This method calculates the mean value of flow and density over time.

A reference line is taken and studied over a
fixed period of time .

Using this method we can obtain the pedestrian flow and the
velocity of each pedestrian passing the reference line directly.
Thus, the flow over time and the time mean
velocity
can be calculated as

where is the number of persons passing the reference line during the time interval .

and are the times when the first and last pedestrians pass the location in .

**Note:**Note: this time period can be different from .

The time mean velocity is defined as the mean value of the instantaneous velocities pedestrians.

is calculated by use of the displacement of pedestrian in a small time interval around :