Defining the Wiedemann 99 model parameters

This model is based on Wiedemann’s 1999 car following model.

The following parameters are available:

Parameters Unit Description

CC0

 m

Standstill distance: The desired standstill distance between two vehicles. No stochastic variation.

You can define the behavior upstream of static obstacles via the attribute Standstill distance in front of static obstacles (Editing the driving behavior parameter Following behavior).

CC1

 s

Gap time distribution: Time distribution from which the gap time in seconds is drawn which a driver wants to maintain in addition to the standstill distance.

At a speed v the desired safety distance is computed as:

dxsafe = CC0 + CC1 • v

At high volumes this distribution is the dominant factor for the capacity.

CC2

 m

'Following' distance oscillation: Maximum additional distance beyond the desired safety distance accepted by a driver following another vehicle before intentionally moving closer.

If this value is set to e.g. 10 m, the distance oscillates between:

dxsafe und dxsafe + 10 m

The default value is 4.0m which results in a quite stable following behavior.

CC3

 s

Threshold for entering ‘BrakeBX’: Time in seconds before reaching the maximum safety distance (assuming constant speed) to a leading slower vehicle at the beginning of the deceleration process (negative value).

CC4

 m/s

Negative speed difference: Lower threshold for relative speed compared to slower leading vehicle during the following process (negative value).

Lower absolute values result in adopting a speed more similar to the leading vehicle.

CC5

 m/s

Positive speed difference: Relative speed limit compared to faster leading vehicle during the following process (positive value).

Recommended value: Absolute value of CC4

Negative values result in adopting a deceleration speed more similar to the leading vehicle.

CC6

 1/(m • s)

Distance impact on oscillation: Impact of distance on limits of relative speed during following process:

  • Value 0: Distance has no impact on limits.
  • Larger values: Limits increase with increasing distance.

CC7

 m/s2

Oscillation acceleration: Acceleration oscillation during the following process.

CC8

 m/s2

Acceleration from standstill: Acceleration when starting from standstill. Is limited by the desired and maximum acceleration functions assigned to the vehicle type.

CC9

 m/s2

Acceleration at 80 km/h: Acceleration at 80 km/h is limited by the desired and maximum acceleration functions assigned to the vehicle type.

 

Notes:  

  • Acceleration follows a linear progression between 0 km/h and 80 km/h; beyond 80 km/h, it maintains the value specified by CC9. Z is added to the value derived from CC8 and CC9: z = a value from the interval [0, 1], normally distributed around 0.5 with a standard deviation of 0.15.

For vehicles in the HGV category, the resulting sum is then divided by two.

The resulting acceleration is capped at the upper limit defined by the functions for maximum acceleration and desired acceleration assigned to the specific vehicle type (Defining acceleration and deceleration functions). The function for maximum acceleration is subject to modification by the current gradient of the route.

The actual acceleration of the vehicle might be less than this calculated result if free acceleration is not feasible, such as when the vehicle is approaching its desired speed or is aware of a slower vehicle ahead.

The change in acceleration, in comparison to the last time step, is further constrained by the jerk limitation (Editing the driving behavior parameter Following behavior).

  • The units of Wiedemann 99 model parameters cannot be edited. These units are independent of the network settings for units in the base data.

Defining the saturation flow rate with the Wiedemann 99 modeling parameters

The saturation flow rate defines the number of vehicles that can flow freely on a link for an hour. Impacts created through signal controls or queues are not accounted for. The saturation flow rate also depends on additional parameters, e.g. speed, share of HGV, or number of lanes.

In the car-following model Wiedemann 99, parameter CC1 has a major impact on the safety distance and saturation flow rate. The scenarios shown below as an example are based on the following assumptions:

  • car-following model Wiedemann 99, containing default parameters with the exception of CC1 that varies across the x-axis
  • one time step per simulation second

The main properties of the following graphs are:

Scenario

Right-side rule

Lane

Speed cars*

Speed HGV*

% HGV

99-1

no

2

80

n/a

0%

99-2

no

2

80

85

15%

99-3

yes

2

80

n/a

0%

99-4

yes

2

80

85

15%

99-5

yes

2**

120

n/a

0%

99-6

yes

2

120

85

15%

* Vissim default setting

** Lane 2 closed for HGV traffic

Note: The graphs show exemplary calculated saturation flow rates. When using a different network, you receive graphs depicting different values.

 

Example: Graphs of saturation flow rate Scenario 99-1 to 99-6

Horizontal x-axis: Variation CC1: 0.1 to 1.5

Vertical y-axis: Veh/h/lane

Superordinate topic:

Editing the driving behavior parameter car following model