\documentclass{abstract}
\begin{document}

\title{Multiscale models for vehicular traffic and crowd dynamics.}
\author{Benedetto Piccoli}
\institute{Rutgers University - Camden}
\email{piccoli@camden.rutgers.edu}
%\coauthor{Coauthor 1,  Coauthor 2, \and Coauthor 3} % comment out if not needed

\mymaketitle

\section{Abstract}
We will start by revising some macroscopic model, based on systems of conservation (or balance) laws, 
for network flows, such as road networks, supply chains, gas pipelines etc., see \cite{book1,book2,survey}.
Such models were successfully employed in traffic monitoring projects \cite{pro1,pro2}.\\
Then we will pass to measure solutions to nonlinear transport equations,
which naturally allow multi-scale approaches.
In particular we can integrate micro and macro scales in a unique representation, see \cite{book3}.
We show how the Wasserstein metric is the natural one in this context and how
to generalize it to deal with source terms \cite{rossi1,rossi2}.
Finally, we show some examples of simulations for crowd dynamics and vehicular traffic \cite{cdc}.

\paragraph{Acknowledgments}
The author acknowledges the partial support
of the NSF Project "KI-Net" Grant DMS \# 1107444.

\begin{thebibliography}{9} 

\bibitem{survey}
{\sc A.~Bressan, S.~Canic, M.~Garavello, M.~Herty and B.~Piccoli}, {\em Flows on networks: recent results and perspectives}, Surverys of the EMS, 1 (2014), to appear.

\bibitem{pro2}
{\sc E.~Cristiani, C.~de Fabritiis and B.~Piccoli}, {\em A 
fluid dynamic approach for traffic forecast
from mobile sensors data}, Communications in Applied and Industrial Mathematics, 1 (2010), pp.~54--71.  

\bibitem{book3}
{\sc E.~Cristiani, B.~Piccoli  and A.~Tosin}, {\em Multiscale Modeling of Pedestrian Dynamics}, 
Springer MS\&A: Modeling, Simulation and Applications, 
Springer-Verlag in print 2014.

\bibitem{cdc}
{\sc E.~Cristiani, B.~Piccoli  and A.~Tosin}, {\em How Can Macroscopic Models Reveal Self-Organization
in Traffic Flow?}, Proceedings of 51st IEEE Conference on Decision and Control (CDC 2012),
pp.~6989--6994, Maui (Hawaii) 2012.


\bibitem{book2}
{\sc C.~D'Apice, S.~Goettlich, M.~Herty and B.~Piccoli}, {\em Modeling, Simulation and Optimiza-
tion of Supply Chains. A Continuous Approach},  SIAM book series on Mathematical Modeling
and Computation, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA,
2010.

\bibitem{book1}
{\sc M.~Garavello and B.~Piccoli}, {\em Traffic flow on networks}, 
Applied Math Series vol. 1, American Institute of Mathematical Sciences, Springfield, 2006.

\bibitem{rossi1}
{\sc B.~Piccoli and F.~Rossi}, {\em Transport equation with nonlocal velocity in Wasserstein spaces}, Acta Applicandae Mathematicae, 124 (2013), pp.~73--105.  

\bibitem{rossi2}
{\sc B.~Piccoli and F.~Rossi}, {\em Generalized Wasserstein distance and its application to transport equation with source}, Archive for Rational Mechanics and Analysis, 211 (2014), pp.~335--358.  



\bibitem{pro1}
{\sc D.~Work, S.~Blandin, O.-P.~Tossavainen, B.~Piccoli  and A.~Bayen}, {\em A traffic model for
velocity data assimilation}, Applied Mathematics Research Express, 2010 (2010), pp.~1--35.  




\end{thebibliography}

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