Equilibrium horizontal queues and a paradox of tolling

Abstract

This paper shows that, in a static traffic model with elastic demand, increasing a toll may raise the equilibrium trip rate through a network. The result is obtained in models with horizontal queues and rules about merges and diverges assumed in the Cell Transmission Model for Network Traffic. The paper looks at three networks: (i) a road with a fixed bottleneck at the end; (ii) a road with a “triggerneck” diverge; and (iii) a ring road with two on-ramps and two off-ramps. In the triggerneck network, a toll increase may raise the total trip rate when traffic using an exit with bottleneck has a lower value of travel time savings than traffic bypassing the bottleneck. In the ring road, a toll increase may raise the total trip rate when the initial equilibrium is hypercongested. The derivations use an extensible “recipe” for analysis of networks with horizontal queues. Many diagrams and numerical examples are provided to illustrate.