Departure time choices and comparisons of household commuting based on the stochastic bottleneck model

This paper investigates the impact of the stochastic bottleneck capacity on morning household trips when the school is located near home. There is a bottleneck on the way from the school to the workplace. Each household first drops off their children at school and then goes to work every morning. Based on the Wardrop’s first principle, which minimizes the expected travel cost for each household, all possible equilibrium departure/arrival patterns are examined. The study analyzes how the total travel cost (TTC) and total queuing cost (TQC) vary with the school-work start time difference, with the degradation ratio of capacity and with the degradation probability. Additionally, we compare the results with the scenario where the school is near the workplace. Our findings show that the TTC is always larger when the school is near the workplace compared to when it is near home. However, the queuing cost comparison depends on the parameters. We further compare the results with those in the deterministic model. We find that the TTC in the stochastic model is always larger than that under the deterministic model, while it is not necessarily true for the TQC. We also analyze the Pareto frontiers of TTC and TQC with respect to the school-work start time difference. This study captures the significance of school location and traffic uncertainty in determining the effectiveness of traffic management policies for household trips.