Table 1.
References for maximum observed upward flows at escalators.
Fig 1.
Qualitative difference between the ‘theoretical’ and the ‘practical’ escalator capacity in the range of typical conveyor speeds.
Regarding the ‘practical’ capacity, linear, saturating, and even decreasing curve progressions can be found in the literature.
Fig 2.
Geometry used for the simulations.
The geometry consists of three parts: a lower floor including the agent sources (right), an escalator with a clear width of w ∈ {0.6, 1.0}m, and a projected horizontal length of lesc = 10 m (middle), as well as an upper floor which is located Δh = 5 m above the lower one (left). The movement direction of the agents and of the escalator is from right to left. The incoming agent flow α can be freely adjusted whereas the flow β is typically measured.
Fig 3.
Speed of a single agent, depending on the position on the escalator.
Shown are simulation results obtained for c = 50 (left) and c = 500 (right), and for the common escalator speeds vesc ∈ {0.50, 0.65, 0.75} ms−1, respectively. The desired speed of free walking on the plain is here v0,horiz. = 1.3 ms−1. The shaded areas indicate regions where the agent speed is adapting to the one of the respective escalator. The corresponding adaptation lengths are approximately 1.0 m (left panel) and 0.4 m (right panel).
Table 2.
Required length of the horizontal flights at the entrance and exit of an escalator according to norm EN 115–1 [7].
Fig 4.
Individual speeds of 1.000 agents, depending on the position on the escalator.
The results are obtained using c = 500, vesc = 0.5 ms−1, and w = 1.0 m. The shaded areas indicated the required length of the horizontal flights according to Table 2.
Fig 5.
Simulation results for spatial distances between the agents.
Shown are results for the clear widths w = 0.6 m (first row) and w = 1.0 m (second row), as well as for the escalator speeds vesc = 0.5 ms−1 (left) and vesc = 0.75 ms−1 (right), respectively. The average values of the distances are obtained from steady-state regions of 60s length (shaded areas) and are indicated by a bar. Since Δy almost vanishes in the upper two diagrams, the total distance s is approximately the same as Δx.
Fig 6.
Minimum spatial separations in movement direction depending on the escalator speed (left) and the model parameter T (right).
The simulation results are obtained by measuring for the escalator widths w = 0.6 m and w = 1.0 m, respectively. Model parameters are fixed by T = 0.25s (left) and vesc = 0.5 ms−1 (right). The approximations follow from Eq (6) using dstep = 0.4 m,
for w = 1.0 m, and
for w = 0.6 m. The shaded area indicates the range of typical escalator speeds.
Fig 7.
Speed dependence of the step occupancy.
The simulation results are obtained from Eq (10) by using results of the spatial separation in movement direction from the previous section. The respective approximations follow from Eq (11) using T = 0.25s, dstep = 0.4 m, for w = 1.0 m, and
for w = 0.6 m.
Fig 8.
Non-linear speed-dependence of the escalator capacity.
Shown are simulation results for the escalator widths w = 1.0 m (blue markers) and w = 0.6 m (green markers). Approximations are obtained by using Eq (16) with dstep = 0.4 m and T = 0.25 s. The shaded area indicates the range of typical escalator speeds.
Fig 9.
Speed-dependent capacity of an escalator for different values of the time gap T.
The diagram compares Eq (16) for different T-values with maximum observed flows summarized in Table 1 and ‘practical’ capacities provided by manufacturers [3–5]. The escalator parameters are fixed by dstep = 0.4 m and w = 1 m . By definition, the capacity should be as big as or larger than observed flows.