Control of Mainstream Traffic Flow: Variable Speed Limit and Lane Change

Abstract

The well-known macroscopic Cell Transmission Model (CTM) has been widely used to develop several Intelligent Transportation Systems (ITS) to mitigate highway traffic congestion. Variable Speed Limit (VSL) and Lane Change (LC) control techniques are the most commonly used and studied ITS applications for regulating the mainstream traffic flow, notably near highway bottleneck locations. While most of the reported macroscopic simulation results showed significant improvements in traffic mobility, the resulting data from microscopic simulations and the deployment of such technologies in real traffic environments were somewhat controversial; some microscopic simulations and field tests demonstrated inconsistency under different traffic conditions and incident scenarios. This raises the question of whether the CTM needs to be modified to accurately capture the traffic dynamics at the bottleneck locations, especially under congested conditions, or whether the proposed mainstream traffic control designs are not robust enough to reject disturbances.

In this dissertation, the CTM version, which considers the effect of both capacity drop and bounded acceleration, is modified to include a constant disturbance term to account for the uncertainties related to modeling and measurement errors. Motivated by the open-loop stability analysis of the modified model, a robust VSL controller is proposed, one which rejects external disturbances while guaranteeing that the traffic density converges to the desired equilibrium state as demonstrated by both macroscopic and microscopic simulations. The robust VSL control design is then extended to a multi-section CTM and combined with an LC control at the discharging section. The section length covered by the most upstream VSL sign is treated as a variable. Via extensive microscopic simulations, the integrated control scheme demonstrates promising improvements in the average travel time, the average number of stops, and the average emission rates when being compared to the cases of no control actions.

Furthermore, a multiple-lane CTM-based VSL control is introduced, where each lane of a motorway is treated as a separate stream; the net lane-changing flow (lateral flow) is modeled as an additional unknown term in the traffic flow conservation equation. This unknown net flow is estimated in real-time, and its estimate, which is developed based on Lyapunov stability analysis, is used at each time in calculating a per-lane VSL control command for each lane of the motorway. Then, a Lane Change (LC) controller is combined with the VSL to prevent creating a queue in the vicinity of the bottleneck. The stability properties of the closed-loop system are analyzed, where the integrated control scheme guarantees that the lane traffic density operates within the free-flow region of the fundamental diagram. Therefore, traffic congestion is relieved, and the per-lane outflow is maximized, except for the blocked lane, when the highway bottleneck is active, as demonstrated by microscopic simulations.