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 .
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 :