Optimal speed limit under multi-class user equilibrium: A prescriptive approach using mathematical programming

In practice, speed limits on road networks are often determined pragmatically, which can give suboptimal solutions for traffic performance and unfair results for the underlying user classes. This study presents an elegant approach to determine optimal speed limits on a traffic network with asymmetric user classes under congested conditions, that minimizes individual user travel time and does justice to differences in economic importance. Existing prescriptive approaches typically lack one or more of these features, cannot guarantee optimality or are difficult to solve. We formulate a new prescriptive method using mixed-integer quadratic programming. The model can be solved with well-established operation research approaches and commercial solvers such as Cplex or Gurobi. To demonstrate the approach, we apply it to a regional network in the Netherlands. The result shows a reduction of travel time of passenger cars by 6% and of trucks by 13%, with mild changes in speed limits compared to the base situation, of between −20% and +10%. The speed limit changes and impacts are in line with the relatively high economic importance of freight traffic. Also we find in this case that the speed limit changes are ordered by major routes through the network, which makes implementation relatively straightforward.