Instability of a user equilibrium traffic assignment integrated with a detailed intersection capacity analysis

The application of traffic models is effective with the increasing urbanization, predicting traffic flows with an equilibrium assignment. A recent model combines traditional equilibrium algorithms with a detailed Intersection Capacity Analysis (ICA), known as the ICA assignment, which promises detailed traffic flow predictions but exhibits instability. This study investigates the causes and the impact of various parameters on this instability. Three equilibrium algorithms—Balancing Equilibrium Assignment (BEA), Bi-Conjugate Frank Wolfe (BFW), and Linear User Cost Equilibrium (LUCE)—are compared within the ICA assignment. The instability is measured by changes in link-flows when traffic demand between a single OD-pair is perturbed. In a small network case study, instability arises during congestion, with the ICA assignment oscillating between solutions due to queuing at the congested intersection. No significant impacts of parameters on instability could be identified. In a real-world network in Utrecht, the ICA assignment with BFW was very unstable, while BEA was the most stable but underestimated reality. Lowering the maximum gap in algorithms improved instability of the ICA assignment. More intersections with ICA led to increased instability due to congestion. Overall, congested ICA intersections are the primary cause of instability.