# Visualization and Analysis of Mapping Knowledge Domain of Heterogeneous Traffic Flow

Authors: Yi He; Qi Feng; Lixin Yan; Xiao-Yun Lu
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

Mapping knowledge domain (MKD) is an important application in bibliometrics, which is a method of visually presenting and explaining newly developed interdisciplinary scientific fields using data mining, information analysis, scientific measurement, and graphic rendering. This study combines applied mathematics, visual analysis technology, information science, and scientometrics to systematically analyze the development status, research distribution, and future trend of the heterogeneous traffic flow by using the MKD software tools VOSviewer and CiteSpace. Based on the MKD and Bibliometrics approaches, 4709 articles have been studied, which were published by Science Citation Index Expanded (SCIE) and Social Sciences Citation Index (SSCI) from 2004 to 2021 in the field of heterogeneous traffic flows. Firstly, this paper presents the annual numbers of articles, origin countries, main research organizations, and groups as well as the source journals on heterogeneous traffic flow studies. Then, cocitation analysis is used to divide heterogeneous traffic flow into three main research directions, which include “heterogeneous traffic flow model,” “traffic flow capacity analysis,” and “traffic flow stability analysis.” The keyword cooccurrence analysis is applied to identify five dominant clusters: “modeling and optimization methods,” “traffic flow characteristics analysis,” “driving behavior analysis,” “simulation experiment,” and “policies and barriers.” Finally, burst keywords were studied according to the publication date to present more clearly the change of research focus and direction over time.


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## Body

## 1. Introduce

As the production and ownership of automobiles increase year by year, vehicles not only provide convenience and comfort to people but also bring many negative impacts, such as traffic safety, congestion, and air pollution [1, 2]. Vehicle crashes result in about 63,194 fatalities in China, and direct property losses reached 11.18672 million yuan in 2018 [3]. In terms of energy consumption, China’s road transportation industry consumes 60.1% of the nation’s oil and produces 14% of greenhouse gases [4], while America’s transportation industry consumes 70% of oil and 33.6% of greenhouse gases [5]. In the face of increasingly severe security, energy, and environmental problems, autonomous driving technology, as an important component of the intelligent transportation system, has incomparable advantages in improving travel efficiency, alleviating traffic congestion, and reducing gasoline consumption and other aspects and is an important way to achieve green and efficient development of the automobile industry.Like many new technologies, although some autonomous driving technologies have been implemented, most of them are still in the experimental and conceptual stage, and the industrialization of autonomous driving vehicles still needs a long process. Boston Consulting Group predicts that “it will take 15–20 years for the global market share of autonomous vehicles to reach 25%,” and as autonomous vehicles are expected to hit the market in 2021, this means that autonomous vehicles will account for 25% of the global market in 2035–2040 [6]. Therefore, in the process of the rapid development of the autonomous vehicle industry, there will be a transitional stage of the heterogeneous transportation system composed of artificial and autonomous vehicles [7].Heterogeneous traffic flow is an extremely complex problem in the field of traffic flow, which involves the combination of traditional traffic flow research and autonomous driving technology. Although some article reviews have studied the related content of heterogeneous traffic flow, previous article reviews have adopted qualitative rather than quantitative methods to conduct research, which largely relies on the author’s experience and subjective judgment in this field, requiring the author to accumulate, summarize, and refine in this field for a long time. In addition, the previous review article lacks visual analysis of all heterogeneous traffic flow studies, so it is difficult to reveal the panorama of heterogeneous traffic flow research, and it is difficult to describe the cocitation relationship and keyword evolution law between articles [8].In this paper, the bibliometrics method was used to review the article. The WOS platform was used to search 4709 related articles published in the field of heterogeneous traffic flow in the recent 17 years (2004–2021). The following tasks were completed: which countries/regions are the most important research results; what is the collaboration between the main authors in the research area; what are the core publications in the research area; what are the most influential research results in the field of heterogeneous traffic flow research; which are the most active research field of heterogeneous traffic flow and its present situation and deficiency? Research and review related aspects from a new perspective clarify the development context of the heterogeneous traffic flow field, identify key topics and research progress in domestic and foreign research, find the shortcomings of current research, and provide reference and comparison for researchers.The rest of the paper is organized as follows: Section2 introduces the data sources of the sample literature as well as the analytical tools and methods; Section 3 carries out quantitative statistical analysis from aspects of publication year, country, institution, journal, and keywords through sorting out 4709 high-level sample literature related to heterogeneous traffic flow; Section 4 draws conclusions and provides a brief discussion of the future research plan.


## 2. Data Sources and Analysis Methods

### 2.1. Data Source

This article aims to conduct a quantitative and visualized analysis of the representative works related to heterogeneous traffic flow through MKD methods. Web of Science (WOS) is an online subscription-based science citation index service that provides access to multiple databases containing more than 148 million records (journals, books, and conference proceedings) dating back to the beginning of the 20th century [9]. Therefore, the SCIE and SSCI citation index database in the WOS Core Collection were retrieved as the source in this study. To obtain the maximum number of relevant documents related to simulated driving, we collected and stored data for the defined search terms using the “Topic” search in Web of Science Core Collection. The keywords used for the initial data collection included “heterogeneous traffic flow∗” OR “Mixed traffic flow∗” OR (“Penetration rate∗”) AND (“connected and autonomous vehicle∗” OR “intelligent connected vehicle∗” OR “connected vehicle∗” OR “autonomous vehicle∗” OR “adaptive cruise control” OR “cooperative adaptive cruise control”), where “∗” represents fuzzy search.The excluded categories were veterinary medicine, clinical medicine, food science, engineering, etc., with a time span of 1985 to 2021 and retrieval date of January 2, 2021, 754 English journal articles, conference papers, research reviews, and conference abstractions were obtained. To ensure the completeness and accuracy of the article collection, this paper added the cited articles of 754 articles obtained from article retrieval and removed the remaining 3955 articles after self-cited articles. Finally, a total of 4709 articles were obtained for article analysis, involving 7046 authors and 13,224 keywords. To cover as much additional information as possible, the “full records and references” of all articles are exported in “TXT” format for bibliometrics analysis.


### 2.2. Analysis Method

Bibliometrics is an interdisciplinary science that uses mathematical and statistical methods to quantitatively analyze relevant articles, mainly studying the quantitative relationship of the article (various publications, in particular, journal papers and citations are in the majority) [10], journal information sources (the situation of journals in which article is published) [11], author relationship (the cooperative relationship between the author, the organization, or the group) [12], and keywords (the core words that repeatedly appear in the article) [13].In bibliometrics analysis, the mapping knowledge domain (MKD) is a method to visually present and explain the newly developed interdisciplinary scientific field using data mining, information analysis, scientific measurement, and graph rendering, aiming at simplifying the information acquisition process in the research field and clarifying the knowledge structure [14]. The MKD has dual properties and characteristics of “graph” and “spectrum,” which means that it is not only a visual knowledge map but also a serialized knowledge map. The MKD can show the development process and structural relations of scientific knowledge as well as the implied complex relations, including network, structure, interaction, intersection, evolution, or derivation between knowledge units or knowledge clusters [15]; understanding these complex knowledge relationships can produce new knowledge.The mapping (or creation) of MKD includes article cocitation analysis, keyword cooccurrence analysis, and burst detection analysis, as described as follows:(a)
Document cocitation analysis: a document cocitation is a new form of article coupling, which refers to the frequency of two articles being cited simultaneously [16]. Document cocitation analysis refers to the statistics of the number of two documents simultaneously cited by one or more documents, to conduct network analysis and cluster analysis on the cited documents, to analyze the knowledge base of the specific subject represented by these documents [17]. The knowledge base of this field is constructed by quoting articles, and the research frontier of a certain field is formed by analyzing the knowledge base.(b)
Keywords cooccurrence analysis: official academic publications are generally accompanied by keywords, which not only reflect the core content of the research results and condense the author’s academic views but also provide an important way of retrieval. Keywords cooccurrence analysis is to count the number of occurrences of a group of keywords in the same article in pairs [17]. Based on this, network analysis and cluster analysis are conducted for these words, to reflect the affinity relationship between these words and the structural changes of the subject they represent [18]. Therefore, the more frequently a keyword appears, the more relevant research results, and the stronger the concentration of research content [19].(c)
Burst detection analysis: the burst detection analysis considers the change of keyword frequency and determines the keywords with the characteristics of burst growth in a certain period in a certain research field, which can be used to study the development trend of a certain topic. It is different from the burst detection analysis based on a threshold value. Although the frequency of each keyword may be relatively low, the burst keyword can be found according to the change of keyword frequency, so the latest research trends can be predicted by such keywords.


### 2.3. Analysis Tools

In this study, the method of MKD in bibliometrics was selected to analyze the article according to its attributes and characteristics, and the knowledge was visualized. CiteSpace and VOSviewer were used in the study. CiteSpace was developed by Professor Chen Chaomei, chair professor of Changjiang Scholars in Dalian University of Technology [20]. The software focuses on the potential knowledge contained in scientific analysis. At first, it specifically analyzes the cocitation of articles and excavates the knowledge clustering and distribution in citation space. In subsequent updates, cooccurrence analysis between other knowledge units will also be provided, such as author, institution, and country or region collaboration. VOSviewer software was developed by Van Eck and Waltman of Leiden University in the Netherlands. Visualization of Similarities (VOS) technology is used to perform a visualization analysis of article knowledge units. Cooccurrence matrix is used to generate a knowledge map. Its core principles include the construction of similarity matrix and the VOS layout method [21].


### 2.4. Construction of MKD

By normalizing the cooccurrence matrix, the similarity matrix was obtained by correcting the differences in the total occurrence times or common frequency of elements in the cooccurrence matrix (i.e., author, institution, country/region, keywords, etc.). VOSviewer uses association strength, also known as proximity index, to measure the similarity between pairs of elements in the cooccurrence matrix. The similaritySij between two items i and j is calculated as(1)Sij=cijwiwj,where Sij denotes the similarity between the elements i and j, cij denotes the number of times the element i and the element j cooccur, and wi and wj denote the total number of occurrences of the element i and the element j, respectively. It can be seen that the normalized value is between 0 and 1, where the larger the value, the higher the similarity between elements, and the smaller the value, the smaller the similarity between elements.


### 2.5. Layout Method

The layout method adopted in this paper is to reflect the similarity between any pair of elementsi and j by the spatial distance sij to determine the position of elements in two-dimensional space. The closer the distance between elements, the higher the similarity [22]. To make the clustering effect more obvious, the main idea of VOS is to minimize the sum of the weighted Euclidean distances of all objects in each cluster; the formula is as follows [21]:(2)Dx1,…,xn=∑i<jsijxi−xj2,where n is the number of elements to be laid out, ||•|| denotes the Euclidean norm, and vector xi=xi1,xi2 denotes the location of item i in a two-dimensional map. To avoid all elements being in the same position, the objective function is minimized under the following constraints:(3)2nn−1∑i<jxi−xj=1.


## 2.1. Data Source

This article aims to conduct a quantitative and visualized analysis of the representative works related to heterogeneous traffic flow through MKD methods. Web of Science (WOS) is an online subscription-based science citation index service that provides access to multiple databases containing more than 148 million records (journals, books, and conference proceedings) dating back to the beginning of the 20th century [9]. Therefore, the SCIE and SSCI citation index database in the WOS Core Collection were retrieved as the source in this study. To obtain the maximum number of relevant documents related to simulated driving, we collected and stored data for the defined search terms using the “Topic” search in Web of Science Core Collection. The keywords used for the initial data collection included “heterogeneous traffic flow∗” OR “Mixed traffic flow∗” OR (“Penetration rate∗”) AND (“connected and autonomous vehicle∗” OR “intelligent connected vehicle∗” OR “connected vehicle∗” OR “autonomous vehicle∗” OR “adaptive cruise control” OR “cooperative adaptive cruise control”), where “∗” represents fuzzy search.The excluded categories were veterinary medicine, clinical medicine, food science, engineering, etc., with a time span of 1985 to 2021 and retrieval date of January 2, 2021, 754 English journal articles, conference papers, research reviews, and conference abstractions were obtained. To ensure the completeness and accuracy of the article collection, this paper added the cited articles of 754 articles obtained from article retrieval and removed the remaining 3955 articles after self-cited articles. Finally, a total of 4709 articles were obtained for article analysis, involving 7046 authors and 13,224 keywords. To cover as much additional information as possible, the “full records and references” of all articles are exported in “TXT” format for bibliometrics analysis.


## 2.2. Analysis Method

Bibliometrics is an interdisciplinary science that uses mathematical and statistical methods to quantitatively analyze relevant articles, mainly studying the quantitative relationship of the article (various publications, in particular, journal papers and citations are in the majority) [10], journal information sources (the situation of journals in which article is published) [11], author relationship (the cooperative relationship between the author, the organization, or the group) [12], and keywords (the core words that repeatedly appear in the article) [13].In bibliometrics analysis, the mapping knowledge domain (MKD) is a method to visually present and explain the newly developed interdisciplinary scientific field using data mining, information analysis, scientific measurement, and graph rendering, aiming at simplifying the information acquisition process in the research field and clarifying the knowledge structure [14]. The MKD has dual properties and characteristics of “graph” and “spectrum,” which means that it is not only a visual knowledge map but also a serialized knowledge map. The MKD can show the development process and structural relations of scientific knowledge as well as the implied complex relations, including network, structure, interaction, intersection, evolution, or derivation between knowledge units or knowledge clusters [15]; understanding these complex knowledge relationships can produce new knowledge.The mapping (or creation) of MKD includes article cocitation analysis, keyword cooccurrence analysis, and burst detection analysis, as described as follows:(a)
Document cocitation analysis: a document cocitation is a new form of article coupling, which refers to the frequency of two articles being cited simultaneously [16]. Document cocitation analysis refers to the statistics of the number of two documents simultaneously cited by one or more documents, to conduct network analysis and cluster analysis on the cited documents, to analyze the knowledge base of the specific subject represented by these documents [17]. The knowledge base of this field is constructed by quoting articles, and the research frontier of a certain field is formed by analyzing the knowledge base.(b)
Keywords cooccurrence analysis: official academic publications are generally accompanied by keywords, which not only reflect the core content of the research results and condense the author’s academic views but also provide an important way of retrieval. Keywords cooccurrence analysis is to count the number of occurrences of a group of keywords in the same article in pairs [17]. Based on this, network analysis and cluster analysis are conducted for these words, to reflect the affinity relationship between these words and the structural changes of the subject they represent [18]. Therefore, the more frequently a keyword appears, the more relevant research results, and the stronger the concentration of research content [19].(c)
Burst detection analysis: the burst detection analysis considers the change of keyword frequency and determines the keywords with the characteristics of burst growth in a certain period in a certain research field, which can be used to study the development trend of a certain topic. It is different from the burst detection analysis based on a threshold value. Although the frequency of each keyword may be relatively low, the burst keyword can be found according to the change of keyword frequency, so the latest research trends can be predicted by such keywords.


## 2.3. Analysis Tools

In this study, the method of MKD in bibliometrics was selected to analyze the article according to its attributes and characteristics, and the knowledge was visualized. CiteSpace and VOSviewer were used in the study. CiteSpace was developed by Professor Chen Chaomei, chair professor of Changjiang Scholars in Dalian University of Technology [20]. The software focuses on the potential knowledge contained in scientific analysis. At first, it specifically analyzes the cocitation of articles and excavates the knowledge clustering and distribution in citation space. In subsequent updates, cooccurrence analysis between other knowledge units will also be provided, such as author, institution, and country or region collaboration. VOSviewer software was developed by Van Eck and Waltman of Leiden University in the Netherlands. Visualization of Similarities (VOS) technology is used to perform a visualization analysis of article knowledge units. Cooccurrence matrix is used to generate a knowledge map. Its core principles include the construction of similarity matrix and the VOS layout method [21].


## 2.4. Construction of MKD

By normalizing the cooccurrence matrix, the similarity matrix was obtained by correcting the differences in the total occurrence times or common frequency of elements in the cooccurrence matrix (i.e., author, institution, country/region, keywords, etc.). VOSviewer uses association strength, also known as proximity index, to measure the similarity between pairs of elements in the cooccurrence matrix. The similaritySij between two items i and j is calculated as(1)Sij=cijwiwj,where Sij denotes the similarity between the elements i and j, cij denotes the number of times the element i and the element j cooccur, and wi and wj denote the total number of occurrences of the element i and the element j, respectively. It can be seen that the normalized value is between 0 and 1, where the larger the value, the higher the similarity between elements, and the smaller the value, the smaller the similarity between elements.


## 2.5. Layout Method

The layout method adopted in this paper is to reflect the similarity between any pair of elementsi and j by the spatial distance sij to determine the position of elements in two-dimensional space. The closer the distance between elements, the higher the similarity [22]. To make the clustering effect more obvious, the main idea of VOS is to minimize the sum of the weighted Euclidean distances of all objects in each cluster; the formula is as follows [21]:(2)Dx1,…,xn=∑i<jsijxi−xj2,where n is the number of elements to be laid out, ||•|| denotes the Euclidean norm, and vector xi=xi1,xi2 denotes the location of item i in a two-dimensional map. To avoid all elements being in the same position, the objective function is minimized under the following constraints:(3)2nn−1∑i<jxi−xj=1.


## 3. Article Statistical Analysis

### 3.1. Annual Distribution Statistics of the Article

The annual distribution of articles refers to the difference in the distribution of the number of articles in the same time zone, which can reflect the development process of people, institutions, or subject research and divide the active trend of subject research. The change in the number of academic papers on a subject is an important indicator of the development trend of the research field, and it is also a reflection of the change in the scope of subject knowledge. By drawing a graph of the number of documents and conducting multivariate statistical analysis, one can understand the research level and future development trend of a certain field.To better explore the relevant characteristics and conditions in the field of heterogeneous traffic flow in a period, this paper considers the number of documents in the field of heterogeneous traffic flow, which are divided into three stages based on the growth of the article during the period, namely, “initial stage (2004–2009),” “preliminary development stage (2010–2015),” and “rapid development stage (2016–2020).” On the one hand, segmenting the field according to the same time can better compare and analyze the growth of articles and the characteristics of research trends in each period. On the other hand, because the research on heterogeneous traffic flow started late and the period is not long, it is relatively reasonable to set 5 years as an academic research cycle.According to the search results, the earliest research article on heterogeneous traffic flow was published in 2004 and lasted until 2021. It already contains 4703 related documents. The annual distribution statistics are shown in Figure1. It is worth noting that due to 2020 the data is still being updated, so the data in the statistics is small.Figure 1
Quantitative distribution of published articles in heterogeneous traffic flow studies, 2004–2020.Initial stage (2004–2009): from the first article published in 2004 to 2008, there were few related research results in this field, and only 73 papers (2009) were published each year, which means that there is research on qualitative traffic flow has just started, and a complete document system has not yet been formed.Primary development stage (2010–2015): as countries pay more and more attention to road safety, autonomous driving has set off a research boom and has begun to enter the primary development stage. The number of relevant documents at this stage has increased significantly, with an average increase of 33 documents per year. It can be considered that the field of heterogeneous traffic flow research was initially formed during this period.Rapid development stage (2016–2020): after the accumulation of knowledge in the initial stage and the primary development stage, the number of relevant documents in this stage has grown rapidly. This shows that the research enthusiasm in the field of heterogeneous traffic flow is continuously increasing and has entered a stage of rapid development.


### 3.2. Country and Regional Statistics

For national and regional factors, this article presents four indicators to analyze the distribution area and situation of the documents, namely, the number of documents (articles), the percentage of documents in the total number of documents, the total number of citations of documents (times), and the average single document. The number of citations is shown in Table1. The use of these indicators mainly considers two aspects: on the one hand, the number of documents in a country can reflect the research enthusiasm of researchers in each country in the field; on the other hand, the total number of citations and the average number of citations per article can be to a certain extent. This indicates the quality of the article of national researchers, reflecting the depth of research in this field by researchers from various countries.Table 1
The top ten countries in the number of articles in the heterogeneous traffic flow research field.
RankCountry/territoriesQuantityPercentageTotal cited timesThe average number of citations per article1China208744.28172518.272USA113924.171151810.113India3427.2628948.464Germany2064.37319015.495England1873.97273214.616Australia1673.54190611.417Netherlands1523.23206313.578Canada1392.9512839.239Japan1312.7811228.5610South Korea1212.577205.95According to the retrieved results, the article on heterogeneous traffic flow mainly comes from 88 countries (or regions). Table1 lists the top 10 countries in the field of heterogeneous traffic flow research from 2004 to the present. Japanese science historian Yuasa (1962) defined a country with more than 25% of the world’s major scientific achievements as the center of scientific activity. According to the data in Table 1, China ranks first with 2087 articles, accounting for 44.28% of the total number of articles. The average number of citations per article is 8.27, followed by the United States (1139) and India (342). The center of scientific activity in the field of heterogeneous traffic flow research is as follows. Four Asian countries (China, India, Japan, and South Korea) among the top ten countries in the number of articles indicate that Asian countries have performed well in research on heterogeneous traffic flow. European countries have excellent performance in the average number of citations per article, such as Germany (average number of citations per article 15.49), the United Kingdom (average number of citations per article 14.61), and the Netherlands (average number of citations per article 13.57), which shows that the article published in these countries has been highly recognized by researchers.In VOSviewer, citation analysis is used to generate a scientific knowledge map of the country in the field of heterogeneous traffic flow. This article uses VOSviewer software to analyze the collected data and make a density view based on the distribution of national documents. The density view can visually display the situation of the country/region in the density dimension. Each label in the figure represents a country, and the label is the center point to form a region. The size and color of the region depend on the country/region represented by the label the number of published documents, the larger the number, the brighter the color, and the smaller the number, the darker the color. The location of the tag depends on the number of items near the tag and their importance. The density view can help understand the overall structure of the map and draw attention to the most important areas of the map.This article sets the display conditions for countries/regions with five or more related article achievements, a total of 60 countries/regions, as shown in Figure2. The density view can see the overall structure of the distribution of national or regional documents. In the figure, China and the United States are in the center of the figure, indicating that China and the United States play an important role in the field of heterogeneous traffic flow.Figure 2
Density distribution of heterogeneous traffic flow in major countries.


### 3.3. Analysis of Main Research Institutions

By analyzing the cooperation relationship between research institutions, information about the most outstanding organizations and groups in a certain field in the discipline can be determined. To analyze the cooperative relationship between the research institutions related to the article, this paper uses VOSviewer to construct a cooperation network between major research institutions to analyze the participating institutions of heterogeneous traffic flow research, as shown in Figure3.Figure 3
Collaborative networks among major research institutions.In the interinstitutional cooperation network diagram, the label is the name of the research institution, the size of the node indicates the number of standardized documents, and the connection indicates the cooperative relationship between the two connected research institutions. The closer the cooperation, the closer the node distance, the wider the scope of cooperation, the more connections. Figure3 shows that Beijing Jiao tong University is at the center of the gathering point, indicating that Beijing Jiao tong University and other research institutions have established close cooperation in the field of heterogeneous traffic flow.The number of published documents of research institutions is also one of the important indicators to measure the contributions made by research institutions in the field. The article in this field comes from a total of 2512 organizations. Table2 lists the top 10 organizations with the largest number of published articles. The research strength of a university is often an indicator of the national scientific research and innovation ability. Table 2 shows that a total of 9 universities contributed 1173 papers, accounting for 24.89% of the total number of heterogeneous traffic flow publications. Among them, Chinese universities and research institutes are heterogeneous traffic. The main contributors to stream research are as follows: these organizations have published 1059 papers, accounting for 22.47% of the total number of papers. Among Chinese universities, Beijing Jiaotong University ranked first in the number of publications of 213 articles, with an average of 161.85 citations per article, indicating that Beijing Jiaotong University is in a leading position in the field of heterogeneous traffic flow research. Southeast University (187 articles) and Tongji University (154 articles) followed closely. Among the 2512 organizations, only 87 organizations published 20 papers or more, accounting for 3.46% of the total. This result shows that the published documents are concentrated in a few organizations.Table 2
Organization of the top 10 research achievements in heterogeneous traffic flow from 2004 to 2021.
RankOrganizationLink strengthQuantityPercentageCited timesThe average number of citations per article1Beijing Jiaotong University1252134.522276161.852Southeast University1291873.971116143.583Tongji University1061543.27852142.864Tsinghua University861332.821200147.995Delft University technology241202.551874192.286Beihang University801002.121803169.317Changan University52931.9745686.698Ningbo University103921.951013128.089Jiangsu Provincial Collaborative Innovation Center modern urban109871.85892110.1610Indian Institute of Technology4811.72110666.43


### 3.4. Coauthor Analysis of the Main Research Group

Counting the number of articles published by authors on the topic and comparing and analyzing them can understand the main authors and core author groups in the field and can further establish their important role and influence in related fields by understanding the author’s research progress and by paying attention to them. The research direction and focus, to understand its leading and leading role in the development of the whole discipline, is of great significance for further understanding the current situation and future development of special research. Because the research in the field of heterogeneous traffic flow is highly interdisciplinary, researchers come from different fields such as traffic engineering, traffic planning, mathematics, psychology, computer science, medicine, and statistics, and cooperation can achieve complementary advantages. The creation and analysis of the knowledge graph of the coauthor network of the article can provide valuable information for research institutions to develop cooperation groups and seek cooperation opportunities for individual researchers and for publishers to form editorial teams (publishing books or special issues in journals). In VOSviewer, use coauthor analysis to generate a knowledge domain map of the coauthors of the main research group.In the coauthor relationship diagram of major research groups, the label is the abbreviation of the author’s name, the node size represents the number of articles published by the author after standardization, and the line represents the cooperative relationship between the two authors connected. The closer the cooperation, the closer the node distance, the wider the scope of cooperation, and the more links. According to VOSviewer’s calculations, there are 7046 authors involved in the heterogeneous traffic flow field. To clearly show the cooperative relationship between authors, the minimum number of published papers of authors is set as 5, the minimum number of citations is set as 100, and a total of 224 authors are displayed at last. Figure4 reflects the visualization of authors’ cooperative relationship network in the heterogeneous traffic flow field, which shows a relatively large number of authors’ achievements with the close cooperative relationships. The results show that the strengthening of cooperative relationships between authors can improve research efficiency and promote the development of heterogeneous traffic flow fields.Figure 4
Coauthor relationships among major research groups.


### 3.5. Source Journal Analysis

The source journal is an important information carrier for the dissemination and inheritance of scientific achievements. The analysis of journals in the academic field will determine the distribution of core journals in the field. According to the retrieved results, 4709 articles were published in 1095 journals, covering engineering, psychology, transportation, computer science, and other research fields.Table3 lists the top ten journals with the number of publications of heterogeneous traffic flow. “Transportation research part c-emerging technologies” publishes the largest number of documents in the field of heterogeneous traffic flow, up to 283 articles, with a total of 6129 citations. The article has been cited 21.66 times, with an impact factor of 6.077. The journal mainly deals with the development, application, and impact of transportation systems and emerging technologies, especially the impact of emerging technologies on the performance of transportation systems in terms of monitoring, efficiency, safety, and reliability. “Physical a-statistical mechanics and its applications” has the second largest number of publications, with a total of 265 articles and a total of 4485 citations, with an average of 16.92 citations per article. The journal’s impact factor is 2.924. “Transportation Research Record” ranked third in the number of articles published, with a total of 235 articles, with a total of 1754 citations, with an average of 7.46 citations per article.Table 3
The top ten journals of heterogeneous traffic flow publications.
RankJournalImpact factorQuantityCited timesThe average number of citations per article1Transportation Research Part C: Emerging Technologies6.077283612921.662Physica A: Statistical Mechanics and Its Applications2.924265448516.923Transportation Research Record1.5623517547.464IEEE Transactions on Intelligent Transportation Systems1.029140203114.515IEEE Access3.7451324733.586Journal of Advanced Transportation1.671295984.647Transportation Research Part B: Methodological4.79697178518.408Acta Physica Sinica0.62484100812.009Sustainability2.576751401.8710Accident Analysis and Prevention3.655726689.28


### 3.6. Cocitation Analysis of Documents

The document cocitation analysis was proposed by Henry Small in 1973. Its main principle is to measure the similarity between the documents by the number of times two documents are cited together; that is, if two documents are cited by the third document at the same time, the first two documents constitute a “cocitation” relationship, and their cocitation relationship increases with the increase in the number of citations. Document cocitation analysis is often used to explore the internal connections of scientific documents and describe the dynamic structure of scientific development. Document cocitation network shows the spatial location of the most cited results in the research field in the form of graphs.This section screens all the documents with the minimum number of citations of 40. A total of 149 documents meeting the threshold condition are extracted from 4709 documents. The visualization results of the document cocitation view are shown in Figure5. The document cocited knowledge graph shows the scientific knowledge base and research frontiers. The size of the node in the graph indicates the total frequency of a document being cited. The larger the node, the higher the cited frequency and the greater the influence of the document; the color of the node indicates the document. Belonging to the cluster, the documents of the same cluster have greater similarity in the research topic. As shown in Figure 5, the entire knowledge network map is divided into three color-coded clusters using the default clustering approach:(1)
Cluster 1 (Red): traffic capacity: in this cluster, the classic article with the largest density is “Enhanced Intelligent Driver Model to Access the Impact of Driving Strategies on Traffic Capacity” by Kesting et al. published in philosophical transactions of the royal society A. The number of cocitations is 283 and the total link strength is 24, indicating that this paper plays an important role in the structure of the cocitations network. In this article, Kesting investigates the influence of variable percentages of ACC vehicles on traffic flow characteristics through simulation and proposes a new car-following model that is based on the intelligent driver model (IDM) and inherits its intuitive behavioral parameters: desired velocity, acceleration, comfortable deceleration, and desired minimum time headway. At the same time, he eliminates some unrealistic behavior of the IDM. Simulation results show that sensitivities of the order of 0.3, i.e., 1 percent more ACC vehicles will lead to an increase in the capacities by about 0.3 percent with a suitable strategy. This sensitivity multiplies when considering travel times at actual breakdowns [23].Another important article is “Impacts of Cooperative Adaptive Cruise Control on Freeway Traffic Flow” by Shladover et al. published in Transportation Research Record: Journal of the Transportation Research Board. The number of cocitations is 247 and the total link strength is 11. This study estimates the effect on highway capacity of varying market penetrations of vehicles with adaptive cruise control (ACC) and cooperative adaptive cruise control (CACC). The results showed that the use of ACC was unlikely to change lane capacity significantly [24].(2)
Cluster 2 (Blue): traffic flow model: in this cluster, the classic article with the largest density is “Short-Term Traffic Forecasting: Where We Are and Where We’re Going” by Vlahogianni et al. published in the Transportation Research Part C: Emerging Technologies. The number of cocitations is 418 and the total link strength is 4. In this article, ten challenging but relatively under-studied directions of short-term traffic forecasting models are presented, and the existing challenges are summarized to make recommendations for future work [25].In this field, we also recommend “A Markov Model for Headway/Spacing Distribution of Road Traffic” and “Three-Phase Traffic Theory and Two-Phase Models with a Fundamental Diagram in the Light of Empirical Stylized Facts” as two important articles according to the ranking.“A Markov Model for Headway/Spacing Distribution of Road Traffic” by Chen and Li is published in IEEE Transactions on Intelligent Transportation Systems. The authors link two research directions of road traffic-the mesoscopic headway distribution model and the microscopic vehicle interaction model-together to account for the empirical headway/spacing distributions. In this model, empirical headway/spacing distributions are viewed as the outcomes of stochastic car-following behaviors and the reflections of the unconscious and inaccurate perceptions of space and/or time intervals that people may have [26].“Three-Phase Traffic Theory and Two-Phase Models with a Fundamental Diagram in the Light of Empirical Stylized Facts” by Treiber et al. is published in Transportation Research Part B. This article compares Kerner’s three-phase traffic theory with the phase diagram approach for traffic models with a fundamental diagram and demonstrates that models created to reproduce three-phase traffic theory create similar spatiotemporal traffic states and associated phase diagrams, no matter whether the parameters imply a fundamental diagram in equilibrium or nonunique flow-density relationships [27].(3)
Cluster 3 (Green): traffic flow stability analysis: traffic jams are usually related to the instability of traffic flow. Two kinds of traffic flow models can be used for stability analysis: the micro model and the macro model. In this cluster, “Analytical Studies on the Instabilities of Heterogeneous Intelligent Traffic Flow” by Ngoduy uses microscopic models, particularly the effect of intelligent vehicles on heterogeneous (or multiclass) traffic flow instabilities. The analytical results show that time delay destabilizes traffic flow as found in the article and that the higher intelligent vehicle percentages, the more stable traffic flow with respect to a small perturbation for a given model parameter set [28].Figure 5
Cluster density view of document cocitation network.In this field, we also recommend “Analysis on Traffic Stability and Capacity for Mixed Traffic Flow with Platoons of Intelligent Connected Vehicles” and “Longitudinal Emissions Evaluation of Mixed (Cooperative) Adaptive Cruise Control Traffic Flow and Its Relationship with Stability” as two important articles.“Analysis on Traffic Stability and Capacity for Mixed Traffic Flow with Platoons of Intelligent Connected Vehicles” by Xin Chang and Haijian Li (2020) is published in Physica A. In this paper, analytical methods for the stability and the fundamental diagram models of mixed traffic flow are developed, and the results of the sensitivity analysis demonstrated that ICVs can improve the stability of the mixed traffic flow at a critical speed. However, if this critical speed is exceeded, an increase in the number of ICVs may degrade the stability of the mixed traffic flow [29].“Longitudinal Emissions Evaluation of Mixed (Cooperative) Adaptive Cruise Control Traffic Flow and Its Relationship with Stability” by Yanyan Qin (2020) shows the impacts of the mixed CACC-MDV traffic on fuel consumption and emissions, by taking into consideration partial degenerations from stable CACC vehicles to unstable ACC vehicles. The results show that stability situations of the mixed traffic qualitatively influence the impact trend of CACC MPRs on fuel consumption and emissions [30].


### 3.7. Keyword Cooccurrence Analysis

Keyword cooccurrence analysis is a common research method in bibliometrics. By studying the cooccurrence relationship of cooccurring keywords in a large number of documents, it is used to analyze the link strength between cooccurring keywords. Its usage is to describe the internal relationship and structure of a certain academic field and to reveal the research front of the subject. The research front refers to the conceptual combination of temporary research topics and basic research issues, as well as theoretical trends and new topics that arise or emerge unexpectedly. In VOSviewer, cooccurrence analysis is used to generate a heterogeneous traffic flow research cooccurring keyword network, as shown in Figure6.Figure 6
Keywords cooccurrence network of intelligent vehicles studies.In Figure6, it can be seen that the frontier topics of heterogeneous traffic flow research form five groups, and the keywords in the same group show greater similarity in the research topics. According to the characteristics and current situation of heterogeneous traffic flow research, the following five categories are analyzed:


#### 3.7.1. Group 1 (Red): Analysis of Modeling and Optimization Methods for Heterogeneous Traffic Flow

This cluster contains a total of 55 keywords, mainly including model, systems, algorithm, optimization, and framework. The visualization results of the cluster show that keywords such as model, algorithm, and optimization are cooccurring high-frequency words.From the perspective of research, the traffic flow model can be divided into a macro traffic flow model and a micro traffic flow model [31]. The microscopic traffic flow model processes traffic flow into dispersed particles to reflect the characteristics of traffic flow [32–35]. The macroscopic traffic flow model regards all vehicles on the whole road as a compressible continuous fluid, deduces the relationship among vehicle density ρ, the average velocity V, and flow Q, and thus describes the mathematical model of traffic flow operation law [36–39]. So far, the researchers have developed a variety of traffic models used to study the complex phenomenon and obtained many important results [40, 41]; however, these traditional traffic flow models did not consider the information interaction between the vehicle and synergy, also lack the research of vehicle heterogeneous factors, and therefore, cannot be directly used to study the heterogeneous traffic flow.To study the heterogeneity of traffic flow, Tang et al. [42] proposed a new vehicle following model based on the properties of heterogeneous traffic flow and the relationship between micro and macro variables, establishing a new dynamic model for heterogeneous traffic flow. Ngoduy et al. [43] established a new macro traffic flow model based on the aerodynamic method to describe the driving behavior of vehicle queues and analyze the influence of intelligent vehicle permeability. Levin M W et al. [44] developed a vehicle following model for predicting scene capacity and wave speed in combination with driver response time. The research results show that travel time has a linear relationship with the proportion of autonomous vehicles, and the travel time will be significantly reduced when the penetration rate of autonomous vehicles reaches over 80%.


#### 3.7.2. Group 2 (Green): Analysis of Macroscopic Traffic Flow Characteristics of Heterogeneous Traffic Flow

This cluster contains a total of 32 keywords, mainly including traffic flow, stability, waves, fuel consumption, and jamming transition.In traffic flow research, the impact of autonomous vehicles on traffic flow stability and traffic flow capacity is an important research topic. Many current works have explored the traffic capacity and stability of heterogeneous traffic flow and intelligent traffic. Kesting et al. [44] proposed an intelligent driver model, that is, automatic real-time detection of traffic conditions based on local information, to adapt to the driving characteristics of ACC.The results of the test show that at a 25% penetration rate, ACC vehicles can eliminate congestion during specific peak periods of the simulation. Shladover et al. [24] conducted a simulation study on the traffic capacity of single-lane expressways with CACC vehicles mixed with different permeability, and the results showed that the ACC model could not significantly improve the traffic capacity, while the CACC model with medium and high permeability could greatly improve the traffic capacity. Arnaout et al. [45] studied the influence of permeability on traffic capacity under different traffic demand conditions and found that CACC permeability had a significant impact on traffic capacity when traffic demand was high. At the same time, Arnaout et al. [46] studied the impact of different CACC permeability on traffic efficiency under different traffic demands, and the results showed that CACC permeability had no impact on traffic capacity when traffic demand was low. However, when the traffic demand is high and the permeability exceeds 40%, the permeability has a substantial impact on the increase of traffic capacity.


#### 3.7.3. Group 3 (Blue): Analysis of Driving Behavior in Heterogeneous Traffic Flow

There are 29 keywords in this cluster, mainly including behavior, time, adaptive cruise control, safety, risk, and accidents.When a car is running, the driver needs to control the car based on information provided by the environment, road signs, signals, and instrumentation in the car. Information can be obtained through visual, tactile, and auditory means. Among them, more than 80% of the driver’s information is obtained through visual channels, followed by hearing. Driving behavior can be seen as a repetitive message processing model composed of information perception, judgment, and decision-making and actions; that is, judgment and decision-making are the execution of manipulation actions after receiving the perception signal [47]. In the traditional traffic flow field, the analysis of driving behavior generally adopts subjective questionnaire data and objective driving data. Through a reasonable questionnaire, drivers can be divided into various types (such as aggressive, cautious, slow). However, drivers tend to hide their usual aggressive driving behaviors when conducting self-evaluation through the questionnaire, so the collected questionnaire cannot truly describe drivers’ driving behaviors. The collected objective driving data of drivers can be used to classify drivers according to clustering analysis or principal component analysis, but during data collection, drivers will feel that they are in a monitoring environment and change their real driving behavior.In the field of heterogeneous traffic flow, researchers have built different driver models mainly to stimulate and recognize the behavior of human-driven vehicles in heterogeneous traffic flow. These researches are mainly divided into driver behavior models based on control theory and driver behavior models based on machine learning theory. The driver behavior model based on control theory mainly assumes that the driving trajectory is known, studies the driver and the vehicle as a whole, and predicts the vehicle trajectory in the future in real-time according to the historical running state of the vehicle. For example, Song et al. [48] established a “single-lane auto-manual driving mixed traffic flow model considering driving behavior” and a “three-lane auto-manual driving mixed traffic flow model considering driving behavior” based on cellular automata and conducted simulation tests. Zhu et al. [49] used Bando’s model and a modified Bando’s model to describe human driver behavior and autonomous vehicle, respectively, and conducted stability analysis on heterogeneous traffic flow. Zheng et al. [50] established a “random model of auto-manual driving mixed traffic flow” based on fully considering the uncertainty of human driving behavior and the interaction between automatic driving and manual driving vehicles. The driver behavior model based on machine learning theory uses the big data of vehicle operation to obtain the characteristic information of the driver and then describes the decision-making process of the driver, to establish the driver behavior model. Wang et al. [51] organized drivers to carry out the following test, analyzed the difference of speed difference cycle in the following process, divided driver types according to driving parameters through cluster analysis, and established an improved IDM model. Michael et al. [44] developed the following model including driver reaction time to study the traffic capacity and backward wave speed of autonomous vehicles under different permeability. Chen et al. [52] used the driver’s driving behavior data obtained by the simulation platform to classify the characteristics of the following behavior obtained and solved the problem of operation difference caused by sequence transformation of vehicles in the fleet.


#### 3.7.4. Group 4 (Yellow): Simulation Experiment Analysis of Heterogeneous Traffic Flow

There are 28 keywords in this cluster, mainly including simulation, cellular-automaton model, delay, and states.With the gradual maturity of autonomous driving technology, the heterogeneous traffic flow phenomenon formed by autonomous driving vehicles and manual driving vehicles must exist for a long time. Due to the uncertainty of heterogeneous traffic flow, such as safety, coordination ability, and efficiency, people have raised doubts about the safety of autonomous vehicles. Although the above problems can be verified by establishing a real road test field for real vehicle test, the cost of real vehicle test is too high, there are too few test bases with test qualification, and the test results are susceptible to the influence of the environment and test conditions. The traffic flow simulation test has the characteristics of repeatability, safety, economy, and effectiveness, which can facilitate researchers to carry out tests at lower costs under the same initial conditions.A simulation model is a mathematical/logical representation of a real-world system, which takes the form of software that is executed experimentally on a digital computer. Common simulation models used in traffic flow include CORSIM, MITSIM, and VISSIM, but most of these models are based on homogeneous traffic conditions and are not suitable for studying the characteristics of heterogeneous traffic flow. Therefore, Vander Werf et al. [53] used Monte Carlo simulation to estimate the impact of vehicle types on lane capacity based on models in the literature and conducted a sensitivity analysis of ACC and CACC vehicle time-interval parameters in simulation tests. Van Arem et al. [54] applied the intelligent vehicle test simulation platform to simulate and analyze the influence of different CACC vehicle ratios on traffic capacity because of the bottleneck section of the expressway with fewer lanes. Talebpour and Mahmassani [55] applied the ACC vehicle and CACC vehicle following model and conducted numerical simulation experiments to present scatter diagrams of mixed traffic flow concerning density under different traffic demands and different CACC/ACC vehicle ratios. The influence of CACC vehicles and ACC vehicles on-ramp capacity is analyzed. Based on simulation experiments, Lioris [56] studied the impact of the Internet of vehicles’ fleet on the capacity of urban road system intersections. Hartmann et al. [57]. studied the influence of CAV on the capacity of the German expressway network through a micro traffic flow simulation experiment. Bujanovic and Lochrane [58] quantitatively analyzed the influence of CAV on the capacity of basic sections of expressways and applied VISSIM simulation software to verify and analyze the proposed model.


#### 3.7.5. Group 5 (Purple): Policies and Barriers in Heterogeneous Traffic Flow

There are 26 keywords in this cluster, mainly including policy, impacts, delay, and emissions.It is widely believed that autonomous driving can provide safer and more comfortable driving and is an important part of urban intelligent transportation systems. In this regard, the United States, Japan, Europe, and other developed countries and regions have increased their research and development and investment in autonomous driving in terms of policies. In particular, the United States has already carried out strategic planning and technical testing of autonomous driving technology as an important part of intelligent transportation systems at the national level.However, on the other hand, the application of autonomous vehicles may also have adverse effects on the existing traffic system, such as interfering with road traffic, affecting the safety of other vehicles, and other potential threats. Due to the high initial cost of autonomous vehicles, unclear accident liability details, and uncertain privacy issues, the acceptance of autonomous vehicles is not high among the general public. Therefore, many domestic and foreign scholars have a strong interest in the policies and obstacles of autonomous driving vehicles.Daniel [59] explores the feasible aspects of AVs and discusses their potential impacts on the transportation system. And this paper explores the feasible aspects of AVs and discusses their potential impacts on the transportation system. Another paper “Policy and Society Related Implications of Automated Driving: A Review of Article and Directions for Future Research” by Milonakis is published in the Journal of Intelligent Transportation Systems. In this paper, the potential effects of automated driving that are relevant to policy and society are explored, findings discussed in the article about those effects are reviewed, and areas for future research are identified [60].


### 3.8. Analysis of Burst Detection: Research Trends of Heterogeneous Traffic Flow

The burst detection algorithm was first proposed by Kleinberg in 2003. It identifies keywords with high-frequency density characteristics in the article by detecting the density of keyword frequency changes. Burst detection analysis can be used to detect the frequency of sudden increase of words in topics and keywords and to obtain the start time, end time, and weight of sudden keywords. Through this information, the emergent hot spots and research trends in the field of heterogeneous traffic flow research can be analyzed. CiteSpace regards this kind of mutation information as a way to measure deeper changes. Burst detection in CiteSpace can be used for two types of variables: one is the frequency of words or phrases used in the cited documents, and the other is the frequency of citations obtained from the cited documents. Import the data into the CiteSpace tool and run it for burst detection. The parameters are set as follows:γ = 1.0, the number of states = 2.0, and minimum duration = 2. Select the top 20 meaningful keywords with the largest burst weight for visual analysis, as shown in Figure 7.Figure 7
Keywords of the top 20 burst weights from 2004 to 2021.As shown in Figure7, “Start year” and “end year” represent the year of burst keyword duration from start to end. Intensity represents the frequency of keyword occurrences. From the point of view of burst intensity, cellular automata, traffic flow, numerical simulation, and other links have high intensity. It can be seen that traditional traffic flow studies focus on using the cellular automata model for modeling and carry out numerical simulation calculation; related articles include spatial-temporal patterns in heterogeneous traffic flow with a variety of driver behavioral characteristics and vehicle parameters. Different from the traditional heterogeneous traffic flow research, heterogeneous traffic flow research in the new period is mostly dependent on artificial intelligence, cloud computing, big data, and other new-generation network technologies represented by the Internet of vehicles. Related articles include Linear Stability Analysis of Heterogeneous Traffic Flow considering Degradations of Connected Automated Vehicles and Reaction Time. Capacity and stability are macro characteristics of heterogeneous traffic flow, which have a great impact on the safety and efficiency of heterogeneous traffic flow. Related articles include Controllability Analysis and Optimal Control of Mixed Traffic Flow with Human-Driven and Autonomous “Vehicles,” Stability Analysis, and the Fundamental Diagram for Mixed Connected Automated and Human-driven Vehicles and Analysis on Traffic Stability and Capacity for Mixed Traffic Flow with Platoons of Intelligent Connected Vehicles.The burst intensity of the dynamic model, car-following model, and adaptive cruise control was 29,108, 55,438, and 3085, respectively. Adaptive cruise control not only has the function of cruise control but also adaptively adjusts the motion state of the vehicle in front according to the motion state of the vehicle, which has a certain influence on the traffic flow research: “Cooperative Adaptive Cruise Control and Exhaust Emission Evaluation Under Heterogeneous Connected Vehicle Network Environment in Urban City,” “Cooperative Adaptive Cruise Control and Intelligent Traffic Signal Interaction: A Field Operational Test with Platooning on a Suburban Arterial in Real Traffic,” and “Longitudinal Emissions Evaluation of Mixed (Cooperative) Adaptive Cruise Control Traffic Flow and Its Relationship with Stability.”


## 3.1. Annual Distribution Statistics of the Article

The annual distribution of articles refers to the difference in the distribution of the number of articles in the same time zone, which can reflect the development process of people, institutions, or subject research and divide the active trend of subject research. The change in the number of academic papers on a subject is an important indicator of the development trend of the research field, and it is also a reflection of the change in the scope of subject knowledge. By drawing a graph of the number of documents and conducting multivariate statistical analysis, one can understand the research level and future development trend of a certain field.To better explore the relevant characteristics and conditions in the field of heterogeneous traffic flow in a period, this paper considers the number of documents in the field of heterogeneous traffic flow, which are divided into three stages based on the growth of the article during the period, namely, “initial stage (2004–2009),” “preliminary development stage (2010–2015),” and “rapid development stage (2016–2020).” On the one hand, segmenting the field according to the same time can better compare and analyze the growth of articles and the characteristics of research trends in each period. On the other hand, because the research on heterogeneous traffic flow started late and the period is not long, it is relatively reasonable to set 5 years as an academic research cycle.According to the search results, the earliest research article on heterogeneous traffic flow was published in 2004 and lasted until 2021. It already contains 4703 related documents. The annual distribution statistics are shown in Figure1. It is worth noting that due to 2020 the data is still being updated, so the data in the statistics is small.Figure 1
Quantitative distribution of published articles in heterogeneous traffic flow studies, 2004–2020.Initial stage (2004–2009): from the first article published in 2004 to 2008, there were few related research results in this field, and only 73 papers (2009) were published each year, which means that there is research on qualitative traffic flow has just started, and a complete document system has not yet been formed.Primary development stage (2010–2015): as countries pay more and more attention to road safety, autonomous driving has set off a research boom and has begun to enter the primary development stage. The number of relevant documents at this stage has increased significantly, with an average increase of 33 documents per year. It can be considered that the field of heterogeneous traffic flow research was initially formed during this period.Rapid development stage (2016–2020): after the accumulation of knowledge in the initial stage and the primary development stage, the number of relevant documents in this stage has grown rapidly. This shows that the research enthusiasm in the field of heterogeneous traffic flow is continuously increasing and has entered a stage of rapid development.


## 3.2. Country and Regional Statistics

For national and regional factors, this article presents four indicators to analyze the distribution area and situation of the documents, namely, the number of documents (articles), the percentage of documents in the total number of documents, the total number of citations of documents (times), and the average single document. The number of citations is shown in Table1. The use of these indicators mainly considers two aspects: on the one hand, the number of documents in a country can reflect the research enthusiasm of researchers in each country in the field; on the other hand, the total number of citations and the average number of citations per article can be to a certain extent. This indicates the quality of the article of national researchers, reflecting the depth of research in this field by researchers from various countries.Table 1
The top ten countries in the number of articles in the heterogeneous traffic flow research field.
RankCountry/territoriesQuantityPercentageTotal cited timesThe average number of citations per article1China208744.28172518.272USA113924.171151810.113India3427.2628948.464Germany2064.37319015.495England1873.97273214.616Australia1673.54190611.417Netherlands1523.23206313.578Canada1392.9512839.239Japan1312.7811228.5610South Korea1212.577205.95According to the retrieved results, the article on heterogeneous traffic flow mainly comes from 88 countries (or regions). Table1 lists the top 10 countries in the field of heterogeneous traffic flow research from 2004 to the present. Japanese science historian Yuasa (1962) defined a country with more than 25% of the world’s major scientific achievements as the center of scientific activity. According to the data in Table 1, China ranks first with 2087 articles, accounting for 44.28% of the total number of articles. The average number of citations per article is 8.27, followed by the United States (1139) and India (342). The center of scientific activity in the field of heterogeneous traffic flow research is as follows. Four Asian countries (China, India, Japan, and South Korea) among the top ten countries in the number of articles indicate that Asian countries have performed well in research on heterogeneous traffic flow. European countries have excellent performance in the average number of citations per article, such as Germany (average number of citations per article 15.49), the United Kingdom (average number of citations per article 14.61), and the Netherlands (average number of citations per article 13.57), which shows that the article published in these countries has been highly recognized by researchers.In VOSviewer, citation analysis is used to generate a scientific knowledge map of the country in the field of heterogeneous traffic flow. This article uses VOSviewer software to analyze the collected data and make a density view based on the distribution of national documents. The density view can visually display the situation of the country/region in the density dimension. Each label in the figure represents a country, and the label is the center point to form a region. The size and color of the region depend on the country/region represented by the label the number of published documents, the larger the number, the brighter the color, and the smaller the number, the darker the color. The location of the tag depends on the number of items near the tag and their importance. The density view can help understand the overall structure of the map and draw attention to the most important areas of the map.This article sets the display conditions for countries/regions with five or more related article achievements, a total of 60 countries/regions, as shown in Figure2. The density view can see the overall structure of the distribution of national or regional documents. In the figure, China and the United States are in the center of the figure, indicating that China and the United States play an important role in the field of heterogeneous traffic flow.Figure 2
Density distribution of heterogeneous traffic flow in major countries.


## 3.3. Analysis of Main Research Institutions

By analyzing the cooperation relationship between research institutions, information about the most outstanding organizations and groups in a certain field in the discipline can be determined. To analyze the cooperative relationship between the research institutions related to the article, this paper uses VOSviewer to construct a cooperation network between major research institutions to analyze the participating institutions of heterogeneous traffic flow research, as shown in Figure3.Figure 3
Collaborative networks among major research institutions.In the interinstitutional cooperation network diagram, the label is the name of the research institution, the size of the node indicates the number of standardized documents, and the connection indicates the cooperative relationship between the two connected research institutions. The closer the cooperation, the closer the node distance, the wider the scope of cooperation, the more connections. Figure3 shows that Beijing Jiao tong University is at the center of the gathering point, indicating that Beijing Jiao tong University and other research institutions have established close cooperation in the field of heterogeneous traffic flow.The number of published documents of research institutions is also one of the important indicators to measure the contributions made by research institutions in the field. The article in this field comes from a total of 2512 organizations. Table2 lists the top 10 organizations with the largest number of published articles. The research strength of a university is often an indicator of the national scientific research and innovation ability. Table 2 shows that a total of 9 universities contributed 1173 papers, accounting for 24.89% of the total number of heterogeneous traffic flow publications. Among them, Chinese universities and research institutes are heterogeneous traffic. The main contributors to stream research are as follows: these organizations have published 1059 papers, accounting for 22.47% of the total number of papers. Among Chinese universities, Beijing Jiaotong University ranked first in the number of publications of 213 articles, with an average of 161.85 citations per article, indicating that Beijing Jiaotong University is in a leading position in the field of heterogeneous traffic flow research. Southeast University (187 articles) and Tongji University (154 articles) followed closely. Among the 2512 organizations, only 87 organizations published 20 papers or more, accounting for 3.46% of the total. This result shows that the published documents are concentrated in a few organizations.Table 2
Organization of the top 10 research achievements in heterogeneous traffic flow from 2004 to 2021.
RankOrganizationLink strengthQuantityPercentageCited timesThe average number of citations per article1Beijing Jiaotong University1252134.522276161.852Southeast University1291873.971116143.583Tongji University1061543.27852142.864Tsinghua University861332.821200147.995Delft University technology241202.551874192.286Beihang University801002.121803169.317Changan University52931.9745686.698Ningbo University103921.951013128.089Jiangsu Provincial Collaborative Innovation Center modern urban109871.85892110.1610Indian Institute of Technology4811.72110666.43


## 3.4. Coauthor Analysis of the Main Research Group

Counting the number of articles published by authors on the topic and comparing and analyzing them can understand the main authors and core author groups in the field and can further establish their important role and influence in related fields by understanding the author’s research progress and by paying attention to them. The research direction and focus, to understand its leading and leading role in the development of the whole discipline, is of great significance for further understanding the current situation and future development of special research. Because the research in the field of heterogeneous traffic flow is highly interdisciplinary, researchers come from different fields such as traffic engineering, traffic planning, mathematics, psychology, computer science, medicine, and statistics, and cooperation can achieve complementary advantages. The creation and analysis of the knowledge graph of the coauthor network of the article can provide valuable information for research institutions to develop cooperation groups and seek cooperation opportunities for individual researchers and for publishers to form editorial teams (publishing books or special issues in journals). In VOSviewer, use coauthor analysis to generate a knowledge domain map of the coauthors of the main research group.In the coauthor relationship diagram of major research groups, the label is the abbreviation of the author’s name, the node size represents the number of articles published by the author after standardization, and the line represents the cooperative relationship between the two authors connected. The closer the cooperation, the closer the node distance, the wider the scope of cooperation, and the more links. According to VOSviewer’s calculations, there are 7046 authors involved in the heterogeneous traffic flow field. To clearly show the cooperative relationship between authors, the minimum number of published papers of authors is set as 5, the minimum number of citations is set as 100, and a total of 224 authors are displayed at last. Figure4 reflects the visualization of authors’ cooperative relationship network in the heterogeneous traffic flow field, which shows a relatively large number of authors’ achievements with the close cooperative relationships. The results show that the strengthening of cooperative relationships between authors can improve research efficiency and promote the development of heterogeneous traffic flow fields.Figure 4
Coauthor relationships among major research groups.


## 3.5. Source Journal Analysis

The source journal is an important information carrier for the dissemination and inheritance of scientific achievements. The analysis of journals in the academic field will determine the distribution of core journals in the field. According to the retrieved results, 4709 articles were published in 1095 journals, covering engineering, psychology, transportation, computer science, and other research fields.Table3 lists the top ten journals with the number of publications of heterogeneous traffic flow. “Transportation research part c-emerging technologies” publishes the largest number of documents in the field of heterogeneous traffic flow, up to 283 articles, with a total of 6129 citations. The article has been cited 21.66 times, with an impact factor of 6.077. The journal mainly deals with the development, application, and impact of transportation systems and emerging technologies, especially the impact of emerging technologies on the performance of transportation systems in terms of monitoring, efficiency, safety, and reliability. “Physical a-statistical mechanics and its applications” has the second largest number of publications, with a total of 265 articles and a total of 4485 citations, with an average of 16.92 citations per article. The journal’s impact factor is 2.924. “Transportation Research Record” ranked third in the number of articles published, with a total of 235 articles, with a total of 1754 citations, with an average of 7.46 citations per article.Table 3
The top ten journals of heterogeneous traffic flow publications.
RankJournalImpact factorQuantityCited timesThe average number of citations per article1Transportation Research Part C: Emerging Technologies6.077283612921.662Physica A: Statistical Mechanics and Its Applications2.924265448516.923Transportation Research Record1.5623517547.464IEEE Transactions on Intelligent Transportation Systems1.029140203114.515IEEE Access3.7451324733.586Journal of Advanced Transportation1.671295984.647Transportation Research Part B: Methodological4.79697178518.408Acta Physica Sinica0.62484100812.009Sustainability2.576751401.8710Accident Analysis and Prevention3.655726689.28


## 3.6. Cocitation Analysis of Documents

The document cocitation analysis was proposed by Henry Small in 1973. Its main principle is to measure the similarity between the documents by the number of times two documents are cited together; that is, if two documents are cited by the third document at the same time, the first two documents constitute a “cocitation” relationship, and their cocitation relationship increases with the increase in the number of citations. Document cocitation analysis is often used to explore the internal connections of scientific documents and describe the dynamic structure of scientific development. Document cocitation network shows the spatial location of the most cited results in the research field in the form of graphs.This section screens all the documents with the minimum number of citations of 40. A total of 149 documents meeting the threshold condition are extracted from 4709 documents. The visualization results of the document cocitation view are shown in Figure5. The document cocited knowledge graph shows the scientific knowledge base and research frontiers. The size of the node in the graph indicates the total frequency of a document being cited. The larger the node, the higher the cited frequency and the greater the influence of the document; the color of the node indicates the document. Belonging to the cluster, the documents of the same cluster have greater similarity in the research topic. As shown in Figure 5, the entire knowledge network map is divided into three color-coded clusters using the default clustering approach:(1)
Cluster 1 (Red): traffic capacity: in this cluster, the classic article with the largest density is “Enhanced Intelligent Driver Model to Access the Impact of Driving Strategies on Traffic Capacity” by Kesting et al. published in philosophical transactions of the royal society A. The number of cocitations is 283 and the total link strength is 24, indicating that this paper plays an important role in the structure of the cocitations network. In this article, Kesting investigates the influence of variable percentages of ACC vehicles on traffic flow characteristics through simulation and proposes a new car-following model that is based on the intelligent driver model (IDM) and inherits its intuitive behavioral parameters: desired velocity, acceleration, comfortable deceleration, and desired minimum time headway. At the same time, he eliminates some unrealistic behavior of the IDM. Simulation results show that sensitivities of the order of 0.3, i.e., 1 percent more ACC vehicles will lead to an increase in the capacities by about 0.3 percent with a suitable strategy. This sensitivity multiplies when considering travel times at actual breakdowns [23].Another important article is “Impacts of Cooperative Adaptive Cruise Control on Freeway Traffic Flow” by Shladover et al. published in Transportation Research Record: Journal of the Transportation Research Board. The number of cocitations is 247 and the total link strength is 11. This study estimates the effect on highway capacity of varying market penetrations of vehicles with adaptive cruise control (ACC) and cooperative adaptive cruise control (CACC). The results showed that the use of ACC was unlikely to change lane capacity significantly [24].(2)
Cluster 2 (Blue): traffic flow model: in this cluster, the classic article with the largest density is “Short-Term Traffic Forecasting: Where We Are and Where We’re Going” by Vlahogianni et al. published in the Transportation Research Part C: Emerging Technologies. The number of cocitations is 418 and the total link strength is 4. In this article, ten challenging but relatively under-studied directions of short-term traffic forecasting models are presented, and the existing challenges are summarized to make recommendations for future work [25].In this field, we also recommend “A Markov Model for Headway/Spacing Distribution of Road Traffic” and “Three-Phase Traffic Theory and Two-Phase Models with a Fundamental Diagram in the Light of Empirical Stylized Facts” as two important articles according to the ranking.“A Markov Model for Headway/Spacing Distribution of Road Traffic” by Chen and Li is published in IEEE Transactions on Intelligent Transportation Systems. The authors link two research directions of road traffic-the mesoscopic headway distribution model and the microscopic vehicle interaction model-together to account for the empirical headway/spacing distributions. In this model, empirical headway/spacing distributions are viewed as the outcomes of stochastic car-following behaviors and the reflections of the unconscious and inaccurate perceptions of space and/or time intervals that people may have [26].“Three-Phase Traffic Theory and Two-Phase Models with a Fundamental Diagram in the Light of Empirical Stylized Facts” by Treiber et al. is published in Transportation Research Part B. This article compares Kerner’s three-phase traffic theory with the phase diagram approach for traffic models with a fundamental diagram and demonstrates that models created to reproduce three-phase traffic theory create similar spatiotemporal traffic states and associated phase diagrams, no matter whether the parameters imply a fundamental diagram in equilibrium or nonunique flow-density relationships [27].(3)
Cluster 3 (Green): traffic flow stability analysis: traffic jams are usually related to the instability of traffic flow. Two kinds of traffic flow models can be used for stability analysis: the micro model and the macro model. In this cluster, “Analytical Studies on the Instabilities of Heterogeneous Intelligent Traffic Flow” by Ngoduy uses microscopic models, particularly the effect of intelligent vehicles on heterogeneous (or multiclass) traffic flow instabilities. The analytical results show that time delay destabilizes traffic flow as found in the article and that the higher intelligent vehicle percentages, the more stable traffic flow with respect to a small perturbation for a given model parameter set [28].Figure 5
Cluster density view of document cocitation network.In this field, we also recommend “Analysis on Traffic Stability and Capacity for Mixed Traffic Flow with Platoons of Intelligent Connected Vehicles” and “Longitudinal Emissions Evaluation of Mixed (Cooperative) Adaptive Cruise Control Traffic Flow and Its Relationship with Stability” as two important articles.“Analysis on Traffic Stability and Capacity for Mixed Traffic Flow with Platoons of Intelligent Connected Vehicles” by Xin Chang and Haijian Li (2020) is published in Physica A. In this paper, analytical methods for the stability and the fundamental diagram models of mixed traffic flow are developed, and the results of the sensitivity analysis demonstrated that ICVs can improve the stability of the mixed traffic flow at a critical speed. However, if this critical speed is exceeded, an increase in the number of ICVs may degrade the stability of the mixed traffic flow [29].“Longitudinal Emissions Evaluation of Mixed (Cooperative) Adaptive Cruise Control Traffic Flow and Its Relationship with Stability” by Yanyan Qin (2020) shows the impacts of the mixed CACC-MDV traffic on fuel consumption and emissions, by taking into consideration partial degenerations from stable CACC vehicles to unstable ACC vehicles. The results show that stability situations of the mixed traffic qualitatively influence the impact trend of CACC MPRs on fuel consumption and emissions [30].


## 3.7. Keyword Cooccurrence Analysis

Keyword cooccurrence analysis is a common research method in bibliometrics. By studying the cooccurrence relationship of cooccurring keywords in a large number of documents, it is used to analyze the link strength between cooccurring keywords. Its usage is to describe the internal relationship and structure of a certain academic field and to reveal the research front of the subject. The research front refers to the conceptual combination of temporary research topics and basic research issues, as well as theoretical trends and new topics that arise or emerge unexpectedly. In VOSviewer, cooccurrence analysis is used to generate a heterogeneous traffic flow research cooccurring keyword network, as shown in Figure6.Figure 6
Keywords cooccurrence network of intelligent vehicles studies.In Figure6, it can be seen that the frontier topics of heterogeneous traffic flow research form five groups, and the keywords in the same group show greater similarity in the research topics. According to the characteristics and current situation of heterogeneous traffic flow research, the following five categories are analyzed:


### 3.7.1. Group 1 (Red): Analysis of Modeling and Optimization Methods for Heterogeneous Traffic Flow

This cluster contains a total of 55 keywords, mainly including model, systems, algorithm, optimization, and framework. The visualization results of the cluster show that keywords such as model, algorithm, and optimization are cooccurring high-frequency words.From the perspective of research, the traffic flow model can be divided into a macro traffic flow model and a micro traffic flow model [31]. The microscopic traffic flow model processes traffic flow into dispersed particles to reflect the characteristics of traffic flow [32–35]. The macroscopic traffic flow model regards all vehicles on the whole road as a compressible continuous fluid, deduces the relationship among vehicle density ρ, the average velocity V, and flow Q, and thus describes the mathematical model of traffic flow operation law [36–39]. So far, the researchers have developed a variety of traffic models used to study the complex phenomenon and obtained many important results [40, 41]; however, these traditional traffic flow models did not consider the information interaction between the vehicle and synergy, also lack the research of vehicle heterogeneous factors, and therefore, cannot be directly used to study the heterogeneous traffic flow.To study the heterogeneity of traffic flow, Tang et al. [42] proposed a new vehicle following model based on the properties of heterogeneous traffic flow and the relationship between micro and macro variables, establishing a new dynamic model for heterogeneous traffic flow. Ngoduy et al. [43] established a new macro traffic flow model based on the aerodynamic method to describe the driving behavior of vehicle queues and analyze the influence of intelligent vehicle permeability. Levin M W et al. [44] developed a vehicle following model for predicting scene capacity and wave speed in combination with driver response time. The research results show that travel time has a linear relationship with the proportion of autonomous vehicles, and the travel time will be significantly reduced when the penetration rate of autonomous vehicles reaches over 80%.


### 3.7.2. Group 2 (Green): Analysis of Macroscopic Traffic Flow Characteristics of Heterogeneous Traffic Flow

This cluster contains a total of 32 keywords, mainly including traffic flow, stability, waves, fuel consumption, and jamming transition.In traffic flow research, the impact of autonomous vehicles on traffic flow stability and traffic flow capacity is an important research topic. Many current works have explored the traffic capacity and stability of heterogeneous traffic flow and intelligent traffic. Kesting et al. [44] proposed an intelligent driver model, that is, automatic real-time detection of traffic conditions based on local information, to adapt to the driving characteristics of ACC.The results of the test show that at a 25% penetration rate, ACC vehicles can eliminate congestion during specific peak periods of the simulation. Shladover et al. [24] conducted a simulation study on the traffic capacity of single-lane expressways with CACC vehicles mixed with different permeability, and the results showed that the ACC model could not significantly improve the traffic capacity, while the CACC model with medium and high permeability could greatly improve the traffic capacity. Arnaout et al. [45] studied the influence of permeability on traffic capacity under different traffic demand conditions and found that CACC permeability had a significant impact on traffic capacity when traffic demand was high. At the same time, Arnaout et al. [46] studied the impact of different CACC permeability on traffic efficiency under different traffic demands, and the results showed that CACC permeability had no impact on traffic capacity when traffic demand was low. However, when the traffic demand is high and the permeability exceeds 40%, the permeability has a substantial impact on the increase of traffic capacity.


### 3.7.3. Group 3 (Blue): Analysis of Driving Behavior in Heterogeneous Traffic Flow

There are 29 keywords in this cluster, mainly including behavior, time, adaptive cruise control, safety, risk, and accidents.When a car is running, the driver needs to control the car based on information provided by the environment, road signs, signals, and instrumentation in the car. Information can be obtained through visual, tactile, and auditory means. Among them, more than 80% of the driver’s information is obtained through visual channels, followed by hearing. Driving behavior can be seen as a repetitive message processing model composed of information perception, judgment, and decision-making and actions; that is, judgment and decision-making are the execution of manipulation actions after receiving the perception signal [47]. In the traditional traffic flow field, the analysis of driving behavior generally adopts subjective questionnaire data and objective driving data. Through a reasonable questionnaire, drivers can be divided into various types (such as aggressive, cautious, slow). However, drivers tend to hide their usual aggressive driving behaviors when conducting self-evaluation through the questionnaire, so the collected questionnaire cannot truly describe drivers’ driving behaviors. The collected objective driving data of drivers can be used to classify drivers according to clustering analysis or principal component analysis, but during data collection, drivers will feel that they are in a monitoring environment and change their real driving behavior.In the field of heterogeneous traffic flow, researchers have built different driver models mainly to stimulate and recognize the behavior of human-driven vehicles in heterogeneous traffic flow. These researches are mainly divided into driver behavior models based on control theory and driver behavior models based on machine learning theory. The driver behavior model based on control theory mainly assumes that the driving trajectory is known, studies the driver and the vehicle as a whole, and predicts the vehicle trajectory in the future in real-time according to the historical running state of the vehicle. For example, Song et al. [48] established a “single-lane auto-manual driving mixed traffic flow model considering driving behavior” and a “three-lane auto-manual driving mixed traffic flow model considering driving behavior” based on cellular automata and conducted simulation tests. Zhu et al. [49] used Bando’s model and a modified Bando’s model to describe human driver behavior and autonomous vehicle, respectively, and conducted stability analysis on heterogeneous traffic flow. Zheng et al. [50] established a “random model of auto-manual driving mixed traffic flow” based on fully considering the uncertainty of human driving behavior and the interaction between automatic driving and manual driving vehicles. The driver behavior model based on machine learning theory uses the big data of vehicle operation to obtain the characteristic information of the driver and then describes the decision-making process of the driver, to establish the driver behavior model. Wang et al. [51] organized drivers to carry out the following test, analyzed the difference of speed difference cycle in the following process, divided driver types according to driving parameters through cluster analysis, and established an improved IDM model. Michael et al. [44] developed the following model including driver reaction time to study the traffic capacity and backward wave speed of autonomous vehicles under different permeability. Chen et al. [52] used the driver’s driving behavior data obtained by the simulation platform to classify the characteristics of the following behavior obtained and solved the problem of operation difference caused by sequence transformation of vehicles in the fleet.


### 3.7.4. Group 4 (Yellow): Simulation Experiment Analysis of Heterogeneous Traffic Flow

There are 28 keywords in this cluster, mainly including simulation, cellular-automaton model, delay, and states.With the gradual maturity of autonomous driving technology, the heterogeneous traffic flow phenomenon formed by autonomous driving vehicles and manual driving vehicles must exist for a long time. Due to the uncertainty of heterogeneous traffic flow, such as safety, coordination ability, and efficiency, people have raised doubts about the safety of autonomous vehicles. Although the above problems can be verified by establishing a real road test field for real vehicle test, the cost of real vehicle test is too high, there are too few test bases with test qualification, and the test results are susceptible to the influence of the environment and test conditions. The traffic flow simulation test has the characteristics of repeatability, safety, economy, and effectiveness, which can facilitate researchers to carry out tests at lower costs under the same initial conditions.A simulation model is a mathematical/logical representation of a real-world system, which takes the form of software that is executed experimentally on a digital computer. Common simulation models used in traffic flow include CORSIM, MITSIM, and VISSIM, but most of these models are based on homogeneous traffic conditions and are not suitable for studying the characteristics of heterogeneous traffic flow. Therefore, Vander Werf et al. [53] used Monte Carlo simulation to estimate the impact of vehicle types on lane capacity based on models in the literature and conducted a sensitivity analysis of ACC and CACC vehicle time-interval parameters in simulation tests. Van Arem et al. [54] applied the intelligent vehicle test simulation platform to simulate and analyze the influence of different CACC vehicle ratios on traffic capacity because of the bottleneck section of the expressway with fewer lanes. Talebpour and Mahmassani [55] applied the ACC vehicle and CACC vehicle following model and conducted numerical simulation experiments to present scatter diagrams of mixed traffic flow concerning density under different traffic demands and different CACC/ACC vehicle ratios. The influence of CACC vehicles and ACC vehicles on-ramp capacity is analyzed. Based on simulation experiments, Lioris [56] studied the impact of the Internet of vehicles’ fleet on the capacity of urban road system intersections. Hartmann et al. [57]. studied the influence of CAV on the capacity of the German expressway network through a micro traffic flow simulation experiment. Bujanovic and Lochrane [58] quantitatively analyzed the influence of CAV on the capacity of basic sections of expressways and applied VISSIM simulation software to verify and analyze the proposed model.


### 3.7.5. Group 5 (Purple): Policies and Barriers in Heterogeneous Traffic Flow

There are 26 keywords in this cluster, mainly including policy, impacts, delay, and emissions.It is widely believed that autonomous driving can provide safer and more comfortable driving and is an important part of urban intelligent transportation systems. In this regard, the United States, Japan, Europe, and other developed countries and regions have increased their research and development and investment in autonomous driving in terms of policies. In particular, the United States has already carried out strategic planning and technical testing of autonomous driving technology as an important part of intelligent transportation systems at the national level.However, on the other hand, the application of autonomous vehicles may also have adverse effects on the existing traffic system, such as interfering with road traffic, affecting the safety of other vehicles, and other potential threats. Due to the high initial cost of autonomous vehicles, unclear accident liability details, and uncertain privacy issues, the acceptance of autonomous vehicles is not high among the general public. Therefore, many domestic and foreign scholars have a strong interest in the policies and obstacles of autonomous driving vehicles.Daniel [59] explores the feasible aspects of AVs and discusses their potential impacts on the transportation system. And this paper explores the feasible aspects of AVs and discusses their potential impacts on the transportation system. Another paper “Policy and Society Related Implications of Automated Driving: A Review of Article and Directions for Future Research” by Milonakis is published in the Journal of Intelligent Transportation Systems. In this paper, the potential effects of automated driving that are relevant to policy and society are explored, findings discussed in the article about those effects are reviewed, and areas for future research are identified [60].


## 3.7.1. Group 1 (Red): Analysis of Modeling and Optimization Methods for Heterogeneous Traffic Flow

This cluster contains a total of 55 keywords, mainly including model, systems, algorithm, optimization, and framework. The visualization results of the cluster show that keywords such as model, algorithm, and optimization are cooccurring high-frequency words.From the perspective of research, the traffic flow model can be divided into a macro traffic flow model and a micro traffic flow model [31]. The microscopic traffic flow model processes traffic flow into dispersed particles to reflect the characteristics of traffic flow [32–35]. The macroscopic traffic flow model regards all vehicles on the whole road as a compressible continuous fluid, deduces the relationship among vehicle density ρ, the average velocity V, and flow Q, and thus describes the mathematical model of traffic flow operation law [36–39]. So far, the researchers have developed a variety of traffic models used to study the complex phenomenon and obtained many important results [40, 41]; however, these traditional traffic flow models did not consider the information interaction between the vehicle and synergy, also lack the research of vehicle heterogeneous factors, and therefore, cannot be directly used to study the heterogeneous traffic flow.To study the heterogeneity of traffic flow, Tang et al. [42] proposed a new vehicle following model based on the properties of heterogeneous traffic flow and the relationship between micro and macro variables, establishing a new dynamic model for heterogeneous traffic flow. Ngoduy et al. [43] established a new macro traffic flow model based on the aerodynamic method to describe the driving behavior of vehicle queues and analyze the influence of intelligent vehicle permeability. Levin M W et al. [44] developed a vehicle following model for predicting scene capacity and wave speed in combination with driver response time. The research results show that travel time has a linear relationship with the proportion of autonomous vehicles, and the travel time will be significantly reduced when the penetration rate of autonomous vehicles reaches over 80%.


## 3.7.2. Group 2 (Green): Analysis of Macroscopic Traffic Flow Characteristics of Heterogeneous Traffic Flow

This cluster contains a total of 32 keywords, mainly including traffic flow, stability, waves, fuel consumption, and jamming transition.In traffic flow research, the impact of autonomous vehicles on traffic flow stability and traffic flow capacity is an important research topic. Many current works have explored the traffic capacity and stability of heterogeneous traffic flow and intelligent traffic. Kesting et al. [44] proposed an intelligent driver model, that is, automatic real-time detection of traffic conditions based on local information, to adapt to the driving characteristics of ACC.The results of the test show that at a 25% penetration rate, ACC vehicles can eliminate congestion during specific peak periods of the simulation. Shladover et al. [24] conducted a simulation study on the traffic capacity of single-lane expressways with CACC vehicles mixed with different permeability, and the results showed that the ACC model could not significantly improve the traffic capacity, while the CACC model with medium and high permeability could greatly improve the traffic capacity. Arnaout et al. [45] studied the influence of permeability on traffic capacity under different traffic demand conditions and found that CACC permeability had a significant impact on traffic capacity when traffic demand was high. At the same time, Arnaout et al. [46] studied the impact of different CACC permeability on traffic efficiency under different traffic demands, and the results showed that CACC permeability had no impact on traffic capacity when traffic demand was low. However, when the traffic demand is high and the permeability exceeds 40%, the permeability has a substantial impact on the increase of traffic capacity.


## 3.7.3. Group 3 (Blue): Analysis of Driving Behavior in Heterogeneous Traffic Flow

There are 29 keywords in this cluster, mainly including behavior, time, adaptive cruise control, safety, risk, and accidents.When a car is running, the driver needs to control the car based on information provided by the environment, road signs, signals, and instrumentation in the car. Information can be obtained through visual, tactile, and auditory means. Among them, more than 80% of the driver’s information is obtained through visual channels, followed by hearing. Driving behavior can be seen as a repetitive message processing model composed of information perception, judgment, and decision-making and actions; that is, judgment and decision-making are the execution of manipulation actions after receiving the perception signal [47]. In the traditional traffic flow field, the analysis of driving behavior generally adopts subjective questionnaire data and objective driving data. Through a reasonable questionnaire, drivers can be divided into various types (such as aggressive, cautious, slow). However, drivers tend to hide their usual aggressive driving behaviors when conducting self-evaluation through the questionnaire, so the collected questionnaire cannot truly describe drivers’ driving behaviors. The collected objective driving data of drivers can be used to classify drivers according to clustering analysis or principal component analysis, but during data collection, drivers will feel that they are in a monitoring environment and change their real driving behavior.In the field of heterogeneous traffic flow, researchers have built different driver models mainly to stimulate and recognize the behavior of human-driven vehicles in heterogeneous traffic flow. These researches are mainly divided into driver behavior models based on control theory and driver behavior models based on machine learning theory. The driver behavior model based on control theory mainly assumes that the driving trajectory is known, studies the driver and the vehicle as a whole, and predicts the vehicle trajectory in the future in real-time according to the historical running state of the vehicle. For example, Song et al. [48] established a “single-lane auto-manual driving mixed traffic flow model considering driving behavior” and a “three-lane auto-manual driving mixed traffic flow model considering driving behavior” based on cellular automata and conducted simulation tests. Zhu et al. [49] used Bando’s model and a modified Bando’s model to describe human driver behavior and autonomous vehicle, respectively, and conducted stability analysis on heterogeneous traffic flow. Zheng et al. [50] established a “random model of auto-manual driving mixed traffic flow” based on fully considering the uncertainty of human driving behavior and the interaction between automatic driving and manual driving vehicles. The driver behavior model based on machine learning theory uses the big data of vehicle operation to obtain the characteristic information of the driver and then describes the decision-making process of the driver, to establish the driver behavior model. Wang et al. [51] organized drivers to carry out the following test, analyzed the difference of speed difference cycle in the following process, divided driver types according to driving parameters through cluster analysis, and established an improved IDM model. Michael et al. [44] developed the following model including driver reaction time to study the traffic capacity and backward wave speed of autonomous vehicles under different permeability. Chen et al. [52] used the driver’s driving behavior data obtained by the simulation platform to classify the characteristics of the following behavior obtained and solved the problem of operation difference caused by sequence transformation of vehicles in the fleet.


## 3.7.4. Group 4 (Yellow): Simulation Experiment Analysis of Heterogeneous Traffic Flow

There are 28 keywords in this cluster, mainly including simulation, cellular-automaton model, delay, and states.With the gradual maturity of autonomous driving technology, the heterogeneous traffic flow phenomenon formed by autonomous driving vehicles and manual driving vehicles must exist for a long time. Due to the uncertainty of heterogeneous traffic flow, such as safety, coordination ability, and efficiency, people have raised doubts about the safety of autonomous vehicles. Although the above problems can be verified by establishing a real road test field for real vehicle test, the cost of real vehicle test is too high, there are too few test bases with test qualification, and the test results are susceptible to the influence of the environment and test conditions. The traffic flow simulation test has the characteristics of repeatability, safety, economy, and effectiveness, which can facilitate researchers to carry out tests at lower costs under the same initial conditions.A simulation model is a mathematical/logical representation of a real-world system, which takes the form of software that is executed experimentally on a digital computer. Common simulation models used in traffic flow include CORSIM, MITSIM, and VISSIM, but most of these models are based on homogeneous traffic conditions and are not suitable for studying the characteristics of heterogeneous traffic flow. Therefore, Vander Werf et al. [53] used Monte Carlo simulation to estimate the impact of vehicle types on lane capacity based on models in the literature and conducted a sensitivity analysis of ACC and CACC vehicle time-interval parameters in simulation tests. Van Arem et al. [54] applied the intelligent vehicle test simulation platform to simulate and analyze the influence of different CACC vehicle ratios on traffic capacity because of the bottleneck section of the expressway with fewer lanes. Talebpour and Mahmassani [55] applied the ACC vehicle and CACC vehicle following model and conducted numerical simulation experiments to present scatter diagrams of mixed traffic flow concerning density under different traffic demands and different CACC/ACC vehicle ratios. The influence of CACC vehicles and ACC vehicles on-ramp capacity is analyzed. Based on simulation experiments, Lioris [56] studied the impact of the Internet of vehicles’ fleet on the capacity of urban road system intersections. Hartmann et al. [57]. studied the influence of CAV on the capacity of the German expressway network through a micro traffic flow simulation experiment. Bujanovic and Lochrane [58] quantitatively analyzed the influence of CAV on the capacity of basic sections of expressways and applied VISSIM simulation software to verify and analyze the proposed model.


## 3.7.5. Group 5 (Purple): Policies and Barriers in Heterogeneous Traffic Flow

There are 26 keywords in this cluster, mainly including policy, impacts, delay, and emissions.It is widely believed that autonomous driving can provide safer and more comfortable driving and is an important part of urban intelligent transportation systems. In this regard, the United States, Japan, Europe, and other developed countries and regions have increased their research and development and investment in autonomous driving in terms of policies. In particular, the United States has already carried out strategic planning and technical testing of autonomous driving technology as an important part of intelligent transportation systems at the national level.However, on the other hand, the application of autonomous vehicles may also have adverse effects on the existing traffic system, such as interfering with road traffic, affecting the safety of other vehicles, and other potential threats. Due to the high initial cost of autonomous vehicles, unclear accident liability details, and uncertain privacy issues, the acceptance of autonomous vehicles is not high among the general public. Therefore, many domestic and foreign scholars have a strong interest in the policies and obstacles of autonomous driving vehicles.Daniel [59] explores the feasible aspects of AVs and discusses their potential impacts on the transportation system. And this paper explores the feasible aspects of AVs and discusses their potential impacts on the transportation system. Another paper “Policy and Society Related Implications of Automated Driving: A Review of Article and Directions for Future Research” by Milonakis is published in the Journal of Intelligent Transportation Systems. In this paper, the potential effects of automated driving that are relevant to policy and society are explored, findings discussed in the article about those effects are reviewed, and areas for future research are identified [60].


## 3.8. Analysis of Burst Detection: Research Trends of Heterogeneous Traffic Flow

The burst detection algorithm was first proposed by Kleinberg in 2003. It identifies keywords with high-frequency density characteristics in the article by detecting the density of keyword frequency changes. Burst detection analysis can be used to detect the frequency of sudden increase of words in topics and keywords and to obtain the start time, end time, and weight of sudden keywords. Through this information, the emergent hot spots and research trends in the field of heterogeneous traffic flow research can be analyzed. CiteSpace regards this kind of mutation information as a way to measure deeper changes. Burst detection in CiteSpace can be used for two types of variables: one is the frequency of words or phrases used in the cited documents, and the other is the frequency of citations obtained from the cited documents. Import the data into the CiteSpace tool and run it for burst detection. The parameters are set as follows:γ = 1.0, the number of states = 2.0, and minimum duration = 2. Select the top 20 meaningful keywords with the largest burst weight for visual analysis, as shown in Figure 7.Figure 7
Keywords of the top 20 burst weights from 2004 to 2021.As shown in Figure7, “Start year” and “end year” represent the year of burst keyword duration from start to end. Intensity represents the frequency of keyword occurrences. From the point of view of burst intensity, cellular automata, traffic flow, numerical simulation, and other links have high intensity. It can be seen that traditional traffic flow studies focus on using the cellular automata model for modeling and carry out numerical simulation calculation; related articles include spatial-temporal patterns in heterogeneous traffic flow with a variety of driver behavioral characteristics and vehicle parameters. Different from the traditional heterogeneous traffic flow research, heterogeneous traffic flow research in the new period is mostly dependent on artificial intelligence, cloud computing, big data, and other new-generation network technologies represented by the Internet of vehicles. Related articles include Linear Stability Analysis of Heterogeneous Traffic Flow considering Degradations of Connected Automated Vehicles and Reaction Time. Capacity and stability are macro characteristics of heterogeneous traffic flow, which have a great impact on the safety and efficiency of heterogeneous traffic flow. Related articles include Controllability Analysis and Optimal Control of Mixed Traffic Flow with Human-Driven and Autonomous “Vehicles,” Stability Analysis, and the Fundamental Diagram for Mixed Connected Automated and Human-driven Vehicles and Analysis on Traffic Stability and Capacity for Mixed Traffic Flow with Platoons of Intelligent Connected Vehicles.The burst intensity of the dynamic model, car-following model, and adaptive cruise control was 29,108, 55,438, and 3085, respectively. Adaptive cruise control not only has the function of cruise control but also adaptively adjusts the motion state of the vehicle in front according to the motion state of the vehicle, which has a certain influence on the traffic flow research: “Cooperative Adaptive Cruise Control and Exhaust Emission Evaluation Under Heterogeneous Connected Vehicle Network Environment in Urban City,” “Cooperative Adaptive Cruise Control and Intelligent Traffic Signal Interaction: A Field Operational Test with Platooning on a Suburban Arterial in Real Traffic,” and “Longitudinal Emissions Evaluation of Mixed (Cooperative) Adaptive Cruise Control Traffic Flow and Its Relationship with Stability.”


## 4. Conclusion

This paper uses VOSviewer software to conduct a bibliometric analysis of 4709 documents related to heterogeneous traffic flow, from the annual distribution statistics of the article, national and regional statistics, analysis of major research institutions, analysis of coauthors of major research groups, analysis of source journals, and key. In terms of word and burst detection analysis, the research results in the field of heterogeneous traffic flow in recent years (2004–2021) are analyzed from multiple angles, and the existing article review in this field is supplemented to consolidate the research results in the field of heterogeneous traffic flow. The analysis results show that cocitation analysis divides heterogeneous traffic flow into three main research directions, which include “heterogeneous traffic flow model,” “traffic flow capacity analysis,” and “traffic flow stability analysis.” The keyword cooccurrence analysis is applied to identify five dominant clusters: “modeling and optimization methods,” “traffic flow characteristics analysis,” “driving behavior analysis,” “simulation experiment,” and “policies and barriers.” The main research conclusions are as follows:(1)
The number of documents in the field of heterogeneous traffic flow research continues to grow, indicating that the international academic community pays more attention to the field of heterogeneous traffic flow, and related research is also in progress. According to the distribution of the article in various countries, China, the United States, and India rank high, indicating that these countries are active areas for heterogeneous traffic flow research. In terms of research institutions, Beijing Jiaotong University, Southeast University, and Tongji University have the highest research output, and the cooperation between major research institutions has been further strengthened. Judging from the analysis results of the main author groups, the international exchanges and cooperation among highly productive authors are quite active. In terms of source journals, “transportation research part c-emerging technologies,” “physical a-statistical mechanics and its applications,” and “transportation research record” are authoritative journals in the field of heterogeneous traffic flow research and are also important platforms for publishing research results.(2)
Through the analysis of the cooccurrence network diagram of heterogeneous traffic flow keywords, the research directions represented by these keywords can be divided into four categories: “modeling and optimization methods,” “macroscopic traffic flow characteristics analysis,” “driving behavior analysis,” “simulation experiment analysis,” and “policies and barriers.” These five representative keywords also reflect the research trends in this field in recent years. The establishment of a safe and reliable model is of great significance to the development of autonomous driving and has received more and more attention in recent years. Related researches on the macroscopic traffic flow characteristics of heterogeneous traffic flow are also emerging. In addition, with the continuous development of information technology, sensor technology, computer technology, and other technologies, there are also many studies exploring the improvement of people’s living standards and traffic environment from the perspective of simulation from the perspective of heterogeneous traffic flow.(3)
This study also has some shortcomings. The search keywords used in this research are representative of the research in this field and cannot completely contain all the keywords in this research field. In addition, the search scope of this study is only for the SCIE and SSCI citation index databases in the core collections of the Web of Science (WOS). This study does not discuss the proportions and partnerships of each topic. At the same time, this research aims to provide a visual analysis method using the MKD method, which is also applicable to other keywords and databases. In terms of visualization methods, different goals based on analysis of different visualization methods can be further considered in future work.



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*Source: 7754961-2022-02-04.xml*