On the morning commute problem at a merge with stochastic capacity

This paper investigates the morning commute problem with two traffic streams merging into one and creating a bottleneck downstream. We consider the downstream capacity being stochastic and combine the traditional bottleneck theory with merging behavior to describe the commuters' departure time choice. We assumed the downstream capacity follows a uniform distribution and develop a stochastic merge model under the give-way merging behavior. The analytical and numerical results show that uncertainty in the downstream bottleneck capacity increases the commuters' mean trip cost and lengthens the peak period. Capacity paradox with dynamic user responses is found under this merging rule. This suggests that carefully designed metering can help improve network efficiency.