 89 (2018), 205-221, link
- Han, B. Piccoli, T.L. Friesz: Continuity of the path delay operator for LWR-based network loading with spillback, submitted to Transportation Research Part B. pdf
- Piccoli, K. Han, T.L. Friesz, T. Yao: Second Order Models and Traffic Data from Mobile Sensors, preprint arXiv:1211.0319, submitted to Transportation Research C. pdf
- Piccoli, K. Han, W.Y. Szeto: Continuous-time link based kinematic wave model: Formulation, solution existence and well-Posedness, to appear on Transportmetrica B: Transport Dynamics. pdf
- Han, V. Gayah, B. Piccoli, T.L. Friesz, T. Yao: On the continuum approximation of the on-and-off signal control on dynamic traffic networks, Transportation Research Part B, 61 (2014), 73-97. pdf
- Garavello, B. Piccoli: Coupling of microscopic and phase transition models at boundary, Networks and Heterogeneous Media, 8 (2013), 649-661. pdf
- Garavello, B. Piccoli: Coupling of LWR and phase transition models at boundary, Journal of Hyperbolic Differential Equations, 10 (2013), 577-636. pdf
- Lattanzio, A. Maurizi, B. Piccoli: Moving bottlenecks in car traffic flow: a PDE-ODE coupled model, SIAM Journal on Mathematical Analysis, 43 (2011), 50-67. pdf
- Blandin, D. Work, P. Goatin, B. Piccoli, A. Bayen: A general phase transition model for vehicular traffic, SIAM Journal on Applied Mathematics, 71 (2011), 107-127. pdf
- Work, S. Blandin, O.-P. Tossavainen, B. Piccoli, A. Bayen: A traffic model for velocity data assimilation, Applied Mathematics Research Express, 2010 (2010), 1-35. pdf
- Cristiani, C. de Fabritiis, B. Piccoli: A fluid dynamic approach for traffic forecast from mobile sensors data, Communications in Applied and Industrial Mathematics, 1 (2010), 54-71. link
- Garavello, B. Piccoli: On fluido-dynamic models for urban traffic, Networks and Heterogeneous Media, 4 (2009), 107-126. pdf
- Garavello, B. Piccoli: Traffic flow on a road network using the Aw-Rascle model, Communications on Partial Differential Equations, 31 (2006), 243-275. link
- Chitour, B. Piccoli: Traffic Circles and Timing of Traffic Lights for Cars Flow, Discrete and Continuous Dynamical Systems Series B, 5 (2005), 599-630. link
- Coclite, M. Garavello, B. Piccoli: Traffic flow on a road network, SIAM J. Math. Analysis, 36 (2005), 1862-1886. pdf