Queueing at a bottleneck with single and multi-step tolls

The paper considers toll systems designed to alleviate queueing problems that result from a road bottleneck. Optimal road pricing is capable of eliminating queueing time completely, but has practical difficulties because it requires continuously changeable charges. Because of these difficulties, a step-toll scheme has been considered as a alternative to reduce queueing time. However, previous literatures do not contain an analysis of the multi-step toll and the amount of queueing time removal that can be achieved by varying amounts of step tolls. They may be important for policy makers who are considering the introduction of step pricing under some circumstances. This paper is proposed to solve these problems. It is shown that at most n/(n+1) of the total queueing time can be eliminated with the optimal n-step toll. Suboptimal n-step tolls are also derived to achieve an under-n/(n+1) queueing removal (where n=1,2 and 3).