ABSTRACT In this paper, we present a technique to redistribute car flows, described by a fluid dynamic model, on a portion of the Caltanissetta city, in Italy, when critical situations, such as car accidents, occur. Using a decentralized approach, a cost functional, that describes the asymptotic average velocity of emergency vehicles, is maximized with respect to distribution coefficients at simple junctions with two incoming roads and two outgoing ones. Then, in order to manage critical situations in high traffic conditions, local optimal coefficients at each node of the network are used. The overall traffic evolution is studied via simulations, that confirm the goodness of the optimization results. It is also proved that optimal coefficients allow a fast transit of emergency vehicles on assigned routes on the network.
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nullPasquino, N. and Rarità, L. (2012) Optimal Flows On Road Networks In Emergency Cases. Open Journal of Applied Sciences, 2, 57-61. doi: 10.4236/ojapps.2012.24B014.
 G. Bretti, and B. Piccoli, “A tracking algorithm for car paths on road networks,” SIAM Journal on Applied Dynamical Systems, vol. 7, pp. 510–531, 2008.
 A. Cascone, C. D’Apice, B. Piccoli, and L. Rarità, “Optimization of traffic on road networks,” Mathematical Models and Methods in Applied Sciences, vol. 17, no. 10, pp. 1587–1617, 2007.
 A. Cascone, C. D’Apice, B. Piccoli, and L. Rarità, “Circulation of car traffic in congested urban areas,” Communication in Mathematical Sciences, vol. 6, no. 3, pp. 765–784, 2008.
 G. Coclite, M. Garavello, and B. Piccoli, “Traffic Flow on Road Networks,” SIAM Journal on Mathematical Analysis, vol. 36, no. 6, pp. 1862–1886, 2005.
 C. D’Apice, R. Manzo, and L. Rarità, “Splitting of Traffic Flows to Control Congestion in Special Events,” International Journal of Mathematics and Mathematical Sciences, vol. 2011, pp. 1–18, 2011, Article ID 563171, doi:10.1155/2011/563171.
 R. Manzo, B. Piccoli, and L. Rarità, “Optimal distribution of traffic flows at junctions in emergency cases,” European Journal of Applied Analysis, vol. 23, no. 4, pp. 515–535, 2012.
 M. J. Lighthill, and G. B. Whitham, “On kinetic waves. II. Theory of Traffic Flows on Long Crowded Roads,” Proc. Roy. Soc. London Ser. A, vol. 229, pp. 317–345, 1955.
 P. I. Richards, “Shock Waves on the Highway,” Oper. Res., vol. 4, pp. 42–51, 1956.