Using the unbiased grey Markov chain optimization model to forecast passenger flows through existing urban rail transit stations

Figures (7) Tables (7)

Figure 1.
Technological road map.
Figure 2.
Route map of Lines 2 and 3. Source: the authors.
Figure 3.
Fitting diagram of the actual passenger flow and the grey model's forecasted passenger flow.
Figure 4.
Comparison of the fits of four datasets.
Figure 5.
Maximum cross-sectional passenger flows through each station before and after the opening of the second phase of Line 2.
Figure 6.
Predicted direction of passenger flows through Wu Si Square Station in the morning and evening peak times. (a) Morning rush hour. (b) Evening rush hour.
Figure 7.
Actual direction of passenger flows through Wu Si Square Station in the morning and evening peak times. (a) Morning rush hour. (b) Evening rush hour.
Inspection-level accuracy First-order accuracy Second-order accuracy Third-order accuracy Fourth-order accuracy

D D < 0.35 0.35 ≤ D < 0.5 0.5 ≤ D < 0.75 D ≥ 0.75

Table 1.
Inspection-level parameters.

Date	Average daily passenger flow (persons)	Date	Average daily passenger flow (persons)
2018.1	6,138	2018.10	8,049
2018.2	6,284	2018.11	8,100
2018.3	7,155	2018.12	8,098
2018.4	8,064	2019.1	7,923
2018.5	8,266	2019.2	7,836
2018.6	9,406	2019.3	8,699
2018.7	11,484	2019.4	8,789
2018.8	13,036	2019.5	9,065
2018.9	8,976	2019.6	10,051

Table 2.

Average daily passenger flows into Shilaoren Bathing Beach Station on weekdays

Table 3.

The grey prediction model's predictions and relative error

Table 6.

Optimized data of the Markov model

Inspection-level accuracy	First-order accuracy	Second-order accuracy	Third-order accuracy	Fourth-order accuracy
D	D < 0.35	0.35 ≤ D < 0.5	0.5 ≤ D < 0.75	D ≥ 0.75

Parameter	$ \overline{X} $	S₁	$ \overline{q} $	S₂	D
Numerical value	8,634	1,661	1,023	1,093	0.658

Status range	E₁	E₂	E₃	E₄	E₅	E₆
Interval division	[−34, −12]	[−10, −9]	[−6, −3]	[−2, 0]	[2, 9]	[24, 34]