On the Morning Commute Problem in a Y-shaped Network with Individual and Household Travelers

This paper examines the morning commute problem when both household commuters and individual commuters are considered in a Y-shaped network with two upstream links and a single downstream link. The household parents daily pass through an upstream bottleneck with a limited capacity before a school and drop off their children. Then, they traverse the downstream bottleneck common to both household and individual commuters and arrive at the workplace. We explore the effects of staggering policy, that is, staggering work and school start times, on the distribution of traffic congestion and social welfare. We analytically solve all the equilibrium cases and reveal all the traffic congestion patterns. The results reveal that the staggering policy may be harmful in certain cases. When the demand of individuals is relatively low, the staggering policy may not improve social welfare. When the demand of individuals is high, social welfare can be significantly improved if the schedule gap between the work start time and school start time is optimized. The effects of the staggering policy on system performance are examined. We derive a Pareto frontier, which provides a good candidate set for policymakers when the two system performance measures, that is, the total system cost and the total congestion cost, are considered. Our results show that the optimal staggering policy on system performance depends on the demand distribution of the two groups. When the demand of individuals is high, there exists a unique optimal staggering policy that optimizes system performance. However, when the demand of individuals is low, the optimal staggering policy should be selected from the Pareto frontier. Furthermore, we re-examine the capacity expansion paradox under the staggering policy. Our study shows the capacity expansion at the downstream bottleneck can always reduce the total system cost. However, the paradoxical phenomenon may arise when the capacity of the upstream bottleneck is expanded, but it can be eliminated if the schedule gap is properly designed.