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

We present a transit model that, based on automated fare collection and train tracking data, describes pedestrian movements in train stations and vehicle-specific train ridership distributions. Our approach differs from existing models in that we describe on-board passenger dynamics and pedestrian dynamics at stations in a joint framework. We assume that travelers first decide on the train(s) they will take, and then pursue their journey through the network by successively choosing pedestrian paths, waiting positions on platforms, and specific train cars. Travelers explicitly maximize their travel utility. We model how crowding influences their walking speeds, and how it affects travel utility both at stations and on-board. To illustrate the framework, we present a real case study of a major Dutch rail corridor, for which we collect a rich set of passenger, pedestrian and train operation data. We observe a good agreement of model estimates with empirical observations, and discuss the use of the model for various transit-related problems including level-of-service assessment, crowding estimation, transit optimization, and integrated investment appraisal.

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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

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

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