Optimising toll prices and speed limits for minimising emissions in Zealand, Denmark, using a dynamic multi-region MFD SUE traffic model

Reducing emissions from road traffic is important for public health and the environment. One way of reducing emissions is electrifying the vehicle fleet. Full electrification, however, will take many years due to constraints on the production of electric vehicles to meet demand. Another effective way is to encourage or legally enforce travellers to drive fossil fuel cars at desirable intermediate speeds. Few studies, however, have explored the combined optimisation of policy schemes aimed at both increasing vehicle speeds where/when speeds are too low and decreasing speeds where/when speeds are too high. This paper addresses this by, for the first time, exploring the joint optimisation of a tolling scheme and fixed speed limit reduction policy for the minimisation of emissions, in a large-scale case study. A joint travel-time-based toll-price and speed limit optimisation framework is developed that minimises CO 2 and NOx emissions, with a constraint that social welfare is no worse than in the do-nothing scenario. Traffic behaviour is modelled using the dynamic multi-region Macroscopic Fundamental Diagram (MFD) Stochastic User Equilibrium (SUE) model recently introduced in Duncan et al. (2025, 2026), where the elastic demand and departure time choice components are updated to improve behavioural realism. Aggregate emission functions are applied to outputs of the traffic model to estimate dynamic emission levels. The optimisation framework is applied in a large-scale case study of Zealand, Denmark where motorways are treated separately, allowing for the targeting of speed limits where speeds are highest. Results find that both tolling the main area of Copenhagen during peak-hours at 2.62 DKK/min and lowering the maximum speed limit to 91.12 km/h on motorways could yield a 10 % and 5 % reduction in CO 2 and NOx emissions, respectively, without a loss in social welfare from the do-nothing scenario. The speed limit reduction reduces CO 2 emissions the most (achieving a 7 % reduction on motorways), while tolling reduces NOx emissions the most (achieving a 4 % reduction within the tolled urban area). Synergistic effects of the joint policy enforcement are uncovered. Numerical experiments illustrate the joint policy’s impact on car travel demand, departure time choices, route choices, vehicle speeds, and travelling costs. It is also explored how results are affected when considering unequal redistribution of toll revenues, the marginal cost of public funds, increasing the social cost of emissions, specifying inner and outer tolling areas, and adopting a distance-based tolling scheme. Tolling is also compared to increasing fuel tax.