The morning commute under flat toll and tactical waiting

This paper studies the morning commute problem under “tactical waiting”, a phenomenon observable under situations when sudden drops in travel costs are present. Under such situations, travelers may find it advantageous to delay reaching the bottleneck by slowing down or waiting beside, even when there is still capacity left to serve them without delay. In this paper, we show that a flat toll during the morning commute potentially incurs tactical waiting under the assumptions of First-In-First-Out (FIFO) queue discipline and identical commuters, and derive all the possible equilibrium traffic patterns resulting from different choices of toll level and tolling period. Under the optimal toll pattern which minimizes the total system cost, we prove that there is no queue at the bottleneck at the starting or ending point of the tolling period and bottleneck capacity is fully utilized except during the period of tactical waiting. The optimal flat toll can reduce up to half of the queuing delay, but is in general not pareto-improving. However, if the revenue collected by the optimal flat toll is redistributed to the road users in the form of capacity expansion, the trip cost of each commuter will be reduced in the long-run. We also show that when building a new highway, the revenue from the optimal flat toll can never cover the capital cost of constructing the optimal capacity.