Extended macroscopic node model for multilane traffic

In a macroscopic assignment model, traffic flows are distributed onto the network by means of a network loading model. The network loading propagates flows along links via a link model and through junctions or intersections via a node model. Most of the travel time delays are caused by queues forming at junctions or intersections, especially in urban networks. Therefore, the efficiency and accuracy of the underlying node model is paramount in capturing these delays (and flows). Existing link-based macroscopic node models make the simplifying assumption that first-in-first-out (FIFO) holds at the link level, which is often unrealistic when a link has multiple approach lanes near an intersection or junction. In this work we propose to relax this assumption such that FIFO holds at the movement level. We do so by developing several model extensions. First, a novel lane-based formulation of the node model is proposed. Secondly, we formulate an equilibrium problem and a general solution algorithm to allocate sending flows to lanes. This allows us to explicitly consider approach lane configurations that contain important information about the layout of an intersection or junction. We show that the conventional link-based node model is a special case of our newly proposed model in case each approach lane on an incoming link allows all possible movements. Various numerical examples are provided, demonstrating the capabilities of the proposed extensions to the node model.