Time-Expanded Graphs for Flow-Dependent Transit Times

Motivated by applications in road tra#c control, we study flows in networks featuring special characteristics. Firstly, there are transit times on the arcs of the network which specify the amount of time it takes for flow to travel through an arc; in particular, flow values on arcs may change over time. Secondly, the transit time of an arc varies with the current amount of flow using this arc. The latter feature is crucial for various real-life applications; yet, it dramatically increases the degree of di#culty of the resulting optimization problems. While almost all flow problems with constant transit times on the arcs can be solved e#ciently by applying classical (static) flow algorithms in a corresponding time-expanded network, no such approach was known for flow-dependent transit times, up to now. One main contribution of this paper is a time-expanded network with flowdependent transit times to which the whole algorithmic toolbox developed for static flows can be applied. Although this approach does not entirely capture the behavior of flows over time with flowdependent transit times, we present approximation results which provide evidence of its surprising quality

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