# An MFD Construction Method Considering Multi-Source Data Reliability for Urban Road Networks

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Materials and Methods

- (1)
- MFD construction using VTD

- (2)
- MFD construction using CSD

- (3)
- MFD construction using multi-source data based on DS evidence theory

#### 3.1. MFD Construction Using VTD

#### 3.2. MFD Construction Using CSD

#### 3.3. A Fusion Method for MFD Construction Using Multi-Source Data

## 4. Case Study

#### 4.1. Data Preprocessing for VTD

#### 4.2. The Data Preprocessing for ALPR Data

#### 4.3. The Preprocessing for Microwave Detector Data

## 5. Results

#### 5.1. Results of Key Parameters of MFD Construction Using Multi-Source Data

#### 5.2. Results of MFD Construction Based on Multi-Source Data

#### 5.3. The Evaluation of Constructed MFD’s Accuracy Based on Traffic Simulation

## 6. Conclusions and Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ALPR data | Automatic license plate recognition data |

ATD | Average traffic density of road network |

ATF | Average traffic flow of road network |

CSD | Cross-sectional data of traffic flow |

DS evidence | Dempster–Shafer evidence theory |

GPS | Global positioning system |

MFD | Macroscopic Fundamental Diagram |

OD | Origins and destinations |

Q-PARAMICS | Quadtone Parallel Microscopic Simulator |

TTS | Total travel time spent |

TTD | Total travel distance |

VTD | Vehicle trajectory data |

$\mathcal{F}{N}_{ij}\left(t\right)$ | The count of detected probe vehicles from ALPR detectors for ${O}_{i}{D}_{j}$ during period $t$ |

$\mathcal{F}N\left(t\right)$ | The count of probe vehicles detected by ALPR detectors during period $t$ (vehs) |

${k}_{t}^{P},{k}_{t}^{S}$ | ATD derived from simulated full-sample data and simulated multi-source data during period $t$ |

${k}_{max}$ | The maximum ATD (vehs/km) |

$L$ | The length of road network(km) |

$\mathcal{L}{N}_{ij}\left(t\right)$ | The count of all detected vehicles from ALPR detectors for ${O}_{i}{D}_{j}$ during period $t$ |

$\mathcal{L}N\left(t\right)$ | The count of all vehicles detected by ALPR detectors during period $t$ (vehs) |

${l}_{i}^{\mathcal{M}}$ | The length of $i$-th link installed with fixed vehicle detector |

$m,n$ | The count of the first links and last links installed with ALPR detectors that the probe vehicles passed by during period $t$ |

${O}_{i},{D}_{j}$ | The first and last link installed with ALPR detectors that the probe vehicles passed by |

${p}_{ij}\left(t\right)$ | The penetration rate of ${O}_{i}{D}_{j}$ during period $t$ |

$\overline{p}\left(t\right)$ | The averaged penetration rate for road network during period $t$ |

${p}_{i}\left({X}_{j}\left(t\right)\right)$ | The basic probability distribution of the decision ${X}_{j}\left(t\right)$ under each type of data |

$q,k$ | Average traffic flow (vehs/h), average traffic density (vehs/km) |

${q}^{\mathcal{F}}\left(t\right),{k}^{\mathcal{F}}\left(t\right)$ | The average traffic flow and traffic density based on vehicle trajectory data during period $t$ |

${q}^{\mathcal{M}}\left(t\right),{k}^{\mathcal{M}}\left(t\right)$ | The average traffic flow and average traffic density based on cross-sectional data during period $t$ |

${q}_{i}^{\mathcal{M}}\left(t\right),{k}_{i}^{\mathcal{M}}\left(t\right)$ | The traffic flow and traffic density of the $i$-th link installed with fixed vehicle detector during period $t$ |

$q\left(t\right),k\left(t\right)$ | The average traffic flow and traffic density with fusion method |

${q}_{t}^{P},{q}_{t}^{S}$ | The ATF derived from simulated full-sample data and simulated multi-source data during period $t$ |

$Q$ | The network traffic capacity (vehs/h) |

$RMSE\left(q,k\right)$ | The root mean square error for ATF and ATD of the test site |

${s}_{i}\left({X}_{j}\left(t\right)\right)$ | The degree of support for the decision ${X}_{j}\left(t\right)$ provided by the $i$-th type of data evidence |

$tt{d}_{ij}^{\mathcal{F}}\left(t\right),tt{s}_{ij}^{\mathcal{F}}\left(t\right)$ | Probe vehicles’ travel distance and travel time of ${O}_{i}{D}_{j}$ in road network during period $t$ |

$W$ | The number of fixed vehicle detectors |

$\Delta $ | Research period |

$\alpha \left(t\right)$ | The weight of VTD and CSD for traffic flow estimation during period $t$ |

$\beta \left(t\right)$ | The weight of VTD and CSD for traffic density estimation during period $t$ |

$\Theta \left(t\right)$ | The recognition framework of DS evidence inference model during period $t$ |

${X}_{1}\left(t\right),{X}_{2}\left(t\right)$ | The decision of ATF based on CSD and VTD |

${X}_{3}\left(t\right)$ | Uncertain decision in DS evidence model |

${\mu}_{i}\left(t\right),$ ${\sigma}_{i}^{2}\left(t\right)$ | The mean and variance of ATF during period $t$ for the historical data of the $i$-th type of data |

$1/{K}_{D}$ | The conflict coefficient between evidence provided by different types of data |

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**Figure 4.**The parameter estimation of MFD for different data sources from 8 January to 14 January 2018. (

**a**) The time series of TTS for probe vehicles. (

**b**) The time series of TTD for probe vehicles. (

**c**) The time series of ATD derived from CSD. (

**d**) The time series of ATF derived from CSD.

**Figure 5.**The boxplot of average penetration rates of probe vehicles from 3 January to 20 January 2018.

**Figure 6.**The boxplot of average penetration rates of probe vehicles in each period for weekdays and weekends from 3 January to 20 January 2018.

**Figure 7.**The dynamic fusion weight of MFD’s parameters for different sources of data on weekdays: (

**a**) the dynamic fusion weight for ATD; (

**b**) the dynamic fusion weight for ATF.

**Figure 8.**The estimated parameters of MFD under different sources of data on 4 January 2018. (

**a**) The ATD of each period under different sources of data. (

**b**) The ATF of each period under different sources of data.

**Figure 9.**The boxplot of the parameters of MFD for weekdays and weekends from 3 January to 20 January 2018. (

**a**) The boxplot of the ATD of each period. (

**b**) The boxplot of the ATF of each period.

**Figure 13.**The parameter and the scatter plot of the constructed MFD using simulated data. (

**a**) The estimated ATD. (

**b**) The estimated ATF. (

**c**) The scatter plot of MFD.

The Type of Data | Data Sources | Method | Representative Research |
---|---|---|---|

Cross-sectional data of traffic flow | Loops and microwave detectors | Weighted average method | Geroliminis and Daganzo [1] |

VISSIM simulation | Weighted average method | Ortigosa and Menendez [7] | |

Loop detectors | Unweighted average method | Buisson and Ladier [8] | |

Simulation | Weighted average method | Courbon and Leclercq [9] | |

Simulation | Weighted average method | Leclercq [10] | |

Vehicle trajectory data | Taxi GPS | Edie’s method | Geroliminis and Daganzo [1] |

Simulation | Edie’s method | Courbon and Leclercq [9] | |

Simulation | Edie’s method | Leclercq [10] | |

Mobile probe data | Edie’s method | Nagle and Gayah [12] | |

Multi-source data | Loop detectors data and floating car data | Weighted average method, Edie’s method, and fusion algorithm considering network coverage of each data type | Ambühl and Menendez [13] |

Loop detector data and floating car data from simulation | Weighted average method, Edie’s method, and Bayesian fusion method | Saffari et al. [16] | |

Loop detectors and taxi GPS | Weighted average method, Edie’s method | Ji et al. [20] | |

Microwave vehicle detectors, automatic license plate recognition equipment, taxi GPS | Weighted average method, Edie’s method, and DS evidence theory fusion method | This article |

License_ Plate | Date_Key | Time_Key | Status | Latitude | Longitude | Speed | Direction |
---|---|---|---|---|---|---|---|

***** ZF | 20180104 | 07:32:04 | 0 | 31.391811 | 120.959656 | 5 | WB |

***** ZF | 20180104 | 07:32:24 | 0 | 31.392311 | 120.959145 | 25 | NB |

***** ZF | 20180104 | 07:32:44 | 0 | 31.39361 | 120.959045 | 27 | NB |

***** ZF | 20180104 | 07:33:04 | 0 | 31.394411 | 120.959045 | 17 | NB |

***** ZF | 20180104 | 07:33:24 | 0 | 31.395313 | 120.959045 | 15 | NB |

***** ZF | 20180104 | 07:33:44 | 0 | 31.39561 | 120.959045 | 0 | NB |

***** ZF | 20180104 | 07:34:04 | 1 | 31.395512 | 120.959045 | 3 | NB |

***** ZF | 20180104 | 07:35:04 | 1 | 31.39592 | 120.962555 | 16 | EB |

***** ZF | 20180104 | 07:36:04 | 1 | 31.394623 | 120.96416 | 18 | SB |

ID | Date_Key | Time_Key | License_Plate | Lane |
---|---|---|---|---|

1995 | 20180104 | 07:13:00 | ***** 70 | 1 |

710 | 20180104 | 07:13:00 | ***** 1N | 3 |

664 | 20180104 | 07:13:00 | ***** 79 | 2 |

459 | 20180104 | 07:13:00 | ***** 27 | 1 |

870 | 20180104 | 07:13:00 | ***** 1K | 1 |

220 | 20180104 | 07:13:00 | ***** 17 | 3 |

156 | 20180104 | 07:13:00 | ***** U9 | 3 |

856 | 20180104 | 07:13:00 | ***** 29 | 1 |

1888 | 20180104 | 07:13:00 | ***** PC | 1 |

1940 | 20180104 | 07:13:00 | unrecognized | 1 |

ID | Lane_ID | Date_Key | Time_Key | Flow | Speed | Occupancy |
---|---|---|---|---|---|---|

14752043516 | 2 | 20180104 | 07:01:30 | 11 | 45 | 0.13 |

14752043516 | 2 | 20180104 | 07:02:00 | 8 | 41 | 0.11 |

14752043516 | 2 | 20180104 | 07:04:00 | 9 | 52 | 0.09 |

14752043516 | 2 | 20180104 | 07:06:00 | 7 | 60 | 0.08 |

14752043516 | 2 | 20180104 | 07:07:30 | 0 | 0 | 0 |

14752043516 | 2 | 20180104 | 07:08:00 | 3 | 59 | 0.02 |

14752043516 | 2 | 20180104 | 07:09:00 | 10 | 55 | 0.09 |

14752043516 | 2 | 20180104 | 07:09:30 | 3 | 54 | 0.05 |

14752043516 | 2 | 20180104 | 07:10:00 | 1 | 48 | 0.01 |

14752043516 | 2 | 20180104 | 07:11:00 | 6 | 45 | 0.08 |

14752043516 | 2 | 20180104 | 07:11:30 | 13 | 47 | 0.13 |

**Table 5.**The penetration rate of some ODs from 7:00 a.m. to 7:15 a.m. from 3 January to 20 January 2018.

Time | Link ID of Origin and Destination | Penetration |

07:00:01–07:15:00 | 105106_105108-888250_105110 | 5.71% |

07:00:01–07:15:00 | 105106_107106-107106_127106 | 14.29% |

07:00:01–07:15:00 | 105110_107110-107110_127110 | 4.60% |

07:00:01–07:15:00 | 107110_105110-127110_107110 | 2.44% |

07:00:01–07:15:00 | 109106_109108-109108_109110 | 3.51% |

07:00:01–07:15:00 | 109106_109108-109110_127110 | 11.11% |

07:00:01–07:15:00 | 111108_111110-111110_111112 | 2.94% |

07:00:01–07:15:00 | 125110_105110-105110_107110 | 3.06% |

07:00:01–07:15:00 | 125110_105110-107110_127110 | 4.55% |

07:00:01–07:15:00 | 129110_111110-111110_111112 | 5.26% |

Detector ID | Time | Link Length (m) | Link Flow (Vehs/15 min) |
---|---|---|---|

D108124 | 6:45:00 | 206 | 96 |

D108127 | 6:45:00 | 391 | 176 |

D108128 | 6:45:00 | 361 | 202 |

D108129 | 6:45:00 | 303 | 157 |

D108224 | 6:45:00 | 206 | 106 |

D108227 | 6:45:00 | 391 | 252 |

D108228 | 6:45:00 | 361 | 244 |

Time | Vehicle ID | Origin ID | Destination ID | Lane | x | y |
---|---|---|---|---|---|---|

6:00:01 | 637893 | 61 | 40 | 1 | 5738.87 | 5261.87 |

6:00:01 | 637894 | 89 | 118 | 1 | 5326.12 | 4727.6 |

6:00:01 | 637893 | 61 | 40 | 1 | 5735.73 | 5261.81 |

6:00:01 | 637894 | 89 | 118 | 1 | 5329.26 | 4727.72 |

6:00:02 | 637893 | 61 | 40 | 1 | 5731.97 | 5261.75 |

6:00:02 | 637894 | 89 | 118 | 1 | 5333.02 | 4727.87 |

6:00:02 | 637894 | 89 | 118 | 1 | 5337.4 | 4728.04 |

Scenario | Error (%) | Improvement of Error (%) | |||||
---|---|---|---|---|---|---|---|

I | II | III | IV | I | II | III | |

1 | 14.8% | 7.8% | 7.8% | 7.7% | 7.1% | 0.1% | 0.1% |

2 | 21.6% | 20.4% | 18.4% | 13.8% | 7.8% | 6.6% | 4.6% |

3 | 21.6% | 12.5% | 15.5% | 10.6% | 11.0% | 1.9% | 4.9% |

4 | 16.7% | 39.5% | 29.9% | 21.8% | −5.1% | 17.7% | 8.1% |

5 | 16.7% | 18.1% | 17.1% | 12.9% | 3.8% | 5.2% | 4.2% |

6 | 16.7% | 7.7% | 13.5% | 9.6% | 7.1% | −1.9% | 3.9% |

7 | 14.8% | 12.7% | 10.2% | 9.4% | 5.4% | 3.3% | 0.8% |

8 | 21.6% | 48.5% | 33.7% | 26.2% | −4.6% | 22.3% | 7.5% |

9 | 21.6% | 25.3% | 18.6% | 21.0% | 0.6% | 4.3% | −2.4% |

10 | 16.7% | 24.4% | 19.1% | 16.3% | 0.4% | 8.1% | 2.8% |

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## Share and Cite

**MDPI and ACS Style**

Hong, R.; Liu, H.; An, C.; Wang, B.; Lu, Z.; Xia, J.
An MFD Construction Method Considering Multi-Source Data Reliability for Urban Road Networks. *Sustainability* **2022**, *14*, 6188.
https://doi.org/10.3390/su14106188

**AMA Style**

Hong R, Liu H, An C, Wang B, Lu Z, Xia J.
An MFD Construction Method Considering Multi-Source Data Reliability for Urban Road Networks. *Sustainability*. 2022; 14(10):6188.
https://doi.org/10.3390/su14106188

**Chicago/Turabian Style**

Hong, Rongrong, Huan Liu, Chengchuan An, Bing Wang, Zhenbo Lu, and Jingxin Xia.
2022. "An MFD Construction Method Considering Multi-Source Data Reliability for Urban Road Networks" *Sustainability* 14, no. 10: 6188.
https://doi.org/10.3390/su14106188