Abstract
The purpose of this study is to derive an optimal distribution of work start times (W-curve) that effectively minimizes the social cost for morning commuters in road networks with queuing. Specifically, we consider the following bi-level programming problem: the lower-level problem describes equilibrium flow patterns under a given W-curve, and the upper-level problem optimizes a W-curve under the equilibrium constraints. We first derive the optimal W-curve for a basic model where homogeneous commuters pass through a single bottleneck. We then extend the analysis to the case where both route choice and departure time choice are simultaneously determined.
