Properties of dynamic traffic equilibrium involving bottlenecks, including a paradox and metering

D. 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. Here the authors 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, the authors 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 capacity for an upstream bottleneck is equal to, or smaller than, optimal capacity downstream. Total construction costs equal total variable travel costs when capacities are optimal and construction costs are independent of scale.