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<p>The constraints on link density and link inflow/outflow must be included in modeling the dynamic user optimal simultaneous departure time and route choice problem (DUO-SDTRC) to be consistent with the reality. However, the research on the DUO-SDTRC problem with the constraints is still rare. In this study, first, a one-level variational inequality (VI) model was presented for the DUO-SDTRC with constraints on link inflow/outflow and link density. Second, a relaxation with multilevel gradient projection (MGP) algorithm incorporated with the penalty function method is presented for solving the model, with the 1st level gradient projection for temporal equilibrium and the 2nd level gradient projection for spatial equilibrium. The model and algorithm were applied to a simulation network. The results indicated that 1) the model and algorithm can find the optimal departure time and optimal routes for travelers at different level of constraints on link inflow/outflow and link density or at different level-of –service (LOS) and 2) the resultant inflow and density are always below the level of the constraints. This shows the validity of the model and algorithm. The model and algorithm are useful in transportation planning and management.</p>

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Dynamic user optimal simultaneous departure time and route choice with inflow, outflow, and density constraints

  • 期刊论文

  • 发表日期：

    2025年12月2日

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  • Tianze Xu,
  • Lunrui Zhang,
  • Xian Du,
  • Leilei Li

摘要

The constraints on link density and link inflow/outflow must be included in modeling the dynamic user optimal simultaneous departure time and route choice problem (DUO-SDTRC) to be consistent with the reality. However, the research on the DUO-SDTRC problem with the constraints is still rare. In this study, first, a one-level variational inequality (VI) model was presented for the DUO-SDTRC with constraints on link inflow/outflow and link density. Second, a relaxation with multilevel gradient projection (MGP) algorithm incorporated with the penalty function method is presented for solving the model, with the 1st level gradient projection for temporal equilibrium and the 2nd level gradient projection for spatial equilibrium. The model and algorithm were applied to a simulation network. The results indicated that 1) the model and algorithm can find the optimal departure time and optimal routes for travelers at different level of constraints on link inflow/outflow and link density or at different level-of –service (LOS) and 2) the resultant inflow and density are always below the level of the constraints. This shows the validity of the model and algorithm. The model and algorithm are useful in transportation planning and management.