Discrete time dynamic traffic assignment models and solution algorithm for managed lanes

‘Managed’ lanes of highways usually refer to lanes that are not open to all types of vehicles, such as ‘High Occupancy Vehicles’ (HOV) lanes and ‘High Occupancy Toll’ (HOT) lanes, etc. The HOV lanes of highways are reserved only for vehicles with a driver and one or more passengers. Whereas, HOT lanes allow all vehicles but require tolls from the vehicles with no passenger except the driver. In this paper, we present a discrete‐time traffic assignment system optimum model to predict the optimal traffic flows on managed lanes at various times in the entire planning horizon. This model minimizes the overall delay (travel time) and belongs to the class of dynamic traffic assignment (DTA) problems. When applied to general networks, DTA problems can be large and difficult to solve, but the problem is manageable when it is applied to a network with managed lanes. In particular, the DTA model in this paper for managed lanes is reduced to a mixed integer program for which several efficient heuristic algorithms exist. This paper also discusses the special properties of the discrete‐time DTA model, based upon which a heuristic algorithm is proposed. Numerical results show that this algorithm is efficient for many cases of the managed lane problems.