# A Comprehensive Comparative Analysis of the Basic Theory of the Short Term Bus Passenger Flow Prediction

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## Abstract

**:**

## 1. Introduction

## 2. Short-Term Bus Passenger Flow Prediction Objects and Data Source

#### 2.1. Short-Term Bus Passenger Flow Prediction Objects

#### 2.2. Data Source

#### 2.3. Data Formats

#### 2.3.1. Data Format of AFC

#### 2.3.2. Data Format of the APC

#### 2.3.3. Data Format of the Vehicle Intelligent Terminal

## 3. Linear Methods for Short-Term Bus Passenger Flow Forecast

#### 3.1. Kalman Filter-Based Method

#### 3.1.1. Kalman Filter

#### 3.1.2. Applications of the Kalman Filter Method in Short-Term Bus Passenger Flow Prediction

#### 3.2. Time Series-Based Method for Short-Term Prediction

#### 3.2.1. Time Series Theory

#### 3.2.2. Applications of Time Series Method in Short-Term Bus Passenger Flow Prediction

^{7}for daily time series, and ARIMA(2,1,0) for hourly time series. Xue [36] selects ARMA(2,2) for weekly time series, SARIMA(2,0,3)(1,0,0)

^{24}for daily time series, and ARIMA(2,1,0) for hourly time series. The models selected by Ma [35] and Xue [36] fully prove that the weekly time series is a stationary sequence, from which it is speculated that the passenger variation is similar in the same time interval on the same weekday. The daily model reveals the cyclical variation of the passenger flow at the same time interval of different weekday during a cycle of week. The hourly model shows the obvious variation trend of the passenger flow in successive time intervals, such as the peak and off-peak period. Different time series model with different sampling interval will reveal different variation rules of passenger flow and, depending on different factors effecting the passenger flow variation, the predicted results will be different. Both studies propose an IMM-based algorithm, which combined different models prediction result together, and output final prediction in order to match the different situation. The details of the IMM algorithm will be discussed in Section 5.

#### 3.3. Other Linear Models for Short-Term Bus Passenger Flow Prediction

## 4. Nonlinear Methods for Short-Term Bus Passenger Flow Prediction

#### 4.1. Support Vector Machine Regression-Based Methods for Short-Term Passenger Flow Prediction

#### 4.1.1. Support Vector Machine Regression

_{i},x

_{j}) = ϕ(x

_{i}) · ϕ(x

_{j}) to change a non-linear regression problem in a low-dimensional space to a linear regression problem in a higher dimensional space. The detailed proof can be found in [39,42]. There are different kinds of kernel functions, such as linear kernel, polynomial kernel, radial base function (RBF), and sigmoid kernel function, etc., used for creating models. More information about the kernel function can be found in [43], which introduces the kernel functions used in the SVM application completely.

#### 4.1.2. Applications of SVR in Short-Term Bus Passenger Flow Prediction

#### 4.2. Artificial Neural Network-Based Methods for Short-Term Passenger Flow Prediction

#### 4.2.1. Artificial Neural Network

#### 4.2.2. Applications of ANN in Short-Term Bus Passenger Flow Prediction

#### 4.3. Other Nonlinear Methods for Short-Term Passenger Flow Prediction

## 5. Combined Methods for Short-Term Bus Passenger Flow Prediction

^{7}model is selected to predict ArPC and ESC. Compared with real data, the average relative errors of prediction results are 2.94% of ArPC and 3.02% of ESC. The second stage is to predict the DPC, which is triggered by the bus arrival events (BAEs) at a bus stop in each time interval. Under the author’s assumption, the boarding count of BAE is the minimum of the passengers waiting at the stop and the empty space available on the bus. The boarding count $d$ is collected from the APC, so the DPC is the sum of the boarding count of every BAE happened during the time interval $t$. Therefore, predicting DPC is equivalent to predicting the BAEs at the corresponding stop. Using bus trajectory records from the AVL, an event-based algorithm is proposed to predict the bus arrival time, and combining with the predict results of ArPC and ESC in the first step, the DPC can be predicted. The third stage has been discussed in the previous section. At the end of the literature, a numerical experiments conducted at three typical bus stops are illustrated to demonstrate that the proposed framework is robust and accurate.

_{1}, M

_{2}, … M

_{z}} is the set of z models of interest to model a given time series and M

_{t}= {M

_{1t}, M

_{2t}, … M

_{zt}} is the set of prediction values of the next period in the time interval t by those models. P

_{i}H is the forecasting accuracy of the model M

_{i}in the time window [t − H, t]. The prediction results show that the accuracy of the ensemble framework is around 79%, which is better than the single models. The ensemble framework in [66] is used to develop a prototype APP for mobile phone users to predict the crowdedness of the bus.

## 6. Big Data Technology and Deep Learning Used for Short-Term Bus Passenger Flow Prediction

## 7. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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Field Name | Illustration |
---|---|

Card ID | The unique number of the smart card |

Type of smart card | Normal card, coupon card, etc. |

Driver ID | The unique number of the current bus driver |

Line ID | The unique number of the bus line |

Vehicle ID | The unique number of the vehicle |

Balance | The balance of the smart card after the last transaction |

Transaction amount | The transaction amount of the last transaction |

Transaction count | The total number of the transaction count with this smart card |

Transaction time | The time of the last transaction |

Field Name | Illustration |
---|---|

Equipment ID | The unique number of the equipment |

On/off | Denotes the passenger getting on or off the bus |

Vehicle ID | The unique number of the vehicle |

Line ID | The unique number of the bus line |

Trip type | Denotes the current trip is up run or down run |

Stop ID | The unique number of stops, where the bus stops at the current time |

Count time | The time when the passenger scans through the AFC |

Stop accumulation | The total number of the passengers getting on or off at a stop |

Field Name | Illustration |
---|---|

Equipment ID | The unique number of the vehicle intelligent terminal system |

Vehicle ID | The unique number of the vehicle |

Driver ID | The unique number of the driver |

Longitude | The longitude of the current vehicle position |

Latitude | The latitude of the current vehicle position |

Speed | The vehicle real-time speed |

Heading | The vehicle heading direction at the current time |

Line ID | The unique number of the bus line |

Stop ID | The unique number of stop, where the bus stops at the current time |

Distance | The relative distance from the current position to the last station |

Cumulative distance | The total mileage of the vehicle |

State | The state of the vehicle intelligent terminal system |

Categories | AR(p) | MA(q) | ARMA(p, q) |
---|---|---|---|

ACF | Tails off exponentially | Cuts off after lag q | Tails off exponentially |

PACF | Cuts off after lag p | Tails off exponentially | Tails off exponentially |

Author(s) | Method | Contrast Method | Method Style | Predict Object | Data Source | Data Structure ^{a} | Modeling Difficulty ^{b} | Universality of Model ^{c} | Accuracy |
---|---|---|---|---|---|---|---|---|---|

Zhang (2011) [23] | Kalman filter | BP-ANN | Single | Stop | AFC Video | Simple | Complex | Weak | around 80% |

Gu (2011) [34] | ARMA(2,1) | GM(1,1) | Single | Hub | Manual survey | Simple | Easy | Middle | around 80% |

Yang(2009) [37] | Linear regression | Real data | Single | Line | AFC | Complex | Easy | Weak | NA |

Yang (2016) [44] | AP(6) based SVM | AP(p) based SVM | Single | Stop | Manual survey | Complex | Low complexity | Middle | Over 85% |

Guo (2013) [45] | LSSVM | LSSVM with different factors | Single | Stop | Manual survey | Low complexity | Low complexity | Weak | MAE 0.625 MSE 0.9145 |

Deng (2012) [12] | Multiple kernel LSSVM | Single kernel LSSVM | Single | Stops | AFC | Simple | Low complexity | Middle | EC 0.9544 |

Yang (2000) [58] | Fuzzy ANN | AR ARMA | Single | Line | Manual survey | Low complexity | Low complexity | Weak | ME 7.47% |

Liu(2008) [59] | BP-ANN | Real data | Single | Stops | NA | Low complexity | Low complexity | Middle | EC 0.901 |

Lu(2015) [14] | RBF-ANN | Real data | Single | Stops | AFC | Simple | Low complexity | High | ME/MSE less 1.5% |

Wen(2009) [60] | Fuzzy ANN | Real data | Single | Line (key stops) | Manual survey | Simple | Low complexity | Middle | ME less 10% |

Dong (2013) [61] | BP-ANN Improved BP-ANN RBF-ANN | Real data | Single | Line | AFC | Simple | Low complexity | Middle | EC 0.9697 EC 0.9758 EC 0.974 |

Liu (2011) [62] | GM(1,1) | Real data | Single | Line | AFC | Simple | Low complexity | Weak | RE less 10% |

Zhang(2017) [63] | GM(1,1) | Real data | Single | Line | Manual survey | Simple | Easy | Middle | RE Less 10% |

Li (2015) [74] | BP-ANN with Hadoop | MA, ES, real data | Single | Lines | AFC | Complex | Complex | Middle | RMSE 21.61% |

^{a}Complexity of data structure increased from simple, low complexity, complex, to highly complex;

^{b}Modeling difficulty increased by easy, low complexity, complex, to highly complex;

^{c}Universality of the model increased from weak, middle, to high.

Author(s) | Method | Contrast Method | Method Style | Predict Object | Data Source | Data Structure | Modeling Difficulty | Universality of Model | Accuracy |
---|---|---|---|---|---|---|---|---|---|

Gong (2014) [13] | Kalman filter based ARIMA | Direct-addition | Combination | Stop | APC and video | Complex | Complex | Weak | RE around 3% |

Ma (2014) [35] | IMMPH with AR, SARIMA, ARIMA | ANNPH | Combination | Line | AFC | Complex | Highly complex | Weak | MAPE 5.82% |

Xue (2015) [36] | IMM with ARMA, SARIMA,ARIMA | Real data | Combination | Line | AFC | Complex | Highly complex | Weak | MAPE 9.084% |

Liu (2010) [38] | Wavelet with ARMA | ARMA | Combination | Stop | Not available | Simple | Complex | Weak | MAPE 0.18 |

Liu (2014) [67] | BP-ANN LSSVM | Real data | Combination | Hub | History statistics | Simple | Low complexity | Middle | 94.05% |

Zhou (2013) [66] | Poisson model ARIMA | Real data | Combination | Stop | APTS | Complex | Complex | Weak | Around 79% |

Pekel (2017) [68] | POA-ANN IWD-ANN | GA-ANN | Combination | Line | AFC | Simple | Low complexity | Middle | MSE less 0.1 |

Liu (2017) [75] | SAE-DNN | Real data | combination | Stops | AFC | Complex | Complex | High | Best MAPE over 75% |

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**MDPI and ACS Style**

Zhai, H.; Cui, L.; Nie, Y.; Xu, X.; Zhang, W.
A Comprehensive Comparative Analysis of the Basic Theory of the Short Term Bus Passenger Flow Prediction. *Symmetry* **2018**, *10*, 369.
https://doi.org/10.3390/sym10090369

**AMA Style**

Zhai H, Cui L, Nie Y, Xu X, Zhang W.
A Comprehensive Comparative Analysis of the Basic Theory of the Short Term Bus Passenger Flow Prediction. *Symmetry*. 2018; 10(9):369.
https://doi.org/10.3390/sym10090369

**Chicago/Turabian Style**

Zhai, Huawei, Licheng Cui, Yu Nie, Xiaowei Xu, and Weishi Zhang.
2018. "A Comprehensive Comparative Analysis of the Basic Theory of the Short Term Bus Passenger Flow Prediction" *Symmetry* 10, no. 9: 369.
https://doi.org/10.3390/sym10090369