Control of a lane-drop bottleneck through variable speed limits

Abstract

Keywords:Capacity drop Variable speed limits Kinematic wave model Link queue model Proportional-integral-derivative controller Stability a b s t r a c tThe discharging flow-rate of a lane-drop bottleneck can drop when its upstream is congested, and such capacity drop leads to additional traffic congestion as well as safety threats. Even though many studies have demonstrated that variable speed limits (VSL) can effectively delay and even avoid the occurrence of capacity drop, there lacks a simple approach for analyzing the performance of a VSL control system. In this study, we formulate the VSL control problem for the traffic system in a zone upstream to a lane-drop bottleneck based on two traffic flow models: the Lighthill-Whitham-Richards (LWR) model, which is an infinite-dimensional partial differential equation, and the link queue model, which is an ordinary differential equation and approximates the LWR model. In both models, the discharging flow-rate is determined by a recently developed model of capacity drop, and the upstream in-flux is regulated by the speed limit in the VSL zone. We first analytically study the properties of the control system with the link queue model. For an open-loop control system with a constant speed limit, we prove that a constant speed limit can introduce an uncongested equilibrium state, in addition to a congested one with capacity drop, but the congested equilibrium state is always exponentially stable. Then we apply a feedback proportional-integral (PI) controller to form a closed-loop control system, in which the congested equilibrium state and, therefore, capacity drop can be removed by both I-and PI-controllers. Both analytical and numerical results show that, with appropriately chosen controller parameters, the closed-loop control system is stable, effect, and robust. Finally, we show that the VSL strategies based on I-and PI-controllers are also stable, effective, and robust for the LWR model. Since the properties of the control system are transferable between the two models, we establish a dual approach for studying the control problems of nonlinear traffic flow systems. We also confirm that the VSL strategy is effective only if capacity drop occurs. The obtained method and insights can be useful for future studies on other traffic control methods and implementations of VSL strategies in lane-drop bottlenecks, work zones, and incident areas.

Characteristics of variable speed limit systems

“…[14,18]. Finally, control theory based VSL control algorithms have been proposed to find the optimal VSL strategy based on local feedback loops, such as the algorithms proposed in [4] and [22] or by using model predictive control, see e.g. [10,15,16,58].…”

Developing and evaluating an eco-speed harmonization strategy for connected vehicles

“…The model was further validated with a benchmark problem where the system inputs included the upstream traffic demand and the downstream traffic density of the roadway link. In [11], Jin and Jin used macroscopic traffic flow models, and proposed a VSL algorithm based on a feedback proportionalintegral (PI) control scheme to regulate traffic conditions in the zone upstream of a lane-drop bottleneck and avoid significant capacity drops. Instead of using occupancy based feedback control, Lu et al put forward a (link) speed-based feedback control law for the speed harmonization strategy in order to maximize the bottleneck throughput [12].…”

Bottleneck mitigation through a variable speed limit system using connected vehicles

“…Therefore, homogenization systems with the goal to improve traffic efficiency have been proposed in the literature, see e.g. Carlson, Papamichail, and Papageorgiou (2011) and Jin and Jin (2015). In homogenization systems, the speed limit is adjusted to reduce deviations in individual vehicle speeds in order to maximize the throughput of vehicles at a bottleneck location.…”

“…The target value can, for example, be the critical density, defined as the density associated with the maximum capacity. Since most of the homogenization systems are not implemented in real traffic, they are evaluated through simulation-based studies (Carlson, Papamichail, and Papageorgiou 2011;Jin and Jin 2015;Müller et al 2015). An exception is the field trial presented by Hegyi and Hoogendoorn (2010).…”

“…traffic efficiency was not increased by the systems. Homogenization algorithms, such as the ones proposed by Hegyi, De Schutter and Hellendoorn (2005), Müller et al (2015) and Jin and Jin (2015), have in simulation-based studies been shown to improve traffic efficiency. Moreover, a field trial by Hegyi and Hoogendoorn (2010) showed improvements in throughput as a result of the decreased time needed to resolve moving shockwaves.…”