Abstract
We study the problem of optimizing traffic in decentralized transportation networks, where the cost of a link depends on its congestion. If users of a transportation network are permitted to choose their own routes, they generally try to minimize their personal travel time. In the absence of centralized coordination, such a behavior can be inefficient for society and even for each individual user. This inefficiency can be quantified by the “price of anarchy”, the ratio of the suboptimal total cost to the socially optimal cost. Here we study the price of anarchy in multi-commodity networks, (i.e., networks where traffic simultaneously flows between different origins and destinations).
Keywords
- flow optimization
- transportation network
- Nash equilibrium
- multi-commodity flow
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74, 47–97 (2002)
Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45, 167–256 (2003)
Argollo de Menezes, M., Barabási, A.-L.: Fluctuations in Network Dynamics. Physical Review Letters 92, 028701 (2004)
Hufnagel, L., Brockmann, D., Geisel, T.: Forecast and control of epidemics in a globalized world. Proceedings of the National Academy of Sciences 101, 15124–15129 (2004)
Wu, F., Huberman, B.A., Adamic, L.A., Tyler, R.J.: Information flow in social groups. Physica A 337, 327–335 (2004)
Kossinets, G., Watts, D.J.: Empirical Analysis of an Evolving Social Network. Science 311, 88–90 (2006)
Jahn, O., Möhring, R.H., Schulz, A.S., Stier-Moses, N.E.: System-Optimal Routing of Traffic Flows with User Constraints in Networks with Congestion. Operations Research 53, 600–616 (2005)
Kim, D.H., Motter, A.E.: Resource allocation pattern in infrastructure networks. Journal of Physics A 41, 224019 (2008)
Kleinberg, J.M.: Navigation in a small world. Nature 406, 845 (2000)
Pigou, A.C.: The Economics of Welfare. Macmillan, London (1920)
Roughgarden, T.: Selfish Routing and the Price of Anarchy. MIT Press, Cambridge (2005)
Papadimitriou, C.: Algorithms, games, and the Internet. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, pp. 749–753 (2001)
Youn, H., Gastner, M.T., Jeong, H.: The price of anarchy in transportation networks: Efficiency and optimality control. Physical Review Letters 101, 128701 (2008)
Carmi, S., Wu, Z., López, E., Havlin, S., Eugene Stanley, H.: Resource allocation pattern in infrastructure networks. European Physical Journal B 57, 165–174 (2007)
Frank, M., Wolfe, P.: An algorithm for quadratic programming. Naval Research Logistics Quarterly 3, 95–110 (1956)
Arezki, Y., van Vliet, D.: A Full Analytical Implementation of the PARTAN/Frank Wolfe Algorithm for Equilibrium Assignment. Transportation Science 24, 58–62 (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
About this paper
Cite this paper
Youn, H., Gastner, M.T., Jeong, H. (2009). Inefficiency in Networks with Multiple Sources and Sinks. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02466-5_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-02466-5_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02465-8
Online ISBN: 978-3-642-02466-5
eBook Packages: Computer ScienceComputer Science (R0)