This method measures the mean value of velocity and density over space and time.

The spatial mean velocity and density are calculated by taking a segment \(\Delta x\) in a corridor as the measurement area.

Method B: Illustration of the measurement interval.

The velocity \(\langle v \rangle_i\) of each person is defined as the length \(\Delta x\) of the measurement area divided by the time he or she needs to cross the area:

\[\langle v \rangle_i=\frac{\Delta x}{t_\text{out}-t_\text{in}},\]

where \(t_\text{in}\) and \(t_\text{out}\) are the times a person enters and exits the measurement area, respectively.

The density \(\rho_i\) for each person \(i\) is calculated as:

\[\langle \rho \rangle_i=\frac{1}{t_\text{out}-t_\text{in}}\cdot\int_{t_\text{in}}^{t_\text{out}} \frac{N^\prime(t)}{b_\text{cor}\cdot\Delta x}dt,\]

where \(b_\text{cor}\) is the width of the measurement area while \(N^\prime(t)\) is the number of person in this area at a time \(t\).