Congestion Tolling−Dollars versus Tokens: Within-day Dynamics

Tradable permit schemes (or tolling in tokens) are a form of quantity control, which promise tobe an appealing alternative to congestion pricing (or tolling in dollars) owing to considerations ofrevenue neutrality, equity, reduced infrastructure costs, and political acceptability. The comparativeperformance of the two instruments under uncertainty in demand and supply has only recently receivedattention in the transportation setting, despite being widely studied for emission markets. In thispaper, we add to this literature by considering a tradable permit scheme in a departure time contextwherein users are provided an initial endowment of tokens by the regulator and incur a token charge(determined prior to all departures) to travel in a specific time period. Tokens can be bought andsold within a marketplace at a price determined by a market clearing mechanism in each time period.A key feature of the market model is that the selling decisions of users are explicitly considered,which enables us to study the impact of selling behavior on performance of the permit system. Traveldemand is modeled using a logit mixture model and supply consists of static congestion.In the case of uncertain demand/supply wherein the tolls (in dollars and tokens) can be adaptedfrom day to day (or alternatively demand/supply are deterministic), the two instruments can be shownanalytically to be equivalent. In contrast, when the tolls are not day to day adaptive, the comparisonof the two instruments is performed numerically. Our experiments over a wide range of demand andsupply scenarios show that although neither instrument is consistently superior in terms of efficiency(overall social welfare), tolling in tokens outperforms tolling in dollars when congestion effects aremore severe (e.g. realistic BPR models and steep congestion functions, high demand levels and highday-to-day variability). Importantly, we find that the token system is robust in efficiency terms (social welfare) with respect to selling behavior in the market, although there can be welfare losses in thequantity control system when selling behavior in the market is too irrational (relative to a quantitycontrol system implementing rational selling behavior). Moreover, when the supply of tokens can beadapted from day to day, the permit system was found to be superior in all tested scenarios in whichthe selling behavior of individuals is rational. Finally, even in the case when toll revenues in theprice instrument are equally redistributed (often difficult in practice), tolling in tokens (when tokensare equally distributed) is marginally more equitable in scenarios where congestion effects are moresevere. These findings make a case for tolling in tokens.