Calculation of the velocity variance and experienced velocity variance

Vissim records values of the Velocity variance of pedestrians in the Vissim network during a simulation run in the following evaluations, if these are selected:

• Area evaluation, ramp evaluation (Output attributes of area and ramp evaluation)
• Grid cell evaluation (Grid-based evaluation of pedestrian density and speed)

Vissim records values of the Experienced velocity variance attributes for each pedestrian in the Vissim network during a simulation run (Showing pedestrians in the network in a list).

Calculation of the velocity variance

The velocity variance in km2/h2 is calculated using the following formula:

Where:

NT	Number of time steps so far in the evaluation time interval
	This sum includes all NP(tj) pedestrians which are on the area, ramp or in the cell at time tj
	Number of measurement points recorded This is the number of pedestrians summed over all time steps in the time interval. vi(tj) denotes the 2D velocity of the ith pedestrian at time tj.
	Average velocity value
N=1, Var(v)=0

Calculation of the experienced velocity variance

The Experienced velocity variance should represent a size that reflects the Impedance of a pedestrian (the ego pedestrian) to other pedestrians in close proximity:

• The experienced velocity variance is ZERO if all pedestrians are walking in the same direction at the same speed.
• The experienced variance is > ZERO if all pedestrians are walking in the same direction, but the ego pedestrian is walking slower or faster than the other pedestrians in close proximity.
• The experienced velocity variance is also > ZERO if all pedestrians are walking at the same speed, but the ego pedestrian is walking in the opposite direction.
• The experienced velocity variance increases the more the pedestrian's direction deviates from the directions of the other pedestrians. The deviation goes from the parallel direction to the opposite direction, at the same speeds.

The calculation of the experienced velocity variance ℇi(t) at time t of an ego pedestrian i is based on the calculation of the velocity variance:

Where:

vk(t)	2D velocity of the kth pedestrian
	Pedestrians (Neighbors) within the pedestrian’s personal area i. This area includes all pedestrians moving around the ego pedestrian defined by the attribute value Radius for the computation of the pedestrian's personal area (Selecting network settings for pedestrian behavior), limited to the central cell and the eight direct neighboring cells around the ego pedestrian with the cell size specified by the Search neighborhood grid size attribute (Selecting network settings for pedestrian behavior).
For the following setting applies: ℇi(t)=0.