Method B

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

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 $t$ .