Victor L. Knoop

Routing Strategies Based on Macroscopic Fundamental Diagram

Traffic management can prevent too many vehicles in a traffic network from reducing traffic performance. In particular, traffic can be routed so that the bottlenecks are not oversaturated. The macroscopic fundamental diagram provides a relationship between the number of vehicles and network performance. Traffic control can be applied on this level to overcome the computational complexity of networkwide control with traditional control levels of links or vehicles. The main questions are (a) how effective traffic control is with aggregate variables compared with full information and (b) whether the shape of the macroscopic fundamental diagram changes under traffic control. A grid network with periodic boundary conditions is used as an example and is split into several subnetworks. The following routing strategies are compared: the shortest paths in distance and time (dynamic due to congestion) and approximations of the path shortest in time but calculated with only variables aggregated for a subnetwork and of the path shortest in time but calculated with only subnetwork accumulation. For the third and fourth routing strategies, only information aggregated over the subnetwork is used. The results show improved traffic flow with detailed information. Effective control is also possible by using aggregated information, but only with the right choice of a subnetwork macroscopic fundamental diagram. Furthermore, when detailed information is used to optimize—and therefore in a subnetwork—the macroscopic fundamental diagram changes.

Integrated Lane Change Model with Relaxation and Synchronization

A proposed lane change model can be integrated with a car-following model to form a complete microscopic driver model. The model resembles traffic better at a macroscopic level, especially regarding the amount of traffic volume per lane, the traffic speeds in different lanes, and the onset of congestion. In a new approach, lane change incentives are combined for determining a lane change desire. Included incentives are to follow a route, to gain speed, and to keep right. Classification of lane changes is based on behavior that depends on the level of lane change desire. Integration with a car-following model is achieved by influencing car-following behavior for relaxation and synchronization, that is, following vehicles in adjacent lanes. Other improvements of the model are trade-offs between lane change incentives and the use of anticipation speed for the speed gain incentive. Although all these effects are captured, the lane change model has only seven parameters. Loop detector data were used to validate and calibrate the model, and an accurate representation of lane distribution and the onset of congestion was shown.

Lane distribution of traffic near merging zones influence of variable speed limits

The congestion at on-ramps of motorways is due to too many vehicles wanting to merge onto the same lane. Ramp metering is usually used as control measure to influence the flows, but a variable speed limit can also have large consequences for the merging process. This paper discusses the change in lane distribution due to a VSL and explicitly considers the influence of an on-ramp. To this end, the lane distribution just upstream of an on-ramp is compared with the lane distribution elsewhere. Just upstream of an on-ramp, a significantly lower fraction of the flow uses the outside (right) compared to a part of the road without any ramps. This holds both for a situation with VSL as without VSL. Besides, VSL increases the use of the outside lane near capacity. This way, VSL influences not only the speed but also the lane distribution, and thereby possibly also the merging ratio. The consequences of this changed lane distribution are site-dependent and should be taken into account when deciding on installing a system of variable speed limits.

Capacity Reduction at Incidents: Empirical Data Collected from a Helicopter

Incidents on freeways cause large delays for road users. These delays depend largely on the capacity at the incident location, which is determined by the drivers’ behavior at the accident location. Few empirical facts are available on traffic operations during an incident. This paper presents high-quality videos of the traffic flow around two accidents recorded from a helicopter. From the collected images, traffic counts have been performed at the exact location of the incident. This has two advantages. First, the capacity at the bottleneck per lane could be estimated. Second, truck counts could be converted to passenger car units at the location of the bottleneck. Counts show that the (outflow) capacity of the remaining lanes is about 50% lower than the (free-flow) capacity of the same number of lanes. This means that the road capacity in the opposite direction is reduced by half by the rubbernecking effect. The capacity of the road in the direction of the accident is reduced by more than half because not all lanes are in use. The images provide information on the causes for the capacity reduction. A leader accelerates and the follower accelerates a short time later. The average time between these two accelerations is estimated at about 3 s, but the video also shows a large spread of these times. The results can be used to assess consequences of incidents, in an analytical way and in macroscopic or microscopic traffic simulators.

Empirics of a Generalized Macroscopic Fundamental Diagram for Urban Freeways

Because of an increasing exchange of data between measurement sites, the area over which traffic control is applied is also increasing. This situation leads to three new challenges: (a) working with the large quantities of data (transmit, store), (b) estimating the traffic state, and (c) controlling a large area with many controllers (and thus large solution space). This paper introduces a new way of describing the traffic state for a large area, one that requires much less data and nevertheless gives an accurate representation of the state. The macroscopic fundamental diagram (MFD) links the production (the average flow) to the accumulation (the average number of vehicles) in an area. This paper shows that MFD can be converted to a generalized MFD (GMFD) for urban freeways; the GMFD relates the production to the accumulation and the spatial spread of density. Analysis of 10 months of data from the Amsterdam, Netherlands, ring road freeway showed that GMFD is a continuous function that increases and decreases with accumulation, as does a fundamental diagram, and decreases with the spatial spread of density. The predictive performance of GMFD was tested with a nonparameterized fit and by fitting a functional form; each test performed equally well. Predicting the production is important, especially near the maximum production. GMFD explains much more of the spread in the production than MFD does, especially near this maximum production. Thus, this lean traffic state description can be used in setting a target for traffic control.

Optimal dynamic route guidance: A model predictive approach using the macroscopic fundamental diagram

Since centralized control of urban networks with detailed modeling approaches is computationally complex and inefficient, hierarchical decentralized methods based on aggregate models are of great importance. In this paper, we use an aggregate modeling approach based on the macroscopic fundamental diagram (MFD), in order to find dynamic optimal routing strategies. An urban area can be divided into homogeneous regions each modeled by a (set of) macroscopic fundamental diagrams. Thus, the problem of route guidance can be solved in a regional fashion by using model predictive control and the novel high-level MFD-based model used for prediction of traffic states in the urban network. The optimal routing advices obtained from the high-level controller can be used as references (to track) for lower-level local controllers installed at the borders of the regions. Hence, the complexity of solving the routing problem will be decreased significantly. The performance of the proposed approach is evaluated using a multi-origin multi-destination grid network. Further, the obtained results show significant performance of the optimal dynamic route guidance over other static routing methods.

Empirical Differences Between Time Mean Speed and Space Mean Speed

Insight into traffic flow characteristics is often gained using local measurements. To determine macroscopic flow characteristics, time aggregation of microscopic information is required.

Macroscopic Modeling Framework Unifying Kinematic Wave Modeling and Three-Phase Traffic Theory

Modeling breakdown probabilities or phase-transition probabilities is an important issue when assessing and predicting the reliability of traffic flow operations. Looking at empirical spatiotemporal patterns, these probabilities clearly are a function not only of the local prevailing traffic conditions (density, speed) but also of time and space. For instance, the probability that a start-stop wave occurs generally increases when moving upstream away from the bottleneck location. A simple partial differential equation is presented that can be used to model the dynamics of breakdown probabilities, in conjunction with the well-known kinematic wave model. The main assumption is that the breakdown probability dynamics satisfy the way information propagates in a traffic flow, that is, they move along with the characteristics. The main result is that the main characteristics of the breakdown probabilities can be reproduced. This is illustrated through two examples: free flow to synchronized flow (F-S transition) and synchronized to jam (S-J transition). It is shown that the probability of an F-S transition increases away from the on ramp in the direction of the flow; the probability of an S-J transition increases as one moves upstream in the synchronized flow area.

Microscopic Traffic Behaviour near Incidents

Much of the delays on road networks are caused by incidents. This is partially caused by blockage or closure of lanes, but also by the change of driving behaviour in the remaining lanes. This contribution analyses traffic flow conditions near an incident both microscopically and macroscopically. A theory is proposed to describe drivers’ behaviour, which is tested using traffic data of individual vehicles, collected using a helicopter. A bimodal headway distribution is observed, centred around two mean values, 2 seconds and 4 seconds. To understand the underlying mechanisms a car-following model is fitted to the drivers’ behaviour. The model parameters show that the reaction time is much higher than usual. Using this model-based analysis, we conclude that the incident distracts the drivers and less attention is paid to the driving process. The consequence is that the queue discharge rate for the unblocked lanes is 30% lower than the usual queue discharge rate per lane.

Mainstream traffic flow control at sags

Sags are freeway sections along which the gradient changes significantly from downward to upward. The capacity of sags is considerably lower than the capacity of normal sections. Consequently, sags are often freeway bottlenecks. Recently, several control measures have been proposed to improve traffic flow efficiency at sags. Those measures generally aim to increase the capacity of the bottleneck, to prevent traffic flow perturbations in nearly saturated conditions, or both. This paper presents an alternative type of measure based on the concept of mainstream traffic flow control. The proposed control measure regulates traffic density at the bottleneck area to keep it below the critical density and hence prevent traffic from breaking down while maximizing outflow. Density is regulated by means of a variable speed limit section that regulates the inflow to the bottleneck. Speed limits are selected on the basis of a feedback control law. The authors evaluate the effectiveness of the proposed control strategy by means of a simple case study by using microscopic traffic simulation. The results show a significant increase in bottleneck outflow, particularly during periods of high demand, which leads to a considerable decrease in total delay. This finding suggests that mainstream traffic flow control strategies that use variable speed limits have the potential to improve substantially the performance of freeway networks containing sags.