Investigating the time evolution of some parameters describing inflow processes of pedestrians in a room

We investigated the properties of pedestrian inflow into a room (with one entrance and one exit) in two different conditions: without inactive persons and with the presence of inactive persons, who are pedestrians that after entering the room find randomly a position to stop, obstructing the inflow of the normal pedestrians. The average mutual distance (MD), calculated averaging over all the distances between any two pedestrians, indicates that the spatial distribution of the pedestrians is different from that obtained by uniformly random distributed pedestrians occupying the same space as that of the room. The comparison of the (MD) with that of uniform spatial distributions obtained by using different room lengths suggests that the position of the exit could affect the spatial distribution of the pedestrians, who tend to randomly occupy the space which is delimited by the position of the exit. The analysis of the distance time series (which is the series of distances between successive positions occupied by a pedestrian) shows that the mean maximum distance is rather large when inactive persons obstructs the movement of the normal pedestrians; furthermore it tends to increase with the increase of the number of inactive persons, while in case of absence of inactive persons there is an apparent decrease with the increase of number of moving people. The detrended fluctuation analysis (DFA) applied to the distance time series shows that in both conditions pedestrians move persistently; however, without inactive persons DFA scaling exponent tends to slightly increase and stabilize with the increase of the number of moving people; with the presence of inactive persons, it tends to slightly decrease with the increase of the number of inactive persons. The obtained results contribute to a better understanding of the dynamical properties of pedestrian inflow processes, maybe leading to a better mathematical assessment of inflow models.