# A Practical and Sustainable Approach to Determining the Deployment Priorities of Automatic Vehicle Identification Sensors

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background

#### 1.2. Literature Review

#### 1.3. Research Gaps and Contributions

**(1) A data-driven approach was proposed to solve the vehicle-path-reconstruction-based AVI sensor location problem.**In order to build a practical, universal, and implementable model, this study found the optimal layout of AVI sensors at the path level first, and then integrated the results of all paths to analyze the region-wide layout. In particular, we simulated massive path data (tracks of vehicles) according to travel characteristics extracted from finite GPS data by using a random walk method; then, for each path, a Path-level Bi-level Programming Model (P-BPM) was constructed to find the optimal layout of the AVI sensors; lastly, we integrated these layouts by using the PageRank algorithm.

**(2) The detection error of the AVI sensors was calculated and applied as one of the optimization objectives when modeling for the AVI-LP.**By deriving it from the tracks of vehicles, the traffic flow distribution of an intersection can be characterized. Then, the detection error can be calculated by finding the location of the AVI sensors in each path. The detection error was applied to an objective equation to ensure that the missing observations of AVI sensors were as few as possible.

**(3) A novel indicator called the deployment score was introduced.**The PageRank algorithm finally output the priority ranking set of the intersections to locate AVI sensors. As a consequence, the installation sequence of the AVI sensors was determined, which is more implementable and practical in decision making.

## 2. Problem Description and Preliminaries

#### 2.1. Problem Description and Assumptions

#### 2.2. Preliminary Representation and Traditional Region-Level BPM

^{2}·|R|) binary variables, O(|N|·|R|) non-negative variables, and O(|N|

^{2}·|R|) constraints, in which |N| is the number of candidate nodes and |R| is the number of vehicle paths in the network. Hence, there is a great number of variables and constraints with greater values of |N| and |R|, making it hard for us to easily obtain optimal solutions. To develop the greatest potential of AVI sensors, huge-magnitude quantities of vehicle paths are necessary, i.e., |R| will be too enormous. Then, with an analysis of the computational complexity, the relationship between the AVI-LP and the mixed-integer linear programming problem (MILPP) is given in the following remark.

**Remark**

**1.**

## 3. Model Formulation and Methodology

#### 3.1. Random-Walk Method

#### 3.1.1. Transferring Probability Calculation

**transferring probability.**The transferring probability was calculated using two indexes: betweenness centrality (denoted as BC, global and static) and transfer connectivity (denoted as TC, local and dynamic).

#### 3.1.2. Simulation Process

Algorithm 1: The pseudo-code for the random walk | |

Input: The surveyed OD matrix, observed trajectory data of the vehiclesOutput: The path set $\mathsf{\Phi}=\left\{\varphi ,{V}_{o},{V}_{d}\right\}$ | |

1: | Initialization of ${V}_{o}$ and ${V}_{d}$ in $\mathsf{\Phi}$, the length threshold ${l}_{max}$ |

2: | Calculate the transferring probability ${\mathrm{p}}_{{v}_{now},{v}_{next}}^{i}$ between each pair of nodes; |

3: | for$i=1to{n}_{r}$do |

4: | initialize ${\varphi}^{i}$ to null and add ${v}_{o}^{i}$ into ${\varphi}^{i}$; walking agent begins at ${v}_{o}^{i}$; ${\hat{\mathrm{p}}}_{{v}_{now},{v}_{next}}^{i}$; |

5: | while the total length of ${\varphi}^{i}$ does not exceed ${l}_{max}$ and the walking agent is not at ${v}_{d}^{i}$ do |

6: | select one of the agent’s adjacent nodes according to the ${\hat{\mathrm{p}}}_{{v}_{now},{v}_{next}}^{i}$ |

7: | if ${\varphi}^{i}$ is not a repeated or circular path do |

8: | add the selected adjacent node into ${\varphi}^{i}$; |

9: | else do |

10: | select another one of the agent’s adjacent nodes according to the ${\mathrm{p}}_{{v}_{now},{v}_{next}}^{i}$, return to line 7; |

11: | end if |

12: | let walking agent move to the last added node; |

13: | return
${\varphi}^{i}$ |

14: | end for |

#### 3.2. Formulating the P-BPM of Each Simulated Path

#### 3.2.1. Problem Restatement

**DN**: The accumulated proportion of the traffic flow that does not pass through node ${\mathit{v}}_{\mathit{i}}$ in a path is denoted as ${\phi}_{i}$. In Figure 4,

**DL**: The proportion of the traffic flow that does not pass through link ${\mathit{l}}_{i\to j}$ from node ${\mathit{v}}_{\mathit{i}}$ to node ${\mathit{v}}_{\mathit{j}+\mathbf{1}}$ is denoted as ${\omega}_{i\to j}$. In Figure 4,

#### 3.2.2. Formulating the P-BPM

**,**an AVI sensor is required, and constraints (15) ensure that, if the distance between node j and node k exceeds ${\mathit{\epsilon}}_{\mathit{l}}$ (the distance of path r), an AVI sensor is required at node j. Constraints (16) indicate the correlations between the DN values of the consecutive points in order to determine if an AVI sensor is required. Generally speaking, ${\phi}_{i}={{\displaystyle \sum}}_{j=\mathrm{max}\left\{i|{x}_{i}=1\right\}}^{i}{\omega}_{j-1\to j}$. Constraints (17) indicate that, once an AVI sensor is established at${\mathit{v}}_{\mathit{i}}$, ${\phi}_{i}$ will be reset to 0. Constraints (18) define the binary variables ${x}_{\mathrm{i}}$ and ${a}_{\left(j,k\right)}^{r}$.

#### 3.3. Calculating the Deployment Score

**Theorem**

**1.**

**Proof**

**1.**

## 4. Experiments

#### 4.1. Dataset

**Road Network:**In our experiments, a part of the road network of Chengdu city in China, with a total length of 257 km, was used, as shown in Figure 6. This city-wide network graph covers a 3.5 × 5.2 km spatial range containing 587 nodes and 1397 road links.

**GPS Dataset:**The GPS dataset was collected in Chengdu city from October 1st to October 31st, 2016, with support from Didi Chuxing. In the third quarter of 2016, Didi Intelligent Travel generated a total of 1 billion GPS trajectory records, which contained 35,450 cars and 202,505 orders in a region of 65 km

^{2}in the northeast section of the Second Ring Area in Chengdu. Each point of the GPS trajectories of the trips was matched to a real road to ensure that the data could correspond to actual road information, as shown in Figure 7.

**AVI Dataset:**Some virtual AVI sensors could be assumed to be located at the intersections of the road network by reference to the GPS trajectory data. If an intersection was assumed to be a location for an AVI sensor, the recorded GPS data within this intersection were valid as observed AVI data; otherwise, they were abandoned.

#### 4.2. Evaluation Methodology

#### 4.2.1. Implementation Procedure

Algorithm 2: The pseudo-code for inferring the whole detected path | |

Input: The candidate graph $\mathrm{G}\prime $, ${\mathsf{\Phi}}_{true}$, ${\widehat{\mathrm{BC}}}_{i}$ and ${\widehat{\mathrm{TC}}}_{i}$ of each candidate nodeOutput: ${\mathsf{\Phi}}_{\mathrm{inferred}}$ | |

1: | Initialize ${\mathsf{\Phi}}_{\mathrm{shortest}}$ and ${\mathsf{\Phi}}_{\mathrm{popular}}$ from the road map and ${\mathsf{\Phi}}_{true}$, respectively |

2: | |

3: | for$\psi =1\mathrm{to}{n}_{\mathrm{evaluation}}$ do |

4: | initialize ${\varphi}_{\mathrm{detected}}^{\psi}$ from ${\varphi}_{\mathrm{true}}^{\psi}$, ${\varphi}_{\mathrm{inferred}}^{\psi}$=${\varphi}_{\mathrm{detected}}^{\psi}$ |

5: | for each segment from ${v}_{{\mathrm{x}}_{1}}^{\psi}$ to ${v}_{{\mathrm{x}}_{2}}^{\psi}$ in ${\varphi}_{\mathrm{detected}}^{\psi}$ do |

6: | if ${v}_{{\mathrm{x}}_{1}}^{\psi}$ is not adjacent to ${v}_{{\mathrm{x}}_{2}}^{\psi}$do |

7: | remove the path ${\varphi}_{\mathrm{shortest}}^{{v}_{{\mathrm{x}}_{1}}^{\psi}\to {v}_{{\mathrm{x}}_{2}}^{\psi}}$ $\leftarrow {v}_{{\mathrm{x}}_{1}}^{\psi}$ to ${v}_{{\mathrm{x}}_{2}}^{\psi}$ from ${\mathsf{\Phi}}_{\mathrm{shortest}}$ |

8: | remove the path ${\varphi}_{\mathrm{popular}}^{{v}_{{\mathrm{x}}_{1}}^{\psi}\to {v}_{{\mathrm{x}}_{2}}^{\psi}}$ $\leftarrow {v}_{{\mathrm{x}}_{1}}^{\psi}$ to ${v}_{{\mathrm{x}}_{2}}^{\psi}$ from ${\mathsf{\Phi}}_{\mathrm{popular}}$ |

9: | calculate the total value $valu{e}_{\mathrm{shortest}}^{{v}_{{\mathrm{x}}_{1}}^{\psi}\to {v}_{{\mathrm{x}}_{2}}^{\psi}}$ of the nodes in ${\varphi}_{\mathrm{shortest}}^{{v}_{{\mathrm{x}}_{1}}^{\psi}\to {v}_{{\mathrm{x}}_{2}}^{\psi}}$ except ${v}_{{\mathrm{x}}_{1}}^{\psi}$ and ${v}_{{\mathrm{x}}_{1}}^{\psi}$ |

10: | calculate the total value $valu{e}_{\mathrm{popular}}^{{v}_{{\mathrm{x}}_{1}}^{\psi}\to {v}_{{\mathrm{x}}_{2}}^{\psi}}$ of the nodes in ${\varphi}_{\mathrm{popular}}^{{v}_{{\mathrm{x}}_{1}}^{\psi}\to {v}_{{\mathrm{x}}_{2}}^{\psi}}$ except ${v}_{{\mathrm{x}}_{1}}^{\psi}$ and ${v}_{{\mathrm{x}}_{1}}^{\psi}$ |

11: | if $valu{e}_{\mathrm{shortest}}^{{v}_{{\mathrm{x}}_{1}}^{\psi}\to {v}_{{\mathrm{x}}_{2}}^{\psi}}\ge valu{e}_{\mathrm{popular}}^{{v}_{{\mathrm{x}}_{1}}^{\psi}\to {v}_{{\mathrm{x}}_{2}}^{\psi}}$ do |

12: | insert ${\varphi}_{\mathrm{shortest}}^{{v}_{{\mathrm{x}}_{1}}^{\psi}\to {v}_{{\mathrm{x}}_{2}}^{\psi}}$ to ${\varphi}_{\mathrm{detected}}^{\psi}$ between ${v}_{{\mathrm{x}}_{1}}^{\psi}$ and ${v}_{{\mathrm{x}}_{2}}^{\psi}$ as ${\varphi}_{\mathrm{inferred}}^{\psi}$ |

13: | else do |

14: | insert ${\varphi}_{\mathrm{popular}}^{{v}_{{\mathrm{x}}_{1}}^{\psi}\to {v}_{{\mathrm{x}}_{2}}^{\psi}}$ to ${\varphi}_{\mathrm{detected}}^{\psi}$ between ${v}_{{\mathrm{x}}_{1}}^{\psi}$ and ${v}_{{\mathrm{x}}_{2}}^{\psi}$ as ${\varphi}_{\mathrm{inferred}}^{\psi}$ |

15: | end if |

16: | end if |

17: | end for |

18: | return ${\varphi}_{\mathrm{inferred}}^{\psi}$ |

#### 4.2.2. Performance Metrics

**Metric 1,**

**F1 score of paths**: We evaluated the results based on the F1 measure, which indicates both accuracy and recall. Accuracy is defined as the percentage of the length of the matched segments of the total paths ${S}_{matched}$ to the length of the inferred segments of the total paths ${S}_{\mathrm{inferred}}$, where ${S}_{matched}$ will be the total length of the common edges between the inferred paths and the ground-truth paths ${S}_{\mathrm{truth}}$. The recall is measured according to the ratio between the length of the matched segments and the length of the ground-truth paths. Hence, the F1 score of the paths is computed as follows:

**Metric 2,**

**F1 score of nodes:**Meanwhile, the F1 score of the nodes is also computed in the same was as

**Metric 1**.

**Metric 3,**

**observability**: Observability evaluates the scope of service of the allocation of AVI sensors, and it is computed as follows:

#### 4.3. Experimental Results

#### 4.4. Comparative Experiments

## 5. Conclusions and Discussions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Disclosure Statement

## Variables

Variables | Details |

${\mathit{x}}_{\mathit{i}}$ | Binary, equal to 1 if there is an AVI sensor established at node $\mathrm{i}$, and 0 otherwise |

${\mathit{a}}_{\mathit{i}\to \mathit{j}}^{\mathit{r}}$ | Binary, equal to 1 if the path from i to j within path r is misidentified, and 0 otherwise |

${\mathit{q}}_{\mathit{i}\to \mathit{j}}^{\mathit{r}}$ | Integer, the misidentified traffic flow from node i to node j of path r |

${\mathit{q}}^{\mathit{r}}$ | Integer, the total true traffic flow of path r |

${\mathit{l}}_{\mathit{i}\to \mathit{j}}^{\mathit{r}}$ | Float, the misidentified length from node i to node j $\in $ path r |

${\mathit{l}}^{\mathit{r}}$ | Float, the total length ofpath r |

C | The set of candidate nodes, C $\in V$ |

L | The set of links between the candidate nodes |

R | The set of the total actual vehicle paths; each path is represented as a sequence of candidate nodes that the vehicle passes |

${\mathit{N}}_{\mathit{r}}$ | The set of the nodes in path r, ${L}_{r}\in R$ |

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**Figure 11.**Results of the P-BPM of fine-grained AVI sensor proportions. (

**a**) F1 scores. (

**b**) Accuracy. (

**c**) Recall. (

**d**) Observability.

**Figure 12.**Performance metrics in comparative experiments. (

**a**) F1 score; (

**b**) accuracy; (

**c**) recall; (

**d**) observability.

Deployment Proportion of AVI Sensors | Link | Node | Observability | ||||
---|---|---|---|---|---|---|---|

$\mathit{A}\mathit{c}\mathit{c}\mathit{u}\mathit{r}\mathit{a}\mathit{c}\mathit{y}$ | $\mathit{R}\mathit{e}\mathit{c}\mathit{a}\mathit{l}\mathit{l}$ | $\mathit{F}1\mathit{s}\mathit{c}\mathit{o}\mathit{r}\mathit{e}$ | $\mathit{A}\mathit{c}\mathit{c}\mathit{u}\mathit{r}\mathit{a}\mathit{c}\mathit{y}$ | $\mathit{R}\mathit{e}\mathit{c}\mathit{a}\mathit{l}\mathit{l}$ | $\mathit{F}1\mathit{s}\mathit{c}\mathit{o}\mathit{r}\mathit{e}$ | ||

10% | 0.9521 | 0.4747 | 0.6335 | 0.9781 | 0.3753 | 0.5425 | 0.2638 |

20% | 0.9421 | 0.6092 | 0.7399 | 0.9697 | 0.5807 | 0.7264 | 0.4558 |

30% | 0.9485 | 0.668 | 0.7839 | 0.9712 | 0.6836 | 0.8024 | 0.5644 |

40% | 0.9572 | 0.7652 | 0.8505 | 0.9771 | 0.7979 | 0.8785 | 0.6878 |

50% | 0.9543 | 0.8164 | 0.88 | 0.9763 | 0.8693 | 0.9197 | 0.7599 |

60% | 0.9614 | 0.8483 | 0.9013 | 0.9788 | 0.9086 | 0.9424 | 0.8358 |

70% | 0.9632 | 0.8647 | 0.9113 | 0.9791 | 0.9347 | 0.9564 | 0.8788 |

80% | 0.967 | 0.9238 | 0.9449 | 0.9813 | 0.9695 | 0.9754 | 0.929 |

90% | 0.9679 | 0.9569 | 0.9624 | 0.9814 | 0.9893 | 0.9853 | 0.9685 |

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**MDPI and ACS Style**

Li, D.; Wang, W.; Zhao, D.
A Practical and Sustainable Approach to Determining the Deployment Priorities of Automatic Vehicle Identification Sensors. *Sustainability* **2022**, *14*, 9474.
https://doi.org/10.3390/su14159474

**AMA Style**

Li D, Wang W, Zhao D.
A Practical and Sustainable Approach to Determining the Deployment Priorities of Automatic Vehicle Identification Sensors. *Sustainability*. 2022; 14(15):9474.
https://doi.org/10.3390/su14159474

**Chicago/Turabian Style**

Li, Dongya, Wei Wang, and De Zhao.
2022. "A Practical and Sustainable Approach to Determining the Deployment Priorities of Automatic Vehicle Identification Sensors" *Sustainability* 14, no. 15: 9474.
https://doi.org/10.3390/su14159474