Generalized velocity–density model based on microscopic traffic simulation
In case of the Intelligent Driver Model (IDM) the actual Velocity–Density law V(D) applied by this dynamic system is not defined, only the dynamic behaviour of the vehicles/drivers is determined. Therefore, the logical question is whether the related investigations enhance an existing and known law or reveal a new connection. Specifically, which function class/type is enhanced by the IDM? The publication presents a model analysis, the goal of which was the exploration of a feature of the IDM, which, as yet, ‘remained hidden’. The theoretical model results are useful, this analysis important in the practice in the field of hybrid control as well. The transfer of the IDM groups through large-scale networks has special practical significance. For example, in convoys, groups of special vehicle, safety measures with delegations. In this case, the large-scale network traffic characteristics and the IDM traffic characteristics should be taken into account simultaneously. Important characteristics are the speed–density laws. In case of effective modelling of large networks macroscopic models are used, however the IDMs are microscopic. With careful modelling, we cannot be in contradiction with the application of speed–density law, where there IDM convoy passes. Therefore, in terms of practical applications, it is important to recognize what kind of speed–density law is applied by the IDM convoys in traffic. Therefore, in our case the goal was not the validation of the model, but the exploration of a further feature of the validated model. The separate validation of the model was not necessary, since many validated applications for this model have been demonstrated in practice. In our calculations, also the applied model parameter values remained in the range of the model parameters used in the literature. This paper presents a new approach for Velocity–Density Model (VDM) synthesis. It consists in modelling separately each of the density and the velocity (macroscopic parameter). From this study, safety time headway (microscopic parameter) can be identified from macroscopic data by mean of interpolation method in the developed map of velocity–density. By combining the density and the velocity models, a generalized new VDM is developed. It is shown that from this one, some literature VDMs, as well as their properties, can be derived by fixing some of its parameters.