Properties of Dynamic Traffic Equilibrium Involving Bottlenecks

Braess and others have shown that creating a new link in a congested network, or adding capacity to an existing link, can raise total travel costs if drivers switch routes. We show that a paradox can also result when routes are fixed but users choose when to travel. As is true of the Braess paradox, the paradox here arises when the inefficiency due to underpricing of congestion increases by more than the direct benefit of the new capacity. For a corridor with two groups of drivers, we show that expanding capacity of an upstream bottleneck raises travel costs when the reduction in congestion upstream is more than offset by increased congestion downstream. Metering can thus improve efficiency. Optimal upstream capacity is equal to or smaller than downstream capacity for the user equilibrium. Total construction costs equal total variable travel costs when capacities are optimal and construction costs are independent of scale.