Manage morning commute problem for household travellers with stochastic bottleneck capacity

This paper investigates the morning commute problem with household travellers under stochastic bottleneck capacity. Adults drop children at school before going to work, considering preferred arrival times and uncertainty. Their departure time choices follow the Wardrop's first principle to minimise the expected travel cost. All possible equilibrium departure patterns, and the boundary conditions are derived analytically. The impacts of the school-work start time difference, the degradation ratio of capacity and the degradation probability on the expected total travel cost (TTC) and on the expected total queueing cost (TQC) are analysed, respectively. Three optimal solutions for school-work start time difference are proposed. Policymakers can adjust the school-work start time difference to balance TTC and TQC. The results of the stochastic and deterministic models are also compared. Ignoring uncertainty always underestimates TTC, but TQC might be overestimated. This study enhances our understanding of the morning commute problem with household travellers under uncertainty.