# Multi-View Travel Time Prediction Based on Electronic Toll Collection Data

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## Abstract

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## 1. Introduction

- We analyze the travel time of expressway, find out there are great differences in the travel time of different types of vehicles, and further verify the necessity of separate predictions for different types of vehicles.
- We propose a road network proximity feature for travel time prediction, which can perceive the correlation of adjacent sections in the space of the road network.
- We propose a novel travel time prediction model, which considers the road network proximity, temporal and spatial correlation, and can capture the key spatial-temporal information.
- We conducted extensive experiments on real- traffic datasets. The results show that our method consistently outperforms the competing baselines.

## 2. Related Work

## 3. Methodology

#### 3.1. Overview

#### 3.2. Notations and Problem Formulation

**ETC data**. When the vehicle passes through the ETC gantry, the Road Side Unit (RSU) on the gantry will conduct an information transaction with the On Board Unit (OBU) of the vehicle. The RSU will record the vehicle ID, the gantry ID, the time of information transaction, the expressway entrance of the vehicle, and other information and then upload it to the ETC system. This uploaded information constitutes the ETC data $Edata$.

**Section**: The ETC gantry of the expressway is called $Node$, the area between two adjacent gantries forms a section which is referred to as $QD=\u2329Dat,dis\u232a$, $Dat=\left\{Nod{e}_{1},Nod{e}_{2}\right\}$, where $dis$ is the distance between two nodes. $Node$ and $QD$ are shown in Figure 2. The set of all sections (i.e., expressway network) can be express as $LW=\{Q{D}_{1},Q{D}_{2},\dots ,Q{D}_{n}\}$.

**Vehicle trajectory**: A set of ETC gantry $Edata$ through which a vehicle passed while driving on the expressway, $Edata=\{RNod{e}_{1},RNod{e}_{2},RNod{e}_{n}\}$, $RNode=\u2329ID,Time,EnterID,\dots .\u232a$. $Edata$ are composed of multiple gantry transaction records, $RNode$. $RNodes$ contain more than 100 data attributes; $ID$ is the gantry Identity Document (ID); $Time$ is the transaction time of the gantry; $EnterID$ is the enter station ID. ETC data, $Edata,$ can be converted into vehicle trajectory data, $Edata\to Traj=\left\{{D}_{0},{D}_{1},Di\dots Dj,{D}_{E}\right\}$, ${D}_{i}=\left({N}_{i},{T}_{i}\right)$, $0\le i\le E$, $\forall i\le j,{T}_{i}\le {T}_{j}$. ${D}_{i}$ is the trajectory point, including node ${N}_{i}$ and time property ${T}_{i}$. ${N}_{i}$ is the label of the i-th node passed by the vehicle, and ${T}_{i}$ is the information interaction time when the vehicle passes through node ${N}_{i}$. ${D}_{0}$ is the start-point of the trajectory, and ${D}_{E}$ is the end-point of the trajectory.

**Vehicle type**: China’s license plates mainly include blue license plates, yellow license plates, green license plates, white license plates, and black license plates. In order to clarify the meaning of the vehicle type, the vehicle is divided into five categories according to the color of the license plate. They are Class A vehicle (blue license plate), Class B vehicle (yellow license plate), Class C vehicle (green license plate), Class D vehicle (white license plate), and Class E vehicle (black license plate). In addition, all vehicles together are called Class F vehicles.

**Travel time**: The time consumed by a vehicle passing a certain section $\u2329Node1,Node2\u232a$ is called travel time $\Delta t$:

**Travel time prediction problem**: The travel time prediction problem aims to predict the travel time of $t+1$ time interval, given the data until time interval $t$. In addition to historical travel time data, we also include relevant context features, including spatial proximity features, spatial correlation features, time correlation features, and traffic situation correlation features. We define the context feature of section $j$ at time point $i$ as a vector ${e}_{i}^{j}\in {\mathbb{R}}^{r}$, and $r$ as the number of features. Therefore, travel time prediction can be expressed as:

#### 3.3. Data Preprocessing

#### 3.3.1. Raw Data Cleaning

**Data redundancy**: The transaction information of each vehicle passing through the ETC gantry should be unique. However, data collection, transmission, storage procedures may not work properly, resulting in multiple uploads of data. Therefore, these data need to be cleaned.

**Data error**: Data attributes differ from normal traffic data. There are three main cases: The first is that the data are not normally collected, which is replaced by special characters (e.g., Error 1). The second is that data are lost due to abnormalities in the system during transmission, and the system uses random characters to replace lost data (e.g., Error 2, Error 4). The third is that the data do not conform to normal traffic rules (e.g., Error 3), the time of the trade station being later than the time of the enter station. Therefore, these data need to be cleaned

#### 3.3.2. Vehicle Travel Time Construction

Algorithm 1 Travel time window construction algorithm. |

Input: ETC data $Edata$; Expressway road network topology data $LW$; |

Output: Vehicle travel time data $Dt$; |

1: $Edata$ = $\left\{RNod{e}_{1},RNod{e}_{2},\dots ,RNod{e}_{n}\right\},$ $LW=\left\{Q{D}_{1},Q{D}_{2},\dots ,Q{D}_{n}\right\}$, $QD=\u2329Dat,Dis\u232a$; |

2: for $i$ = 0 to $i$ = $n-1$ do |

3: $\Delta {t}_{i}$ = $Tim{e}_{i+1}-Tim{e}_{i}$//Calculating the time difference of adjacent nodes; |

4: $Dat=\u2329RNod{e}_{i},Tim{e}_{i},RNod{e}_{i+1},Tim{e}_{i+1}\u232a$//save the information of adjacent nodes; |

5: $Dt$ = $\left(Dat,\Delta {t}_{i}\right)$,//save the vehicle passage information; |

6: end for |

7: if $RNod{e}_{i}$ and $RNod{e}_{i+1}$ in $LW$//if adjacent nodes are in topological data; |

8: $Dt$ = $\left(Dat,\Delta {t}_{i}\right)$//the vehicle passage time remains unchanged; |

9: else |

10: $Dis$ = {} |

11: $\left\{{N}_{1},{N}_{2},\dots ,{N}_{m}\right\}$ ← shortest path($LW,N$)//search for the shortest path, which $N=\left\{RNod{e}_{i},RNod{e}_{i+1}\right\}$; |

12: $Dis\leftarrow \left\{{N}_{1},{N}_{2},\dots ,{N}_{m}\right\}$//the shortest distance is converted into distance; |

13: ${v}_{i}=Dis/{N}_{i.Time}$//calculate the speed of the front and back gantry; |

14: $\Delta {t}_{i}={N}_{i+1.Time}-{N}_{i.Time}$ |

15: $Dat=\u2329{N}_{i},{N}_{i.Time},{N}_{i+1},{N}_{i+1.Time},\Delta t\u232a$ |

16: $Dt$ = $\left(Dat,\Delta {t}_{i}\right)$,//save the vehicle passage information; |

17: Return $Dt$ |

#### 3.3.3. Repair of Missing Data of Time Interval

Algorithm 2 The addition algorithm of missing data in time window. |

Input: $data=\left\{{x}_{1},{x}_{2},{x}_{3}\dots ,{x}_{n}\right\}$//The sequences with missing values; |

Output: $dat{a}^{*}=\left\{{x}_{1},{x}_{2},{x}_{3},{x}_{4}\dots ,{x}_{n}\right\}$//The complete sequence; |

1: for $i$ ← 0 to $n$ do |

2: if $i==0$ |

3: if $data\left[i\right]$ is $nan$ and $data\left[i+1\right]$, data $data\left[i+2\right]$ is not $nan$ |

4: $data\left[i\right]\leftarrow \left(\mathrm{data}\left[i+1\left]+\mathrm{data}\right[i+2\right]\right)/2$; |

5: end if |

6: end if |

7: if $i==1$ |

8: if $data\left[i\right]$ is $nan$ and $data\left[i-1\right]$, $data\left[i+1\right]$ is not $nan$ |

9: $data\left[i\right]\leftarrow \left(\mathrm{data}\left[i-1\left]+\mathrm{data}\right[i+1\right]\right)/2$; |

10: end if |

11: end if |

12: if $i>=2$ and $i<=\left(\mathrm{n}-3\right)$ |

13: if $data\left[i\right]$ is $nan$ and $data\left[i-1\right]$, $data\left[i+1\right]$ is not $nan$ |

14: $data\left[i\right]\leftarrow \left(\mathrm{data}\left[i-1\left]+\mathrm{data}\right[i+1\right]\right)/2$; |

15: end if |

16: if $data\left[i\right]$, $data\left[i+1\right]$ is $nan$ and $data\left[i-1\right]$, $data\left[i-2\right]$ is not $nan$: |

17: $data\left[i\right]\leftarrow \left(\mathrm{data}\left[i-1\left]+\mathrm{data}\right[i-2\right]\right)/2$; |

18: end if |

19: if $data\left[i\right]$, $data\left[i-1\right]$ is $nan$ and $data\left[i+1\right]$, $data\left[i+2\right]$ is not $nan$ |

20: $data\left[i\right]\leftarrow \left(\mathrm{data}\left[i+1\left]+\mathrm{data}\right[i+2\right]\right)/2$; |

21: end if |

22: end if |

23: if $i==n-2$ |

24: if $data\left[i\right]$ is $nan$ and $data\left[i-1\right]$, $data\left[i+1\right]$ is not $nan$ |

25: $data\left[i\right]\leftarrow \left(\mathrm{data}\left[i-1\left]+\mathrm{data}\right[i+1\right]\right)/2$; |

26: end if |

27: if $data\left[i\right]$, $data\left[i+1\right]$ is $nan$ and $data\left[i-1\right]$, $data\left[i-2\right]$ is not $nan$ |

28: $data\left[i\right]\leftarrow \left(\mathrm{data}\left[i-1\left]+\mathrm{data}\right[i-2\right]\right)/2$; |

29: end if |

30: end if |

31: if $i==n-1$ |

32: if $data\left[i\right]$ is $nan$ and $data\left[i-1\right]$, $data\left[i-2\right]$ is not $nan$ |

33: $data\left[i\right]\leftarrow \left(\mathrm{data}\left[i-1\left]+\mathrm{data}\right[i-2\right]\right)/2$; |

34: end if |

35: end if |

36: end for |

37: $dat{a}^{*}$←$data$ |

38: return $dat{a}^{*}$ |

#### 3.4. Travel Time Analysis and Modeling

#### 3.4.1. Differentiation Analysis of Vehicles

#### 3.4.2. Context Features Modeling

- (1)
- Spatial proximity features

- (2)
- Spatial correlation features

- (3)
- Temporal correlation features

- (4)
- Traffic situation features

#### 3.5. Deep Learning Prediction Model

#### 3.5.1. CNN-ATTENTION

#### 3.5.2. BiLSTM-ATTENTION

## 4. Results

#### 4.1. Experimental Settings and Data Description

#### 4.2. Evaluation Metric

#### 4.3. Analysis of Sequence Length

#### 4.4. Analysis of Classification Based on Vehicle Type

#### 4.5. Analysis of Spatial Proximity

#### 4.6. Analysis of Spatial-Temporal Attention Mechanism

#### 4.7. Comparative Analysis of Prediction Models

**HA:**Historical Average, the traditional time-series prediction methods, which predicts the travel time using average values of previous travel time values at the location given in the same relative time interval.

**KNN**: K-Nearest Neighbor, which is one of the most classical classification and regression methods in data mining.

**SVR**: Support vector regression model applies the support vector machine (SVM) similarity method for regression analysis.

**AdaBoost**: Adaptive Boosting. AdaBoost is a robust boosting tree-based method that is widely used in data mining applications.

**LSTM**: Long Short-Term Memory, a kind of time-recurrent neural network, which is good at processing time series data.

**CNN**: Convolutional Neural Network, which is widely used to capture the spatial correlation of time series for time series prediction.

**BiLSTM**[51]: Bi-directional Long Short-Term Memory, which is composed of forward LSTM and backward LSTM.

**TGCN**[52]: Time Domain Graph Convolutional Network, which is a well-known traffic forecasting method.

**STDN**[21]: Spatial-Temporal Dynamic Network, a method to jointly model both spatial and temporal dependencies by integrating CNN and LSTM.

## 5. Conclusions

- (1)
- There are big differences in travel time among all types of vehicles. The travel time of big vehicles with yellow license plates is much longer than others types of vehicles. The main difference in travel time can be divided into two categories: big vehicles with yellow license plates and small vehicles with the rest of the plate colors.
- (2)
- The predicted travel time without considering vehicle type is higher than the real travel time of small vehicles and smaller than the real travel time of big vehicles. The error of travel time prediction without considering the type of vehicle is about 10%. After considering the type of vehicle, the prediction performance of the model has been significantly improved, and the predicted values of the model are close to the real travel time values of the vehicle.
- (3)
- The expressway network has close proximity, and the travel time prediction model can further improve the prediction performance after using the road network proximity. At the same time, the temporal attention mechanism and spatial attention mechanism can capture more important information, which can further improve the prediction performance of the model, and the model combining the two attention mechanisms has the best prediction performance.
- (4)
- This proposal can accurately predict the travel time of each section, which is of great significance for the fine management of the expressway and the development of smart expressways.

## 6. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Travel times visualization of all types of vehicles: (

**a**) is a visualization of section 1; (

**b**) is a visualization of section 2.

**Figure 5.**Travel time statistics of different types of vehicles: (

**a**) is the statistics for section 1; (

**b**) is the statistics for section 2.

**Figure 6.**Average absolute error of travel time between different types of vehicles: (

**a**) is the statistics for section 1; (

**b**) is the statistics for section 2.

**Figure 13.**Visualization of travel time prediction, (

**a**) is a visualization of section 1; (

**b**) is a visualization of section 2; (

**c**) is a visualization of section 3; (

**d**) is a visualization of section 4.

Tradeid | Obuid | Tradetime | Flagid | Carplate | … |
---|---|---|---|---|---|

G001639 ** | 6A59 ** | 27 May 2021 6:21:38 | 3402 * | Blue MinA12 | … |

G001639 ** | 6A59 ** | 27 May 2021 6:21:38 | 3402 * | Blue Min A12 | … |

G001639 ** | 6A59 ** | 27 May 2021 6:21:38 | 3402 * | Blue Min A12 | … |

G001639 ** | 6A59 ** | 27 May 2021 6:21:38 | 3402 * | Blue Min A12 | … |

Class | Obuid | Entime | Flagid | Ttradetime | … |
---|---|---|---|---|---|

Error 1 | 62F3 ** | 000000 | 3502 * | 20 May 2021 11:21:38 | … |

Error 2 | 6873 ** | 22 May 2021 7:31:54 | a6p823 | 22 May 2021 13:11:50 | … |

Error 3 | 628A ** | 25 May 2021 8:21:38 | 350A * | 25 May 2021 0:56:32 | … |

Error 4 | 236d45 | 29 May 2021 9:29:11 | 3502 * | 29 May 2021 15:23:11 | … |

Adjacent sections | ${T}_{j-1}$ | ${T}_{j-2}$ | ${T}_{j-3}$ | ${T}_{j-4}$ |

$\mathit{\rho}$ | 0.63 | 0.59 | 0.36 | 0.32 |

Adjacent sections | ${T}_{j+1}$ | ${T}_{j+2}$ | ${T}_{j+3}$ | ${T}_{j+4}$ |

$\mathit{\rho}$ | 0.60 | 0.51 | 0.38 | 0.263 |

Attribute Name | Examples | Attribute Name | Examples |
---|---|---|---|

Trade ID | 452 *** 56 | OBU Plate | Blue Fujian A1 ** 45 |

Trade time | 6 September 2020 21:29:26 | Vehicle Class | 1 |

Flag ID | 33 ** 21 | Enter Time | 6 September 2020 20:23:51 |

Flag Type | 0 | Enter Station | 16 * 7 |

Flag Index | 1 | OBU ID | 11C *** B6 |

LAT | 118.39 ** | LNG | 24.66 *** |

Model | Class II Vehicles | Class I Vehicles | ||
---|---|---|---|---|

MAE | RMSE | MAE | RMSE | |

Unconsidering vehicle type | 36.3128 | 57.9982 | 59.3436 | 84.8430 |

MVPPT | 8.50313 | 19.1132 | 11.5529 | 18.6298 |

Model | Class II Vehicle | Class I Vehicle | ||
---|---|---|---|---|

MAE | RMSE | MAE | RMSE | |

MVPPT without spatial closeness | 9.0033 | 21.7577 | 11.8418 | 19.6733 |

MVTTP | 8.50313 | 19.1132 | 11.5529 | 18.6298 |

Model | Class II Vehicles | Class I Vehicles | ||
---|---|---|---|---|

MAE | RMSE | MAE | RMSE | |

MVTTP without any Attention | 8.9798 | 19.9776 | 11.8078 | 19.4728 |

MVTTP without spatial Attention | 8.890931878 | 19.80547952 | 11.6711 | 19.4977 |

MVTTP without temporal Attention | 8.852875979 | 19.86132629 | 11.6877 | 19.4169 |

MVTTP | 8.50313 | 19.1132 | 11.5529 | 18.6298 |

Model | Class II Vehicles | Class I Vehicles | ||
---|---|---|---|---|

MAE | RMSE | MAE | RMSE | |

HA | 19.7064 | 37.3719 | 23.1210 | 33.7131 |

KNN | 15.9966 | 31.5796 | 18.2482 | 28.7021 |

SVR | 11.8366 | 23.1494 | 14.9408 | 20.9557 |

AdaBoost | 12.464 | 28.9111 | 13.7415 | 21.3218 |

CNN | 12.6426 | 26.7706 | 15.5382 | 24.5275 |

LSTM | 9.7911 | 20.8325 | 12.0161 | 19.4116 |

BiLSTM | 9.5706 | 22.7144 | 11.8629 | 19.2269 |

TGCN | 14.7399 | 30.7650 | 16.4463 | 31.8081 |

STDN | 9.3075 | 20.5715 | 11.9132 | 19.3659 |

MVPPT | 8.50313 | 19.1132 | 11.5529 | 18.6298 |

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## Share and Cite

**MDPI and ACS Style**

Luo, S.; Zou, F.; Zhang, C.; Tian, J.; Guo, F.; Liao, L.
Multi-View Travel Time Prediction Based on Electronic Toll Collection Data. *Entropy* **2022**, *24*, 1050.
https://doi.org/10.3390/e24081050

**AMA Style**

Luo S, Zou F, Zhang C, Tian J, Guo F, Liao L.
Multi-View Travel Time Prediction Based on Electronic Toll Collection Data. *Entropy*. 2022; 24(8):1050.
https://doi.org/10.3390/e24081050

**Chicago/Turabian Style**

Luo, Sijie, Fumin Zou, Cheng Zhang, Junshan Tian, Feng Guo, and Lyuchao Liao.
2022. "Multi-View Travel Time Prediction Based on Electronic Toll Collection Data" *Entropy* 24, no. 8: 1050.
https://doi.org/10.3390/e24081050