# Artificial Neural Networks for Forecasting Passenger Flows on Metro Lines

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Background

#### 2.1. Artificial Neural Networks

#### 2.2. Road Traffic Flow Forecasting

#### 2.3. Metro Passenger Flow Forecasting

#### 2.4. Contribution of the Paper

## 3. Problem Description and ANN Approach

## 4. Generation of Training Datasets

- platforms can accommodate all passengers (incoming, waiting and outgoing);
- at each station and for each direction there is only one platform available;
- the dwell time is constant and independent of the number of passengers alighting and boarding;
- there is no interaction on the platform between alighting, boarding and waiting passengers;
- the capacity of each train is fixed;
- passengers are distributed uniformly among the train coaches;
- there is no interaction in the train between alighting, boarding and onboard passengers.

- -
- ds is the number of datasets;
- -
- t is the period under analysis;
- -
- c
^{i}_{j,t}is the passenger count at turnstile j in period t for dataset i; - -
- f
^{i}_{k,t}is the load on railway section k in period t for dataset i.

## 5. Case Study and Numerical Results

^{2}) for each case, referring to the 50 datasets not used in the training phase, and the corresponding averages and variances. The datasets for which R

^{2}is lower than 0.9, 0.8, 0.7 and 0.6 are reported in Table 5. In these tables, the best values for each ANN are underlined.

^{2}are reported in Figure 3 and Figure 4.

## 6. Conclusions and Research Prospects

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Types of metro stations: (

**a**) turnstiles at the entrance; (

**b**) turnstiles at platform accesses.

Dataset → | 1 | 2 | … | ds |
---|---|---|---|---|

Input data | ||||

Turnstile 1–Period t − 1 | c^{1}_{1,t−1} | c^{2}_{1,t−1} | … | c^{ds}_{1,t−1} |

Turnstile 2–Period t − 1 | c^{1}_{2,t−1} | c^{2}_{2,t−1} | … | c^{ds}_{2,t−1} |

… | … | … | … | … |

Turnstile ts–Period t − 1 | c^{1}_{ts}_{,t−1} | c^{2}_{ts}_{,t−1} | … | c^{ds}_{ts}_{,t−1} |

Turnstile 1–Period t − 2 | c^{1}_{1,t−2} | c^{2}_{1,t−2} | … | c^{ds}_{1,t−2} |

Turnstile 2–Period t − 2 | c^{1}_{2,t−2} | c^{2}_{2,t−2} | … | c^{ds}_{2,t−2} |

… | … | … | … | … |

Turnstile ts–Period t − 2 | c^{1}_{ts}_{,t−2} | c^{2}_{ts}_{,t−2} | … | c^{ds}_{ts}_{,t−2} |

Turnstile 1–Period t − 3 | c^{1}_{1,t−3} | c^{2}_{1,t−2} | … | c^{ds}_{1,t−2} |

Turnstile 2–Period t − 3 | c^{1}_{2,t−2} | c^{2}_{2,t−3} | … | c^{ds}_{2,t−3} |

… | … | … | … | … |

Turnstile ts–Period t − 3 | c^{1}_{ts}_{,t−3} | c^{2}_{ts}_{,t−3} | … | c^{ds}_{ts}_{,t−3} |

Turnstile 1–Period t − 4 | c^{1}_{1,t−4} | c^{2}_{1,t−4} | … | c^{ds}_{1,t−4} |

Turnstile 2–Period t − 4 | c^{1}_{2,t−4} | c^{2}_{2,t−4} | … | c^{ds}_{2,t−4} |

… | … | … | … | … |

Turnstile ts–Period t − 4 | c^{1}_{ts}_{,t−4} | c^{2}_{ts}_{,t−4} | … | c^{ds}_{ts}_{,t−4} |

Output data | ||||

Railway section 1–Period t | f^{1}_{1,t} | f^{2}_{1,t} | … | f^{ds}_{1,t} |

Railway section 2–Period t | f^{1}_{2,t} | f^{2}_{2,t} | … | f^{ds}_{2,t} |

… | … | … | … | … |

Railway section rs–Period t | f^{1}_{rs}_{,t} | f^{2}_{rs}_{,t} | … | f^{ds}_{rs}_{,t} |

Stations | 18 |

Working day runs | 241 |

Convoy capacity (pax/convoy) | 864 |

Line length (km) (outward/return direction) | 18.8/18.6 |

Headway (min) | 8–20 |

Case | ANN | Input Nodes | Output Nodes | Hidden Layers | Neurons |
---|---|---|---|---|---|

a | a_1_6 | 72 | 34 | 1 | 6 |

a | a_1_10 | 72 | 34 | 1 | 10 |

a | a_1_20 | 72 | 34 | 1 | 20 |

a | a_2_6 | 72 | 34 | 2 | 6/6 |

a | a_2_10 | 72 | 34 | 2 | 10/10 |

a | a_2_20 | 72 | 34 | 2 | 20/20 |

b | b_1_6 | 136 | 34 | 1 | 6 |

b | b_1_10 | 136 | 34 | 1 | 10 |

b | b_1_20 | 136 | 34 | 1 | 20 |

b | b_2_6 | 136 | 34 | 2 | 6/6 |

b | b_2_10 | 136 | 34 | 2 | 10/10 |

b | b_2_20 | 136 | 34 | 2 | 20/20 |

ANN | Best | Worst | Average | Variance |
---|---|---|---|---|

a_1_6 | 0.9946 | 0.5487 | 0.7984 | 0.0124 |

a_1_10 | 0.9941 | 0.4990 | 0.8108 | 0.0160 |

a_1_20 | 0.9931 | 0.5613 | 0.8332 | 0.0157 |

a_2_6 | 0.9916 | 0.5353 | 0.7949 | 0.0121 |

a_2_10 | 0.9930 | 0.4638 | 0.8136 | 0.0175 |

a_2_20 | 0.9933 | 0.5342 | 0.8244 | 0.0162 |

b_1_6 | 0.9875 | 0.5460 | 0.8016 | 0.0129 |

b_1_10 | 0.9905 | 0.3505 | 0.8115 | 0.0202 |

b_1_20 | 0.9882 | 0.4226 | 0.8291 | 0.0160 |

b_2_6 | 0.9785 | 0.5119 | 0.7775 | 0.0132 |

b_2_10 | 0.9889 | 0.4935 | 0.8221 | 0.0132 |

b_2_20 | 0.9852 | 0.4492 | 0.8075 | 0.0245 |

ANN | R^{2} < 0.9 | R^{2} < 0.8 | R^{2} < 0.7 | R^{2} < 0.6 |
---|---|---|---|---|

Number of datasets | ||||

a_1_6 | 41 | 25 | 9 | 4 |

a_1_10 | 36 | 22 | 7 | 4 |

a_1_20 | 33 | 18 | 7 | 3 |

a_2_6 | 43 | 25 | 10 | 3 |

a_2_10 | 35 | 21 | 8 | 4 |

a_2_20 | 34 | 19 | 9 | 5 |

b_1_6 | 37 | 24 | 10 | 2 |

b_1_10 | 34 | 23 | 8 | 5 |

b_1_20 | 32 | 19 | 8 | 3 |

b_2_6 | 43 | 25 | 10 | 6 |

b_2_10 | 35 | 20 | 7 | 2 |

b_2_20 | 30 | 21 | 9 | 7 |

Percentage of datasets | ||||

a_1_6 | 82% | 50% | 18% | 8% |

a_1_10 | 72% | 44% | 14% | 8% |

a_1_20 | 66% | 36% | 14% | 6% |

a_2_6 | 86% | 50% | 20% | 6% |

a_2_10 | 70% | 42% | 16% | 8% |

a_2_20 | 68% | 38% | 18% | 10% |

b_1_6 | 74% | 48% | 20% | 4% |

b_1_10 | 68% | 46% | 16% | 10% |

b_1_20 | 64% | 38% | 16% | 6% |

b_2_6 | 86% | 50% | 20% | 12% |

b_2_10 | 70% | 40% | 14% | 4% |

b_2_20 | 60% | 42% | 18% | 14% |

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**MDPI and ACS Style**

Gallo, M.; De Luca, G.; D’Acierno, L.; Botte, M.
Artificial Neural Networks for Forecasting Passenger Flows on Metro Lines. *Sensors* **2019**, *19*, 3424.
https://doi.org/10.3390/s19153424

**AMA Style**

Gallo M, De Luca G, D’Acierno L, Botte M.
Artificial Neural Networks for Forecasting Passenger Flows on Metro Lines. *Sensors*. 2019; 19(15):3424.
https://doi.org/10.3390/s19153424

**Chicago/Turabian Style**

Gallo, Mariano, Giuseppina De Luca, Luca D’Acierno, and Marilisa Botte.
2019. "Artificial Neural Networks for Forecasting Passenger Flows on Metro Lines" *Sensors* 19, no. 15: 3424.
https://doi.org/10.3390/s19153424