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A cell-based simultaneous route and departure time choice model with elastic demand

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  • Szeto, W. Y.
  • Lo, Hong K.

Abstract

This paper develops a cell-based formulation for the simultaneous route and departure time choice problem with elastic demands through a variational inequality problem (VIP). This formulation follows the ideal Dynamic User Optimal (DUO) route and departure time choice principle and encapsulates a network version of the cell transmission model to improve the accuracy of dynamic traffic modeling. To solve the formulation, we adopt a descent method developed for co-coercive VIP. Two numerical studies are set up to demonstrate the quality of the solutions. The results show that the formulation correctly determines the DUO solution even in the presence of queue spillback and junction blockage. In the analysis, we prove that the origin-destination (OD) first-in-first-out (FIFO) property is only maintained under certain conditions of the travel time and schedule delay costs. These conditions on the cost parameters are, interestingly, consistent with the empirical results. Thus, the theoretical analyses together with the empirical results indicate that OD FIFO should hold in reality. This finding is a reasonable reflection of our experience, which shows that OD FIFO generally holds subject to overtaking not occurring commonly.

Suggested Citation

  • Szeto, W. Y. & Lo, Hong K., 2004. "A cell-based simultaneous route and departure time choice model with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 38(7), pages 593-612, August.
  • Handle: RePEc:eee:transb:v:38:y:2004:i:7:p:593-612
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    1. Huang, Hai-Jun & Lam, William H. K., 2002. "Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 253-273, March.
    2. Lo, Hong K. & Szeto, W. Y., 2002. "A cell-based variational inequality formulation of the dynamic user optimal assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 421-443, June.
    3. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    4. Wie, Byung-Wook & Tobin, Roger L. & Carey, Malachy, 2002. "The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation," Transportation Research Part B: Methodological, Elsevier, vol. 36(10), pages 897-918, December.
    5. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-479, June.
    6. Yang, Hai & Meng, Qiang, 1998. "Departure time, route choice and congestion toll in a queuing network with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 32(4), pages 247-260, May.
    7. Braid, Ralph M., 1989. "Uniform versus peak-load pricing of a bottleneck with elastic demand," Journal of Urban Economics, Elsevier, vol. 26(3), pages 320-327, November.
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