Domains and Solutions of the Braess Paradox

• Autorzy: Nikolova N. D. , Armenski I. S. , Tenekedjieva L.-T. K. , Mednikarov B.
• Języki publikacji: EN

Abstrakty

EN

The Braess paradox in road planning presents a case, where adding a new connection in a road network may lead to delayed arrival because of violation of the balance in the traffic flow. The paper discusses a generalization of this paradox. The initial, the asymmetrical, and the Pareto optimal domain are identified. Administrative solution with the participation of a controller is introduced, which aims to minimize the time of arrival, and thus has an environmental aspect. The preferences of the groups of passengers in the vehicles are modeled by an analytical arctan-approximated utility. Nash arbitration is employed to find an optimal solution that maximizes the Nash utility criterion. It is performed over the optimal Pareto domain that is outlined in four stages. A numerical example with 40 vehicles and five types of preferences of the passengers demonstrates the ideas.

Słowa kluczowe

EN

Nash arbitration; bargaining set; absolute Pareto domain; arctan-approximated utilities; disagreement point controversy; environmentally-friendly solutions

• Wydawca: Społeczna Akademia Nauk w Łodzi
• Czasopismo: Journal of Applied Computer Science Methods
• Rocznik: 2011
• Tom: Vol. 3 No. 2
• Strony: 17--43
• Opis fizyczny: Bibliogr. 11 poz., rys., tab.

Twórcy

autor

Nikolova N. D.

• N. Vaptsarov Naval Academy, 73 V. Drumev Str., 9026 Varna, Bulgaria

autor

Armenski I. S.

• Technical University – Gabrovo, 4 Hadji Dimitar Str., 5400 Gabrovo, Bulgaria

autor

Tenekedjieva L.-T. K.

• Dr. Petar Beron Mathematical Highschool, Chaika, 9010 Varna, Bulgaria

autor

Mednikarov B.

• N. Vaptsarov Naval Academy, 73 V. Drumev Str., 9026 Varna, Bulgaria

Bibliografia

• 1. Braess, D., Nagurney, A.,Wakolbinge T., 2005, On a Paradox of Traffic Planning, Transportation Science, Vol. 39, No. 4, pp. 446-450.
• 2. French, S, 1993, Decision theory: an Introduction to the Mathematics of Rationality, Elis Horwood.
• 3. Knödel, W., 1969, Graphentheoretische Methoden und ihre Anwendun-gen, Springer-Verlag. pp. 57–9.
• 4. Kolata, G., 1990, What if They Closed 42d Street and Nobody Noticed?, New York Times, Retrieved 2008-11-16.
• 5. Nash, J., 1950, The Bargaining Problem, Econometrica, Volume 18, No. 2, pp. 155–162.
• 6. Nikolova, N.D., 2007, Arctg-approximation of Monotonically Decreasing Utility Functions, Computer Science and Technology, Volume 1, pp. 60- 69
• 7. Nikolova, N.D., Armenski, I., Tenekedjieva, L-T., Toneva-Zheynova, D., 2012, Multi-dimensional Nash arbitration in the Braess Paradox, Proc. 13th International IFAC Symposium on Control in Transportation Systems CTS’2012, September 2012, Sofia, Bulgaria (in print)
• 8. Osborne, M.J., Rubenstein A., 1994, А Course in Game Theory, The Maple-Vail Book Manufacturing Group
• 9. Tenekedjieva, L-T., 2012a, Finding the Pareto domain in the Braess pa-radox for even number of vehicles, 12th Student Conference of the Insti-tute of Mathematics and Informatics, Gabrovo, Bulgaria (in Bulgarian).
• 10. Tenekedjieva, L., 2012, Administrative and Arbitrary Decisions in Braess’s Paradox, XXXXI Spring Conference of the Union of the Mathe-maticians in Bulgaria, Student Section, Borovetz, 9-12 April 2012, Bul-garia (in Bulgarian).
• 11. Von Neumann, J., O. Morgenstern, 1947, Theory of Games and Economic Behavior. Second Edition. Princeton University Press.