Car following model

Simulation uses a simplified car following model which distinguishes between two states:

• A vehicle travels at maximum possible speed.
• A temporal distance is kept to the rear end of the preceding vehicle. The temporal distance corresponds to the reaction time, plus the time required by the vehicle to come to a standstill.

This allows us to make the following formulations for the car following model,

where:

xFollower	Front end position of following vehicle on current link
xLeader	Front end position of leading vehicle on current link
VLink	Max. link speed
τFollower	Reaction time of following vehicle
λLeader	Effective vehicle length of preceding vehicle

Table 146 lists the input parameters relevant for the car following model.

Object	Parameters	Meaning
TSys	SBA reaction time	Temporal safety distance (s)
TSys	SBA effective vehicle length	Standstill distance plus vehicle length (m)
Links	V0	Max. link speed
Links	SBA reaction time factor	Reaction time factor for vehicles on the link, e.g. to calibrate link capacity
Links	SBA is reaction time factor transport system dependent	Activates the input option of transport system-dependent factors for the reaction time
Links	SBA reaction time factor-PrTSys-PrTSys (PrTSysx, PrTSysy)	Factor for the reaction time of a vehicle of PrTSysx following a vehicle of PrTSysy (one attribute per pair of existing PrT transport systems)
Links	SBA effective vehicle length factor	Effective vehicle length factor for vehicles on the link, e.g. to calibrate link storage capacity

Table 146: Input attributes for the car following model

Table 147 lists additional parameters used in simulation. Please note that link capacity is not an input attribute used in simulation.

The link attributes SBA reaction time factor and SBA factor effective vehicle length are applied by default. As long as the default value of 1 is not changed, this means that the settings of the transport system are adopted. The factors can be used to calibrate the capacity of a link or to adapt to local conditions such as gradients or road parking. For special applications, especially the modeling of autonomous vehicles, a more detailed modeling is required. For detailed modeling, activate the attribute SBA is reaction time factor transport system dependent. Thus, the reaction time factor does not only apply to the vehicle itself, but depends on the combination of the vehicle's transport systems and those of the vehicle in front. If, for example, an autonomous vehicle follows another autonomous vehicle, the factor may be smaller than if the autonomous vehicle follows a conventional vehicle. In general, the reaction time factor can then be defined for all pairs of PrT transport system combinations.

Object	Parameters	Meaning
Links	TSysSet	Number of transport systems allowed
(Main)turn	TSysSet	Number of transport systems allowed
Connectors	TSysSet	Number of transport systems allowed
Links	Number of lanes	Influences the link capacity and, in conjunction with the node topology of the To-node, the lane selection on the link
Nodes	Control type	Defines gap acceptance and the parameters used
Junction control		Signal controllers, major flow
Node geometry		Lanes, lane turns Note Please note that the TSys set from objects of node geometry is not taken into account. Whether a lane turn can be used depends on the transport systems allowed on higher-level network objects (links, (main) turns).
Node geometry	See Table 148
TSys	SBA maximum wait time	Maximum time for a vehicle of the minor approach before it forces its entry into the higher ranked traffic stream, even if the time gap is not sufficient

Table 147: Additional input attributes for simulation

 

Note: In the directory C:\Users\Public\Documents\PTV Vision\PTV Visum 2021/Examples, you can find an example of use on this topic. The PrT Modeling AV example demonstrates how autonomous vehicles can be accounted for in macroscopic models, more precisely in PrT assignments.