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This study investigates the theoretical properties of a departure time choiceproblem considering commuters' heterogeneity with respect to the value ofschedule delay in corridor networks. Specifically, we develop an analyticalmethod to solve the dynamic system optimal (DSO) and dynamic user equilibrium(DUE) problems. To derive the DSO solution, we first demonstrate thebottleneck-based decomposition property, i.e., the DSO problem can bedecomposed into multiple single bottleneck problems. Subsequently, we obtainthe analytical solution by applying the theory of optimal transport to eachdecomposed problem and derive optimal congestion prices to achieve the DSOstate. To derive the DUE solution, we prove the queue replacement principle(QRP) that the time-varying optimal congestion prices are equal to the queueingdelay in the DUE state at every bottleneck. This principle enables us to derivea closed-form DUE solution based on the DSO solution. Moreover, as anapplication of the QRP, we prove that the equilibrium solution under variouspolicies (e.g., on-ramp metering, on-ramp pricing, and its partialimplementation) can be obtained analytically. Finally, we compare theseequilibria with the DSO state.

Queue replacement principle for corridor problems with heterogeneous commuters