Game-Theoretic Formulations of Interaction Between Dynamic Traffic Control and Dynamic Traffic Assignment
Abstract
The dynamic traffic control problem and the dynamic traffic assignment problem are integrated as a noncooperative game between a traffic authority and highway users. The objective of the combined control-assignment problem is to find a mutually consistent dynamic system-optimal signal setting and dynamic user-optimal traffic flow. The combined control-assignment problem is first formulated as a one-level Cournot game: the traffic authority and the users choose their strategies simultaneously. The combined control-assignment problem is subsequently formulated as a bi-level Stackelberg game. The traffic authority is the leader; it determines the signal settings in anticipation of the users’ reactions. The users are followers who choose their routes after the signal settings have been determined. Finally, the system-optimal control-assignment problem is formulated as a Monopoly game. The sole player—the traffic authority—determines both signal settings and traffic flows to achieve a dynamic system-optimal solution. A numerical example is provided to illustrate the equilibria of the games.
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References
1. Webster F. V. Traffic Signal Settings. Road Research Technical Paper 39. Road Research Laboratory, London, 1958.
2. Robertson D. I. TRANSYT Method for Area Traffic Control. Traffic Engineering and Control, Vol. 11, No. 10, 1969, pp. 259–275.
3. Hunt P. B., Robertson D. I., Bretherton R. D., and Winton R. I. SCOOT—A Traffic Responsive Method of Coordinating Signals. TRRL Report LR 1014. Transport and Road Research Laboratory, Crowthorne, U.K., 1981.
4. Gartner N. H. OPAC: A Demand-Responsive Strategy for Traffic Signal Control. In Transportation Research Record 906, TRB, National Research Council, Washington, D.C., 1983, pp. 75–81.
5. Allsop R. E. Some Possibilities for Using Traffic Control to Influence Trip Distribution and Route Choice. Proc., 6th International Symposium on Traffic and Transportation Theory, 1974.
6. Smith M. J. Traffic Control and Route Choice: A Simple Example. Transportation Research, Vol. 13B, No. 4, 1979, pp. 289–294.
7. Smith M. J. Properties of a Traffic Control Policy Which Ensure the Existence of Traffic Equilibrium Consistent with the Policy. Transportation Research, Vol. 15B, No. 6, 1981, pp. 453–462.
8. Al-Malik M. An Investigation and Development of a Combined Traffic Signal Control-Traffic Assignment Model. Ph.D dissertation. Georgia Institute of Technology, Atlanta, 1991.
9. Al-Malik M., and Gartner N. H. Development of a Combined Traffic Signal Control-Traffic Assignment Model. In Urban Traffic Networks (Gartner N. H. and Improta G., eds.), Springer-Verlag, Berlin, 1995, pp. 155–186.
10. Gartner N. H., and Al-Malik M. Combined Model for Signal Control and Route Choice in Urban Traffic Networks. In Transportation Research Record 1554, TRB, National Research Council, Washington, D.C., 1996, pp. 27–35.
11. Gartner N. H. Area Traffic Control and Network Equilibrium. In Proc., International Symposium on Traffic Equilibrium Methods, Springer-Verlag, Berlin, 1976, pp. 274–297.
12. Tan H.-N., Gershwin S., and Athans M. Hybrid Optimization in Urban Traffic Networks. Report DOT-TSC-RSPA-79-7. Research and Special Programs Administration, U.S. Department of Transportation, 1979.
13. Sheffi Y., and Powell W. Optimal Signal Settings over Transportation Networks. Journal of Transportation Engineering, Vol. 109, No. 6, 1983, pp. 824–839.
14. Smith M. J., and Ghali M. O. The Dynamics of Traffic Assignment and Traffic Control: A Theoretical Study. Transportation Research, Vol. 24B, No. 6, 1990, pp. 409–422.
15. Smith M. J., and Van Vuren T. Traffic Equilibrium with Responsive Traffic Control. Transportation Science, Vol. 27, No. 2, 1993, pp. 118–132.
16. Yang H., and Yagar S. Traffic Assignment and Traffic Control in General Freeway Arterial Corridor Systems. Transportation Research, Vol. 28B, No. 6, 1994, pp. 463–486.
17. Yang H., and Yagar S. Traffic Assignment and Traffic Control in a Saturated Road Network. Transportation Research, Vol. 29A, No. 2, 1995, pp. 125–139.
18. Gartner N. H., and Stamatiadis C. Framework for the Integration of Dynamic Traffic Assignment with Real-Time Control. Proc., 3rd Annual World Congress on Intelligent Transportation Systems, Orlando, Fla., 1996.
19. Chen H.-K., and Hsueh C.-F. Combining Signal Timing Plan and Dynamic Traffic Assignment. Presented at 76th Annual of the Transportation Research Board Meeting, Washington, D.C., January 12–16, 1997.
20. Wardrop J. G. Some Theoretical Aspects of Road Traffic Research. Proc., Institute of Civil Engineers II, Vol. 1, 1952, pp. 278–325.
21. Nash J. F. Equilibrium Points in n-Person Games. Proc., National Academy of Sciences, USA, Vol. 36, 1950, pp. 48–49.
22. Fisk C. S. Game Theory and Transportation Systems Modeling. Transportation Research, Vol. 18B, 1984, pp. 301–313.
23. Stackelberg H. V. Marktform und Gleichgewicht. Julius Springer, Vienna, 1934.
24. Cournot A. Recherches sur les Principes Mathématiques de la Théorie des Richesses, 1838. English edition: Researches into Mathematical Principles of the Theory of Wealth, Macmillan, New York, 1897.
25. Nagurney A. Network Economics: A Variational Inequality Approach. Kluwer Academic Publishers, Dordrecht, Netherlands, 1993.
26. Ran B., and Boyce D. Modeling Dynamic Transportation Networks: An Intelligent Transportation System Oriented Approach. Springer, Berlin, 1996.
27. He Y. A Flow-Based Approach to the Dynamic Traffic Assignment Problem: Formulations, Algorithms and Computer Implementations. Master’s thesis. Massachusetts Institute of Technology, Cambridge, 1997.
28. Luo Z.-Q., Pang P. S., and Ralph D. Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge, U.K., 1996.
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Article first published: January 1998
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