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Optimal distribution of traffic flows in emergency cases

Published online by Cambridge University Press:  12 April 2012

R. MANZO ,
B. PICCOLI  and
L. RARITÀ
R. MANZO
Affiliation:
Dipartimento di Ingegneria Elettronica e Ingegneria Informatica, University of Salerno, Fisciano (SA), Italy email: rmanzo@unisa.it, lrarita@unisa.it
B. PICCOLI
Affiliation:
Department of Mathematical Sciences, Rutgers University, Camden, NJ, USA email: piccoli@camden.rutgers.edu
L. RARITÀ
Affiliation:
Dipartimento di Ingegneria Elettronica e Ingegneria Informatica, University of Salerno, Fisciano (SA), Italy email: rmanzo@unisa.it, lrarita@unisa.it
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Abstract

The aim of this work is to present a technique for the optimisation of emergency vehicles travel times on assigned paths when critical situations, such as car accidents, occur. Using a fluid-dynamic model for the description of car density evolution, the attention is focused on a decentralised approach reducing to simple junctions with two incoming roads and two outgoing ones (junctions of 2 × 2 type). We assume the redirection of cars at junctions is possible and choose a cost functional that describes the asymptotic average velocity of emergency vehicles. Fixing an incoming road and an outgoing road for the emergency vehicle, we determine the local distribution coefficients that maximise such functional at a single junction. Then we use the local optimal coefficients at each node of the network. The overall traffic evolution is studied via simulations, both for simple junctions or cascade networks, evaluating global performances when optimal parameters on the network are used.

Keywords

Conservation lawstraffic problemsoptimal redistribution of flows
Type
Papers
Information
European Journal of Applied Mathematics , Volume 23 , Issue 4 , August 2012 , pp. 515 - 535
Copyright
Copyright © Cambridge University Press 2012

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References

[1]Bressan, A. (2000) Hyperbolic Systems of Conservation Laws – The One-Dimensional Cauchy Problem, Oxford University Press, Oxford, UK.Google Scholar
[2]Bretti, G., Natalini, R. & Piccoli, B. (2006) Numerical approximations of a traffic flow model on networks. Netw. Heterogeneous Media 1, 57–84.Google Scholar
[3]Cascone, A., D'Apice, C., Piccoli, B. & Rarità, L. (2007) Optimization of traffic on road networks. Math. Models Methods Appl. Sci. 17 (10), 1587–1617.Google Scholar
[4]Cascone, A., D'Apice, C., Piccoli, B. & Rarità, L. (2008) Circulation of car traffic in congested urban areas. Commun Math. Sci. 6 (3), 765–784.CrossRefGoogle Scholar
[5]Coclite, G., Garavello, M. & Piccoli, B. (2005) Traffic flow on a road network. SIAM J. Math. Anal. 36 (6), 1862–1886.Google Scholar
[6]Cutolo, A., D'Apice, C. & Manzo, R. (2011) Traffic optimization at junctions to improve vehicular flows. ISNR Appl. Math. 2011, 1–19, article ID 670956.Google Scholar
[7]D'Apice, C. & Piccoli, B. (2008) Vertex flow models for vehicular traffic on networks. Math. Models Methods Appl. Sci. 18, 1299–1315.Google Scholar
[8]Garavello, M. & Piccoli, B. 2006 Traffic Flow on Networks, Applied Math Series vol. 1, American Institute of Mathematical Sciences, Springfield, MO.Google Scholar
[9]Garavello, M. & Piccoli, B. (2009) Time-varying Riemann solvers for conservation laws on networks. J. Differ. Equ. 247 (2), 447–464.Google Scholar
[10]Godlewsky, E. & Raviart, P. 1996 Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer-Verlag, Heidelberg, Germany.Google Scholar
[11]Godunov, S. K. (1959) A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics. Matematicheskii Sbornik 47, 271–290.Google Scholar
[12]Holden, H. & Risebro, N. H. (1995) A mathematical model of traffic flow on a network of unidirectional roads. SIAM J. Math. Anal. 26, 999–1017.CrossRefGoogle Scholar
[13]Lebacque, J. P. (1996) The Godunov scheme and what it means for first-order traffic flow models. In: Proceedings of the Internaional Symposium on Transportation and Traffic Theory, Vol. 13, Lyon, Pergamon Press, Oxford, UK, pp. 647–677.Google Scholar
[14]Lighthill, M. J. & Whitham, G. B. (1955) On kinetic waves – II. A theory of traffic flows on long crowded roads. Proc. R. Soc. 229, 317–345.Google Scholar
[15]Richards, P. I. (1956) Shock waves on the highway. Oper. Res. 4, 42–51.CrossRefGoogle Scholar