The role of speed–flow relationship in congestion pricing implementation with an application to Singapore

The paper aims to address the practical relevance of each of three empirical elements, namely, the speed–flow relationship, the demand function and the generalized cost that affect the implementation of a congestion pricing system. We first derive the theoretical congestion toll estimate for a class of speed–flow relationship known as the generalized Drake model. We then propose an iterative procedure to pinpoint the optimal congestion toll based on a speed–flow relationship and a value of the generalized cost in the absence of a demand function. Several practical implications will be highlighted concerning, in particular, the treatment of peak and off-peak congestion pricing. For the role of the generalized cost, we show that, in the absence of a demand function, an inaccurate value of the generalized cost will almost always lead to non-optimal, but convergent outcome. A practical implication of this ‘false convergence’ is that a rough estimate of the generalized cost will be sufficient to obtain a congestion toll that is quite close to the optimal toll value by realizing that a speed–flow relationship is just an average relationship that is subject to certain degree of variations. We conclude the paper by applying these results to Singapore's road pricing system. Generic distance-based toll estimation tables are given for the purpose of checking the optimality of actual congestion tolls on the expressways and the restricted zone when the information on the observed traffic situation and the value of the generalized cost become available.