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Res 345 Assignments

  • [1]

    Burkard, R. E.: Numerische Erfahrungen mit Summen- und Bottleneck-Zuordnungsproblemen, in: Numerische Methoden bei graphentheoretischen und kombinatorischen Problemen (Collatz L., Werner H., eds.), pp. 9–25. (ISNM, Vol. 29.) Basel-Stuttgart: Birkhäuser 1975.Google Scholar

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    Burkard, R. E., Hahn, W., Zimmermann, U.: An Algebraic Approach to Assignment Problems. Math. Prog.12, 318–327 (1977).Google Scholar

  • [3]

    Burkard, R. E., Zimmermann, U.: Weakly Admissible Transformations. Report Nr. 77-3. Mathematisches Institut, Universität zu Köln, Köln, 1977.Google Scholar

  • [4]

    Dijkstra, E. W.: A Note on Two Problems in Connection with Graphs. Numerische Mathematik1, 269–271 (1959).Google Scholar

  • [5]

    Dorhout, B.: Het Lineaire Toewijzungsproblem, Vergelijken van Algorithmen. Report BN 21/73 Stichting Mathematisch Centrum, Amsterdam, 1973.Google Scholar

  • [6]

    Edmonds, J., Fulkerson, R.: Bottleneck Extrema. J. Comb. Theory8, 299–306 (1970).Google Scholar

  • [7]

    Esser, R., Meis, T.: Sortieren und Suchen. Vorlesungsskriptum, Mathematisches Institut, Universität zu Köln, Köln, 1977.Google Scholar

  • [8]

    Fulkerson, R., Glicksberg, I., Gross, O.: A Production Line Assignment Problem. RAND Res. Mem. RM-1102 (1953).Google Scholar

  • [9]

    Garfinkel, R.: An Improved Algorithm for the Bottleneck Assignment Problem. Op. Res.19, 1747–1751 (1971).Google Scholar

  • [10]

    Greenwood, J. A.: A Fast Machine-Independent Long-Periodical Generator for 31-Bit Pseudo-Random Integers. From Compstat 1976, Proceedings in Computational Statistics, Wien: 1976.Google Scholar

  • [11]

    Gross, O.: The Bottleneck Assignment Problem. Report P-1630, RAND Corp. (1959).Google Scholar

  • [12]

    Hammer, P. L.: Time Minimizing Transportation Problems. Nav. Res. Log. Quart.16, 345–367 (1969);18, 487–490 (1971).Google Scholar

  • [13]

    Herrmann, H.: Anwendung der Ungarischen Methode auf die Lösung von Engpaß-Zuordnungsproblemen. (Unpublished.) Inst. für Rechentechnik, TU Braunschweig (1967).Google Scholar

  • [14]

    Hoare, C. A. R.: Quicksort. Comp. Journal5, 10–15 (1962).Google Scholar

  • [15]

    Kuhn, H. W.: The Hungarian Method for the Assignment Problem. Nav. Res. Log. Quart.2, 83–97 (1955).Google Scholar

  • [16]

    Page, E. S.: A Note on Assignment Problems. Comp. Journal6, 241–243 (1963).Google Scholar

  • [17]

    Pape, U., Schön, B.: Verfahren zur Lösung von Summen- und Engpaß-Zuordnungsproblemen. Elektronische Datenverarbeitung4, 149–163 (1970).Google Scholar

  • [18]

    Srinivasan, V., Thompson, G. L.: Algorithms for Minimizing Total Cost, Bottleneck Time and Bottleneck Shipment in Transportation Problems. Nav. Res. Log. Quart.23, 567–595 (1976).Google Scholar

  • [19]

    Swarcz, N.: Some Remarks on the Time Transporation Problem. Nav. Res. Log. Quart.18, 473–484 (1971).Google Scholar

  • [20]

    Tomizawa, N.: On Some Techniques Useful for Solution of Transportation Network Problems. Networks1, 179–194 (1972).Google Scholar

  • [21]

    Zimmermann, U.: Boolesche Optimierungsprobleme mit separabler Zielfunktion und matroidalen Restriktionen. Thesis, Universität zu Köln, Köln, 1976.Google Scholar

  • This article presents a model and a procedure for determining traffic assignment and optimizing signal timings in saturated road networks. Both queuing and congestion are explicitly taken into account in predicting equilibrium flows and setting signal split parameters for a fixed pattern of origin-to-destination trip demand. The model is formulated as a bilevel programming problem. The lower-level problem represents a network equilibrium model involving queuing explicitly on saturated links, which predicts how drivers will react to any given signal control pattern. The upper-level problem is to determine signal splits to optimize a system objective function, taking account of drivers' route choice behavior in response to signal split changes. Sensitivity analysis is implemented for the queuing network equilibrium problem to obtain the derivatives of equilibrium link flows and equilibrium queuing delays with respect to signal splits. The derivative information is then used to develop a gradient descent algorithm to solve the proposed bilevel traffic signal control problem. A numerical example is included to demonstrate the potential application of the assignment model and signal optimization procedure.

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