2021/06/18 by Michael E. Cao, Cao, Michael Enqi, Gustav Nilsson +3
Engineering · Social Sciences · #FOS: Electrical engineering #Systems and Control (eess.SY) #Traffic Prediction and Management Techniques #Traffic control and management #Transportation Planning and Optimization #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2106.10347
openalex publication_date 2021/06/18 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28
Capacity drop is an empirically observed phenomenon in vehicular traffic flow\non freeways whereby, after a critical density is reached, a state of congestion\nsets in, but the freeway does not become decongested again until the density\ndrops well below the critical density. This introduces a hysteresis effect so\nthat it is easier to enter the congested state than to leave it. However, many\nexisting first-order models of traffic flow, particularly those used for\ncontrol design, ignore capacity drop, leading to suboptimal controllers. In\nthis paper, we consider a cell transmission model of traffic flow that\nincorporates capacity drop to study the problem of optimal freeway ramp\nmetering. We show that, if capacity drop is ignored in the control design, then\nthe resulting controller, obtained via a convex program, may be significantly\nsuboptimal. We then propose an alternative model predictive controller that\naccounts for capacity drop via a mixed integer linear program and show that,\nfor sufficiently large rollout horizon, this controller is optimal. We also\ncompare these approaches to a heuristic hand-crafted controller that is viewed\nas a modification of an integral feedback controller to account for capacity\ndrop. This heuristic controller outperforms the controller that ignores\ncapacity drop but underperforms compared to the proposed alternative model\npredictive controller. These results suggest that it is generally important to\ninclude capacity drop in the controller design process, and we demonstrate this\ninsight on several case studies.\n