Morning commute in a Y-shaped traffic network with early and late arrivals

This paper studies the morning commute problem when both early and late arrivals are considered in a Y-shaped network with two upstream links and a downstream link. Commuters from one origin pass through an upstream bottleneck with a limited capacity and then traverse the downstream bottleneck common to commuters from two origins before arriving at their workplace in the central business district (CBD). We aim to examine the queuing patterns at user equilibrium and provide policy guidance on improving social welfare under different scenarios. First, we analytically characterize the equilibrium travel patterns of two commuter groups in a Y-shaped network, allowing both early and late arrivals. Based on the given bottleneck capacities and demand distributions, we identify the conditions under which each equilibrium pattern emerges. Second, we explore commuters’ schedule preferences and queuing patterns at the upstream bottleneck under user equilibrium. Third, we investigate strategies to improve social welfare through capacity management interventions, including capacity expansion, ramp metering, and adjustments to spatial demand distribution. Our results show that expanding the downstream bottleneck capacity consistently improves system performance when the demand and capacity ratios are not large. The effectiveness of upstream capacity management also depends on the demand and capacity ratios between the two bottlenecks. Given the demand ratio, we derive the optimal ramp metering strategy that minimizes the total travel cost. Notably, this strategy equalizes the upstream and downstream capacities when the demand ratio is low. Furthermore, when bottleneck capacities are fixed, combining spatial demand redistribution with capacity management at the upstream bottleneck (i.e., ramp metering or capacity expansion) can lead to improvements in social welfare. Finally, we illustrate the main analytical results with numerical analysis.