Interactions among different modes or vehicle classes in urban road networks affect the network performance in different and complex ways. Thus, an answer to the question of “how many cars are too many for a city?” is not trivial. However, multi-modal macroscopic fundamental diagrams (MFD) offer a novel opportunity to answer this question. So far, no methodology exists to estimate multi-modal MFDs resulting from arbitrary multi-modal interactions. In this paper, we propose a methodology to capture additional delays in the shape of the MFD and derive an approach for estimating multi-modal MFDs thereof. The influence on the MFD shape is established using the two-fluid theory of urban traffic by defining pairwise copula functions between travel times of each mode. In contrast to many existing approaches, the presented approach retains individual mode's speed information. We show the applicability of the approach with a tri-modal case of bicycles, buses, and cars with empirical data from Amsterdam (The Netherlands) and London (United Kingdom). Although the approach is not limited to this specific tri-modal case, we use the example to discuss the initial policy question by deriving optimal modal splits for a given accumulation of travelers. Last, we compare the new approach to existing estimation methods for bi-modal MFDs describing car and bus traffic.@en

This dissertation studies the dynamics of bicycle traffic flow. The research focuses on busy situations such as bicycle queues at intersections and congestion upstream of a bottleneck. The cycling movements are analyzed on the aggregated scale in terms of density, speed and flow. Furthermore, cyclists are included in a traffic flow model by introducing a mode-specific speed function, which enables the modeling of a mixed traffic situation. @en

Density is one of the most relevant variables in a traffic flow description. For objects in 2 dimensions, density can be determined by the space that is allocated to each of the objects. This paper introduces a new way of computing the space available for a bicyclist, accounting for speed and accounting for the non-zero size of a bicycle. This changes local densities. The proposed method modifies the Voronoi densities, and assigns space to a bicycle. We assign space to bicycle A if it has a closer proximity to any point of bicycle A than any point of any other bicycle. The proximity is determined by the distance and the angle in relation to velocity of the bicycle. Specific proximity functions need to be formulated and calibrated to match cyclist behavior. This method helps to define a density level for cyclists, which in turn can for instance lead to a better indication of a Level of Service.@en

Congestion in bicycle traffic is a daily occurrence at many urban intersections. It is known that a higher density in the queue leads to a higher discharge rate. In theory, higher jam densities than those currently observed in practice are feasible. This leads to our hypothesis that the delay at intersections can be further reduced when cyclists are encouraged to queue up closer together. To explore this option, we carried out an experiment in which the queue configuration was influenced to increase the jam density. This paper presents ways to increase the queuing density, up to twice the density found without instructions. Results show that increasing the jam density does indeed increase the queue discharge rate; this also holds for jam density values that exceed those observed in normal queuing conditions. The efficiency of the queue discharge process, captured by the discharge rate, was found to increase by 40% when cyclists queue up closely together. Qualitative comparison of the queuing positions and discharge patterns showed that the discharge sequence is largely determined by the queuing position, and that cyclists keep a distance from each other in both time and space during the queue discharge phase. When applied in practice, these findings can be used to update the signal length and green phases for all traffic, thereby reducing congestion in urban areas.@en

Bicycles are gaining popularity as a mode of transport resulting in a mixed bicycle–car traffic situation on urban roads. Cyclists however, are hardly included in traffic flow models which complicates the design of safe and congestion-free traffic situations. This work introduces class-specific speed functions based on two variables, being space headway for both cars and cyclists. This enables the macroscopic modelling of mixed bicycle–car traffic. The multi-class macroscopic flow model is successfully tested for different traffic situations that occur on urban roads where cyclists and cars share the same infrastructure, e.g. cyclists overtaking a queue of cars and cars overtaking cyclists with reduced speed. The mixed bicycle–car flow model allows travel time estimation of both classes, which in turn can be used to evaluate the overall performance of a mixed traffic road.@en

Traffic flow might be limited by cross-traffic which has priority. A typical example of such a situation is a location where cyclists or pedestrians cross a stream of car traffic. Splitting the cross-traffic into two separate sub-streams (for instance left?right and right?left) can increase the capacity of the main stream. This is because it is no longer necessary to have a sufficiently large gap in both sub-streams simultaneously. This paper introduces a method to compute the resulting capacity of roads with cross-traffic. Without loss of generality, we introduce three transformations to simplify computations. These transformations are an important contribution of the paper, allowing us to create scalable graphs for capacity. Overall, the research shows that splitting a crossing stream into two equally large sub-streams increases the capacity of the main stream. If there is place for one vehicle in between two sub-streams, the capacity can increase up to threefold. Even larger gains are possible with more vehicles in between. This paper presents graphs which can be used to find the capacity for generic situations, and can be used for developing guidelines on intersection design.@en

An increasing number of people use the bicycle for urban trips resulting in local congestion at intersections, especially during peak hours. Understanding the queue dynamics is key to find the correct measures that can reduce the delays for cyclists without affecting other traffic modes. To this end, the discharge process of bicycle queues is studied, focusing on the impact of jam density on the queue discharge rate and how this process is affected by cyclists that merge into the queue during the discharge phase. The impact of merging cyclists is captured by a newly introduced bicycle equivalent (BE) value. This direction-specific BE value is used to convert a merging cyclist into a cyclist that is waiting in the original queue. Results show that the queue discharge rate increases with increasing density of the queue. Furthermore, cyclists that merge by overtaking contribute to the queue discharge rate, while cyclists who merge from a perpendicular direction hinder the discharge process, thereby decreasing the bicycle flow at the intersection. The insights can be used to develop measures which minimise delay at intersections and to design efficient infrastructure for bicyclists.@en

Bicycle usage is encouraged in many cities because of its health and environmental benefits. As a result, bicycle traffic increases which leads to questions on the requirements of bicycle infrastructure. Design guidelines are available but the scientific substantiation is limited. This research contributes to understanding bicycle traffic flow by studying the aggregated movements of cyclists before and after the onset of congestion within the setting of a controlled bottleneck flow experiment. The paper quantitatively describes the relation between capacity and path width, provides a qualitative explanation of this relation by analyzing the cyclist configuration for different path widths, and studies the existence of a capacity drop in bicycle flow. Using slanted cumulative curves and regression analysis, the capacity of a bicycle path is found to increase linearly with increasing path width. A steady drop in flow rate is observed after the onset of congestion, indicating that the capacity drop phenomenon is observed in bicycle traffic. The results presented in this paper can help city planners to create bicycle infrastructure that can handle high cyclist demand.@en

Cycling research at the operational behavioral level is limited, mainly because of the lack of empirical data. To overcome this data shortage, we performed a controlled, large-scale cycling experiment in the Netherlands. In this paper we describe the methodology for setting up and implementing such an experiment, from the motivation of its design using a conceptual model describing cyclist behavior to adjustments that were required during the experiment. The main contribution of this paper is, therefore, to be used as a guide in future experimental data collections. Moreover, we present the characteristics of the participants and their bicycles, and provide a qualitative description of phenomena observed during the experiment. Finally, we elaborate on the potential that the collected dataset holds for future research into understanding and modeling operational cycling behavior.@en

In many countries, an increasing number of people are using the bicycle for urban trips. The increased bicycle flow sometimes creates local congestion at intersections and demands better bicycle traffic management. To provide policy makers with models and advice on how to prevent congestion, an increased understanding of queue dynamics is required. This study analyzed the queue discharge process of cyclists at a controlled intersection, focusing on how queue density and merging cyclists influence the discharge rate. A bicycle equivalent (BE) value was introduced to correct for the impact of merging cyclists from different directions, with respect to the impact of cyclists in the original queue. For an intersection in Delft, the Netherlands, the discharge rate was found to increase for increasing queue density. Furthermore, cyclists who merged by overtaking were found to contribute more to the discharge rate compared to cyclists that were standing in the original queue. Cyclists that merged from a direction perpendicular to the queuing direction were found to hinder the discharge process, decreasing the observed outflow rate. These insights can be used as input for bicycle flow models to assess new plans for bicycle infrastructure and to develop measures to minimize delay at intersections.@en

Traffic in urban environments often share the same infrastructure and in places with high cyclist volumes, such as in The Netherlands, the roads are used simultaneously by cyclists and cars. This creates a mixed traffic situation in which both modes can be the fastest moving one, depending on the traffic state. In low demand situations, cars have the opportunity to overtake cyclists while in a congested state, the cyclists can still pass a queue of cars. Existing macroscopic flow models handle mixed traffic situations by selecting cars as the mode of reference and expressing the other modes in passenger car equivalents (pce) based on their impact to the traffic flow. A consequence of using this method is that one mode is always the fastest class, which does not fully represent the traffic situation observed in a mixed bicycle-car street. Therefore, this study takes another approach by introducing two-dimensional speed functions. These speed functions are based on the space headway of cars and cyclists, which ensures that both modes can be the fastest moving one depending on the traffic state. This work presents a multi-class macroscopic flow model using two-dimensional speed functions. A Lagrangian approach is used, following platoons of cars and cyclists over time. Both platoon size and time are discretized in the numerical implementation, while position is continuous. The two-dimensional speed functions takes into account the space headway of both cars and cyclists, and functions are class specific. The model is successfully tested for different traffic situations occurring on urban roads. Besides mixed bicycle-car traffic, the model could also be applied to other combination of modes as long as the class-specific two-dimensional speed functions are updated to match the situation. Besides travel time estimation, the model can also be used for demand estimation, which is relevant input data to network-wide traffic models and route choice models.@en