Operational macroscopic modeling of complex urban road intersections

Abstract

This article describes a new approach to the macroscopic first order modeling and simulation of traffic flow in complex urban road intersections. The framework is theoretically sound, operational, and comprises a large body of models presented so far in the literature.Working within the generic node model class of Tampere et al. (forthcoming), the approach is developed in two steps. First, building on the incremental transfer principle of Daganzo et al. (1997), an incremental node model for general road intersections is developed. A limitation of this model (as of the original incremental transfer principle) is that it does not capture situations where the increase of one flow decreases another flow, e.g., due to conflicts. In a second step, the new model is therefore supplemented with the capability to describe such situations. A fixed-point formulation of the enhanced model is given, solution existence and uniqueness are investigated, and two solution algorithms are developed. The feasibility and realism of the new approach is demonstrated through both a synthetic and a real case study.

The Multi-Agent Transport Simulation MATSim

“…This is again consistent with Flötteröd and Rohde (2011) and constitutes a concrete "supply constraint interaction rule", as required by Tampere et al (2011).…”

“…Surprisingly, this node model can be traced back at least to (Cetin et al, 2003, under the name of "fair intersections"), while the literature establishing its consistency with the KWM is only a few years old (Tampere et al, 2011;Flötteröd and Rohde, 2011;Corthout et al, 2012). Nodes in MATSim have no spatial dimension; they merely connect up-and downstream links.…”

“…This is an informal description of how the incremental node model of Flötteröd and Rohde (2011) works, given that one adopts the conventions that the sending ow of a link is stored in its "bu er" and that the receiving ow of a link is labeled here as free space in (the upstream queue of) that link. A more detailed inspection of the underlying implementation reveals no inconsistencies with incremental node model speci cation.…”

Partial Outer Convexification for Traffic Light Optimization in Road Networks

“…In the two-phase heuristic, we drop the constraint (8) in this paper for reasons explained in section 3.1. For the comparison of the achieved objective values in section 5, however, we take (8) into account through another simulation of the full forward dynamics using the heuristically obtained ω t .…”

“…With their seminal papers [22,25] in the 1950s on timedependent models for traffic flow with continuous densities instead of individual vehicles, Lighthill and Whitham and Richards established a new area of mathematical research in traffic modeling. The area is still highly active, e.g., for the case of traffic intersections (see, e.g., [5,8]), which constitute a building block of larger road networks. Our goal in this paper is to devise efficient heuristics to approximately solve the problem of optimal traffic light settings for road networks.…”