A Macroscopic Flow Model for Mixed Traffic using Two-Dimensional Speed Functions

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.Transport and PlanningTransport and Plannin