Probability of nosing:

The probability of nosing is a function of the vehicle's position, the number of necessary lane changes, and the time the vehicle has been waiting for the lane change. It is calculated by:

where:

probability of nosing for vehicle n;

maximum probability of nosing, and it is a function of traffic conditions;

3.14159 ;

relative position in the link or view range, i.e. , where is the vehicle's position and L the length of the link or view range.

a scaling variable defined as the following:

where:

number of necessary lane changes in order to connect to the next link on its path (or to an open lane in case of incidents);

K

indicator of traffic condition (i.e. density divided by jam density);

time since the vehicle has been in mandatory lane change state; and

's

model parameters (see Table C.11).

  
Figure 3.9: Probability of nosing

The probability given by Eq (3.21-3.22) (see Figure 3.9 (a)) has the following characteristics:

• increases from 0 to 1 as the driver moves from the beginning to the end of the link, and;
• increases with the number of lanes that the vehicle must cross and the time it has been looking for a gap.