Congestion tolling - dollars versus tokens: A comparative analysis

The case for some form of congestion tolling has long been made given the extent of traffic congestion in most urban transportation networks. However, there is little consensus on whether this tolling should be in the form of dollars (traditional congestion pricing schemes or price regulation) or in the form of tokens (credit based mobility schemes or quantity regulation). Although the comparison of price and quantity regulation has received significant attention in the economics community, the literature is relatively sparse in the context of transportation systems. The two systems differ not only in terms of transaction costs but also in their efficiency in dealing with demand and capacity shocks, frequent in road transport systems. This difference has been explored by economists in market contexts but the possible parallel in transport systems has largely been overlooked. This paper develops a methodology to compare the performance of price and quantity instruments under uncertainty using a simple transportation network consisting of parallel highway routes and a public transport alternative. Tolls (in dollars or tokens) are differentiated across roads and the permits or tokens can be traded across roads at fixed rates. The demand for each route is determined by a logit mixture model and the supply consists of static congestion. The comparison is based on the optimum social welfare which is computed for each instrument by solving a non-convex optimization problem involving stochastic user equilibrium constraints. Equity considerations are also examined. Numerical experiments across a wide range of demand/supply inputs lead us to the following insights. First, when the tolls in dollars and tokens can be fully adapted to demand and supply shocks (i.e. are day-to-day adaptive), both instruments are equivalent and attain the same optimum social welfare. Second, when the tolling system is not day-to-day adaptive and the supply of tokens is fixed, the quantity instrument performs better than the price instrument typically when the marginal external congestion function has a steeper slope than the demand function. Third, when the tolling system is non-adaptive, but the supply of tokens is day-to-day adaptive, the quantity instrument always outperforms the price instrument in terms of social welfare. Fourth, when the toll revenues and permits are distributed uniformly, this has a positive equity effect but the quantity instrument is more equitable than the price instrument. In view of these results, we argue the case for quantity control in the presence of uncertainty and strongly convex congestion costs. (C) 2017 Elsevier Ltd. All rights reserved.