Abstract
This paper introduces a new model for describing intersections in road networks, whose load dynamics is governed by the Lighthill–Whitham–Richards model. More precisely we define a solution for intersections using a multibuffer, i.e. a set of buffers, one for each outgoing road. We compare the obtained dynamics with those of some models previously introduced in the literature. In particular, we are able to respect the preferences of drivers and to not block the intersection when only one outgoing road is full. This improves some weaknesses of previous models.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bardos C, le Roux AY, Nédélec J-C. First order quasilinear equations with boundary conditions. Comm Part Differ Equat. 1979;4(9):1017–34.
Chitour Y, Piccoli B. Traffic circles and timing of traffic lights for cars flow. Discrete Continuous Dyn Syst Ser B 2005;5(3):599–630.
Coclite GM, Garavello M, Piccoli B. Traffic flow on a road network. SIAM J Math Anal. 2005;36(6):1862–86 (electronic).
Daganzo CF. The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transport Res Part B 1994;28(4):269–87.
D’Apice C, Manzo R. A fluid dynamic model for supply chains. Netw Heterog Media 2006;1(3):379–98 (electronic).
D’apice C, Manzo R, Piccoli B. Packet flow on telecommunication networks. SIAM J Math Anal. 2006;38(3):717–740 (electronic).
D’Apice C, Piccoli B. Vertex flow models for vehicular traffic on networks. Math Models Methods Appl Sci. 2008;18 Suppl:1299–1315.
Garavello M, Piccoli B. Source-destination flow on a road network. Commun Math Sci. 2005;3(3):261–83.
Garavello M, Piccoli B. Traffic flow on networks. Volume 1 of AIMS series on applied mathematics. Springfield, MO: American Institute of Mathematical Sciences (AIMS); 2006 [Conservation laws models].
Garavello M, Piccoli B. Conservation laws on complex networks. Ann H Poincaré 2009;26(5):1925–51.
Garavello M, Piccoli B. Time-varying Riemann solvers for conservation laws on networks. J Differ Equat. 2009;247(2):447–64.
Newell GF. A simplified theory of kinematic waves in highway traffic, part i: general theory. Transport Res Part B 1993;27(4):281–7.
Newell GF. A simplified theory of kinematic waves in highway traffic, part ii: queueing at freeway bottlenecks. Transport Res Part B 1993;27(4):289–303.
Newell GF. A simplified theory of kinematic waves in highway traffic, part iii: multi-destination flows. Transport Res Part B 1993;27(4):305–13.
Godunov SK. A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics. Mat Sb (NS) 1959;47(89):271–306.
Göttlich S, Herty M, Klar A. Network models for supply chains. Commun Math Sci. 2005;3(4):545–59.
Göttlich S, Herty M, Klar A. Modelling and optimization of supply chains on complex networks. Commun Math Sci. 2006;4(2):315–30.
Greenshields BD. A study of traffic capacity. Proc Highway Res Board 1935;14(1):448–77.
Helbing D, Siegmeier J, Lämmer S. Self-organized network flows. Netw Heterog Media 2007;2(2):193–210 (electronic).
Herty M, Klar A, Piccoli B. Existence of solutions for supply chain models based on partial differential equations. SIAM J Math Anal. 2007;39(1):160–73.
Herty M, Lebacque J.-P., Moutari S. A novel model for intersections of vehicular traffic flow. Netw Heterog Media 2009;4(4):813–26 (electronic).
Holden H, Risebro NH. A mathematical model of traffic flow on a network of unidirectional roads. SIAM J Math Anal. 1995;26(4):999–1017.
Lebacque J. The godunov scheme and what it means for first order macroscopic traffic flow models. In: Lesort JB. Proceedings of the 13th ISTTT; 1996. p. 647–77.
Lighthill MJ, Whitham GB. On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc R Soc Lond A 1955;229:317–45.
Marigo A, Piccoli B. A fluid dynamic model for T-junctions. SIAM J Math Anal. 2008;39(6):2016–32.
Richards PI. Shock waves on the highway. Oper Res. 1956;4:42–51.
Sun D, Strub IS, Bayen AM. Comparison of the performance of four Eulerian network flow models for strategic air traffic management. Netw Heterog Media 2007;2(4):569–95 (electronic).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Garavello, M., Piccoli, B. (2013). A Multibuffer Model for LWR Road Networks. In: Ukkusuri, S., Ozbay, K. (eds) Advances in Dynamic Network Modeling in Complex Transportation Systems. Complex Networks and Dynamic Systems, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6243-9_6
Download citation
DOI: https://doi.org/10.1007/978-1-4614-6243-9_6
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-6242-2
Online ISBN: 978-1-4614-6243-9
eBook Packages: Business and EconomicsBusiness and Management (R0)