Stochastic bottleneck capacity, merging traffic and morning commute

• A stochastic bottleneck model is formulated for morning commute problem at a merge.
• Two merging behavior is considered: priority merge and fixed-rate merge.
• User equilibrium departure patterns are derived analytically.
• Stochastic bottleneck capacity increased mean trip cost and lengthened peak periods.
• Capacity paradox in one upstream bottleneck suggests metering is beneficial.

This paper investigates the impact of stochastic capacity at the downstream bottleneck after a merge and the impact of merging behavior on the morning commuters’ departure-time patterns. The classic bottleneck theory is extended to include a uniformly distributed capacity and the commuters’ equilibrium departure patterns are derived for two different merging rules. The results show that uncertainty in the bottleneck capacity increases the commuters’ mean trip cost and lengthens the peak period, and that the system total cost is lower under give-way merging than under a fixed-rate merging. Capacity paradoxes with dynamic user responses are found under both merging rules.