Business Process Complexity Measurement: A Systematic Literature Review

Business process complexity is an important factor that affects process quality and has a significant impact on the maintenance, optimization, and execution efficiency of processes. To review the application progress and trends of process complexity measurement in business process management, this study uses the systematic literature review (SLR) method to qualitatively and quantitatively analyze the theoretical background, rationality, effectiveness, and comprehensiveness of 92 process complexity metrics. The findings showed that the measurement of process complexity primarily encompasses four dimensions: activity complexity, control-flow complexity, data-flow complexity, and resource complexity. However, most metrics consider only one or two aspects of complexity in the process and rely mainly on empirical validation, thus lacking theoretical validation support. Currently, the most popular and widely used complexity metric is Control Flow Complexity (CFC). Process complexity metrics mainly focus on measuring the complexity of process models, and the majority of them focus on activity complexity or control-flow complexity. The future research trend is to combine data mining techniques with process log data to analyze process complexity.


I. INTRODUCTION
Business processes are the core assets of an enterprise and play an important role in creating value and revenue for the enterprise. In the face of increasingly fierce competition, enterprises require high-quality business processes to promote reasonable and efficient production and service delivery. Process complexity is a significant factor that affects the process quality. The higher the complexity of a process, the more difficult it is to understand, the higher the error rate, and the higher the cost of management and maintenance, resulting in a lower process efficiency. Process complexity has a significant impact on the readability of process models, process efficiency, and business agility.
The associate editor coordinating the review of this manuscript and approving it for publication was Yilun Shang.
The first step in reducing the complexity is to recognize its existence and then measure it. Measurement is a fundamental activity in any system improvement approach and is the foundation of scientific methodology [1]. If the complexity of business processes is measured, the process elements that are suitable for improvement and simplification can be identified, which can guide the optimization and redesign of processes in intelligent process management [2]. Therefore, some researchers have begun to analyze the complexity of processes in depth and develop metrics for measuring process complexity. Process complexity metrics can assist in analyzing and improving business processes and serve as predictors of the workload required to manage and complete new instances of the process.
To summarize the metrics of process complexity and describe the current state and trends of the research on process complexity, this paper systematically reviews the literature related to process complexity research from 2005 to 2022 based on a systematic literature review [3]. We analyzed the effectiveness, validity, and coverage of the overall complexity of the process for each metric. The overall quality of the existing metrics is comprehensively evaluated to identify high-quality metrics of process complexity. The focus and future development trends of the existing research are determined to provide a reference for process designers and related researchers.
The remainder of this paper is organized as follows. In the next section, we introduce the relevant background and theories. In Section III, we describe the implementation process of the systematic review, including identifying the research questions, formulating literature search strategies, and conducting quality assessments. In Section IV, we present the results of data extraction and statistical synthesis. Section V discusses relevant issues to answer each research question. Finally, the conclusions and future research prospects are presented.

II. RESEARCH BACKGROUND A. BUSINESS PROCESS AND ITS MODELS
A business process is defined as a set of related and structured activities or tasks that provides specific products or services to customers [4]. Business processes exist in every enterprise, running through the organization's internal structure and forming a system of related tasks, technologies, and personnel [5]. As business processes are intangible and cannot be directly observed and managed, they must be expressed and described through the corresponding process models.
The goal of a business process model is to accurately describe a process in a simple and understandable manner, thereby facilitating information exchange and dissemination among process participants [6]. Business process models have a wide range of uses and can be used to support the design, management, maintenance, and optimization of business processes. These are fundamental to the development of process systems. The importance of business process models has been widely recognized, and many researchers have used different forms of modeling languages to construct them. Currently, the most popular modeling languages include Business Process Model Notation (BPMN), event-driven process chain (EPC), and Petri Nets.

B. BUSINESS PROCESS COMPLEXITY
Complexity is considered to be one of the most important factors affecting contemporary science and has a significant impact on the development of many fields. This is an inherent and implicit property of these systems [7]. Complexity has different meanings in different fields. Curtis [8] defined complexity as a characteristic of software programs that affects the resources consumed or invested during the interaction of software systems. In the process field, Cardoso [9] defined process complexity as the degree to which a process is difficult to analyze, understand, or explain, based on IEEE standard terminology.
Business processes have their complexity, which is influenced by various factors such as activities, structure, data, and resources. Process complexity can affect people's understanding, maintenance, and process optimization. The high complexity of business processes may lead to increased resource consumption, longer running times, and decreased execution efficiency, resulting in a series of errors and exceptions. The overall quality of the process is greatly reduced, which cannot provide satisfactory products or services to customers. Therefore, it is necessary to reduce the complexity of business processes. Complexity analysis helps design and implement simpler, more reliable, and robust process models. Currently, research on the complexity of business processes mainly focuses on the complexity of the process models.

C. PROCESS COMPLEXITY METRICS
Process complexity metrics are key indicators for quantitatively analyzing the complexity level of processes [10]. Measurement is defined as the process of assigning numbers or symbols to entity attributes in the real or abstract worlds [4]. Process complexity metrics can evaluate the complexity of business information system processes and provide important information for maintaining and improving business processes and information systems.
Fenton and Bieman [11] proposed three steps to define a new metric: definition, theoretical validation, and empirical validation of the metric. Polancic et al. [4] proposed a fourth step based on existing work, which is the development of measurement tools. The measurement tools can automatically calculate complexity values, as shown in Fig.1. Validation of the process complexity metrics serve as the basis for assessing the rationality and effectiveness of a particular metric. The validation includes both theoretical and empirical validations. Some researchers validated the proposed complexity metrics by verifying that it satisfies the required structure and properties of a metric. Only validated metrics can provide reliable measurement results.

1) THEORETICAL VALIDATION
Theoretical validation is an evaluation of the process complexity metrics that require it to satisfy certain accepted attributes or characteristics (soundness). There are a few proposed methods for theoretical validation in the literature, and the two commonly used methods are Briand's theoretical framework [12] and Weyuker's theoretical properties [13].

2) EMPIRICAL VALIDATION
Empirical validation involves specific practical operations to test the proposed process complexity metrics against actual situations (validity), such as surveys, experiments, and case studies [14]. Compared with theoretical validation, empirical validation is simpler, and it is more difficult to propose new theoretical validation methods. Therefore, most researchers tend to evaluate complexity metrics through empirical validations. If a process complexity metric passes both theoretical and empirical validation, its rationality and validity in measuring process complexity are higher.

III. SYSTEMATIC LITERATURE REVIEW METHOD
A systematic Literature Review (SLR) is a method proposed by Kitchenham [3] for identifying, evaluating, and interpreting all available studies related to a specific research problem, topic, or phenomenon of interest. Initially used in the field of software engineering to provide comprehensive guidelines for software engineers to conduct literature reviews, the SLR method has been widely applied in various fields and is recognized as a literature review guide.
The SLR method differs from the traditional literature review methods in that it standardizes the review process to ensure that relevant studies on a specific topic can be obtained objectively. The results of this review are authentic, comprehensive, rigorous, and reproducible [15]. The SLR method can be summarized into three main parts: developing the review protocol, conducting the review, and discussing the results. This section mainly focuses on developing the review protocol, including defining the research problem, searching and screening the literature, and evaluating the quality of the studies.

A. DEFINING THE RESEARCH QUESTION
Defining the research problem is the most crucial part of a systematic literature review (SLR), as it enables researchers to focus on a specific research topic, analyze literature related to the research topic, and provide direction to the entire review process. Based on the Population Intervention Comparison Outcome (PICOC) criteria [16] and the purpose of this study, the primary research question (RQ) is defined as: ''What are the existing metrics for business process complexity?'' To further investigate the metrics of process complexity, this study narrows the primary research question into four sub-questions. RQ1: What is the theoretical foundation and domain background of each metric? (The purpose of this question is to clarify the research background of process complexity metrics, that is to understand their theoretical basis and domain background.) RQ2: Which aspects of process complexity are measured by each metric? (The purpose of this question is to clarify the perspective of the process complexity metrics and determine the extent to which it covers the overall process complexity.) RQ3: Has each metric been supported by theoretical and empirical validation? (The purpose of this question is to clarify whether the metric has been validated to determine the rationality and validity of its measuring results.) RQ4: What is the comprehensive quality evaluation score for each metric? (The purpose of this question is to comprehensively analyze the overall quality of each metric, and then compare the comprehensive level of different metrics under the same standard.)

B. STUDY SEARCH AND SELECTION
After identifying the research background and research questions, it was necessary to search and screen the literature relevant to the research topic.

1) SEARCH STRATEGY
The search process involved finding literature relevant to the research topic, analyzing data related to the research questions in each literature, and conducting statistical analysis on the extracted data to answer the research questions. The databases used for the literature search mainly include IEEExplore, Science Direct, Springer Link, Web of Science, ACM Digital Library, and China National Knowledge Infrastructure (CNKI). The defined search keywords primarily include two aspects: process complexity and measurement. In the English databases, the search keywords include ''process complexity'', ''business process complexity'', ''metric'', ''measure'', ''analysis'', and ''evaluation'', forming eight groups of search keywords. Relevant literature from 2005 onwards was searched in the databases using the search keywords. Because some literature may exist in multiple databases, duplicate literature needs to be distinguished and not counted in the search results.

2) INCLUSION CRITERIA
First, this paper introduces a new method to measure the complexity of processes, which includes improving existing metrics and combining multiple metrics into a single metric or measurement framework. Second, the complexity of the process was analyzed by referencing existing metrics. Third, the main focus of this paper is to study and analyze the complexity of processes, which facilitates the understanding, maintenance, and optimization of processes.

3) SELECTION PROCESS
After conducting keyword searches, the retrieved papers were filtered. This section defines the inclusion criteria for literature and describes each stage of the screening process, ultimately obtaining literature relevant to the topic of this 47942 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. study. In this study, a five-stage process was implemented to conduct a systematic literature review (Table 1).

C. QUALITY ASSESSMENT
Quality assessment is an important component of the SLR method, which involves analyzing the content of screened literature, examining the overall quality of the proposed methods in the studies, and identifying high-quality research. Objective evaluation criteria must be established for quality assessment to ensure the rationality of the results without any subjective factors. Based on the requirements for quality assessment in [3], combined with the research topic of this article, five quality issues (QQ1-QQ5) were summarized, and the corresponding quality scores were set to evaluate the quality of complexity metrics. As shown in Table 2, each quality issue corresponds to the relevant scoring criteria and the final quality score is the cumulative score for each quality issue. The total score is six, and the higher the score, the higher the overall quality of the metric, indicating a relatively higher comprehensive level.

IV. CONDUCTING THE REVIEW PROTOCOL
In this section, we follow the review protocol to carry out relevant implementation work and describe the results. To answer these research questions, we extracted and synthesized useful data from the selected papers.

A. DATA EXTRACTION PROCESS
Based on the selection strategy in this study, 63 research articles were ultimately identified that matched our research topic. The details are shown in Fig.2.

B. SYNTHESIS OF THE EXTRACTED DATA
Each of the 63 collected studies was analyzed in detail to study the complexity metrics of each literature process. The comprehensive analysis results showed that process complexity can be divided into ''static model complexity'' and ''dynamic runtime complexity'' from both static and dynamic perspectives [17]. Currently, most process complexity metrics focus on analyzing the complexity of process static models, with a few studies beginning to consider the complexity of the process runtime. Research on process complexity metrics has mainly focused on four aspects: activity complexity, controlflow complexity, data-flow complexity, and resource complexity. Some metrics may simultaneously involve multiple aspects of complexity. The following introduces representative metrics for the different aspects of process complexity.

1) ACTIVITY COMPLEXITY
Activity complexity metrics primarily measure the impact of the number of activities and connections between activities on process complexity. Cardoso [18] proposed the number of activities (NOA) based on the lines of code (LOC) of software programs. NOA mainly calculates the number of activities in a process and describes the size of the overall process view. The greater the number of activities in the process, the more complex the process. Although this metric only describes the number of process activities and lacks comprehensiveness, it is essential to expand the other metrics. For example, the number of activities and control-flow elements (NOAC) and the number of activities, joins, and splits (NOAJS) build upon the NOA by considering the influence of activities and control flows on process complexity. Rolón [19] proposed a set of metrics based on the FMESP framework to measure the complexity of BPMN-based process models, including the CLA, which measures the overall connectivity level between activities in the process. With a constant number of activities in the process, the more sequence flows between activities, the lower the overall connectivity level and the higher the process complexity. Vanderfeesten [20] introduced the cross-connectivity (CC) to quantify the connection strength  between any activity pairs in a process in terms of the cognitive dimension. CC analyzes the impact of closeness between activity pairs on the process model's understandability. The larger the cross-connectivity value, the higher the strength of the connections between activity pairs, and the easier it is to understand the process model. The experimental results showed that the CC significantly improved the prediction of process error probability and enhanced process comprehensibility.

2) CONTROL FLOW COMPLEXITY
The control-flow complexity is mainly measured by the impact of control structures, such as splits, joins, and loops, on the complexity of the process. Cardoso [9] proposed a control-flow complexity (CFC) by considering the influence of control structures on the execution order of activities based on the analysis of process activities. CFC describes the impact of the number and execution status of subsequent activities after three types of branching structures (AND-split, ORsplit, and XOR-split) on the process complexity. Among them, the impact of the AND-split branching structure on process complexity was the lowest, while the impact of the OR-split branching structure was the highest. However, Gruhn and Laue [21] believed that the CFC can only cover the number of all possible paths in the control flow and cannot help better understand the business process model. They assigned cognitive weights to the control structures in the process from the perspective of cognitive dimensions and proposed a cognitive complexity to quantify the difficulty of understanding the control structures in the process. The cognitive complexity of the process is the sum of the cognitive weights of all control elements in the process: the higher the cognitive weight, the higher the process complexity, and the harder it is to understand. Mendling et al. [22] proposed a set of control flow complexity metrics (Cyclicity, Connector Mismatch, Connector Heterogeneity, etc.) to analyze the impact of the complexity of control structures in the process on the probability of process errors. A large number of EPC models were used to analyze the statistical relationships between the metrics and errors in the process model. Sánchez-González synthesized previous research [23] and proposed the Gateway Complexity Indicator (GCI) to analyze the impact of gateway complexity on the understandability and maintainability of the process and extracted the threshold of this metric in experiments. When the value of gateway complexity exceeds the predetermined value, it has a significant impact on the understandability and maintainability of the process and reduces the quality of the process.

3) DATA FLOW COMPLEXITY
Data-flow complexity metrics primarily assess the impact of data dependencies among various activities on process complexity. According to Cardoso [24], data flow complexity increases with the complexity of data structures and mapping relationships between data. To analyze the impact of data structures and dependencies between data on the process, Cardoso proposed data-flow metrics. The higher the data flow complexity, the lower the sensitivity of the process, and the more fragile it becomes. Rolón [19] proposed a set of metrics for measuring data flow complexity based on BPMN process models, such as the number of information flow (NMF), the total number of data objects (TNDO), the number of intermediate information events (NIMsE), and the number of end message events (NEMsE). NMF calculates the number of information flows between process participants. TNDO counts the number of input and output data objects in the process model. NIMsE and MEMsE counted the number of intermediate and ending information events, respectively. Cardoso and Mendling [18] proposed an interface complexity (IC) based on Henry and Kafura's software information flow metrics. The IC considers both the input and output data of the interface and analyzes the data flow complexity of the business process. The input and output data of an interface describe the inflow and outflow of relevant information. The data flow complexity of an activity is considered to be zero if it does not interact with the outside world.

4) RESOURCE COMPLEXITY
Resources are defined as entities required to perform activities. Currently, resource complexity metrics primarily assess the impact of relationships between roles in executing activities on process complexity. Yan et al. [25] considered roles as important execution resources for process activities and proposed a metric of role complexity for processes based on the concepts of ''cohesion'' and ''coupling'' of process activities. Role complexity consists of role cohesion and coupling. Role cohesion analyses the degree of closeness between the activities that the role is responsible for (activity cohesion), as well as the degree of closeness between data of the activities (data cohesion). Role coupling describes the degree of association between the activities for which different roles are responsible. The higher the role cohesion and the lower the role coupling, the lower is the role complexity of the process. Zhao et al. [26] proposed the concept of ''role compatibility'' and ''key roles'', which combined with the role interaction frequency implied in the workflow logs, yields a metric of process complexity based on role compatibility. The smaller the role compatibility, the more key roles there are, and the higher the role interaction frequency, the greater is the interaction complexity of the process.
Although process complexity metrics mainly focus on the above four aspects of process models, namely activity complexity, control flow complexity, data flow complexity, and resource complexity, many metrics have been improved and expanded to not only consider the complexity of a single aspect of the process, but also involve the complexity of multiple aspects of the process. We analyzed each study based on the proposed research questions and collected 92 process complexity metrics. Based on the research questions proposed in this paper, 92 process complexity metrics were collected and analyzed for each literature. To answer each research question more intuitively, the framework structure of Polancic [4] was supplemented and improved; the data synthesis results are shown in Table 3. The first column shows the number of metrics. The second column shows the name of the metrics. The third column describes the foundation of metrics (RQ1), and the fourth column answers RQ2, with ''+'' indicating that the metric considers a certain aspect of the process complexity. A is the activity complexity, CF is the control-flow complexity, DF is the data-flow complexity and R is the resource complexity. The fifth column answers RQ3, indicating whether the metric has been validated by theoretical validation (T) or empirical validation(E). In theoretical validation, the superscript ''a'' in the reference indicates that the corresponding metric has passed Briand's theoretical validation in that literature, and ''b'' indicates that it has passed Weyuker's theoretical validation. The sixth column answers RQ4, providing the quality score for each metric (out of six). The last column is the reference sources for each metric, with ''P'' representing the source literature that initially defined the metric, and ''S'' the citation literature that uses the metric. The empty in the table indicates that there is no corresponding data to support the metric.
In addition to the static model complexity metrics mentioned above, it has been found in recent years from the literature that researchers have begun to focus on process logs [69]. Using process mining techniques to obtain process logs generated during process runtime, the complexity of the process can be described by analyzing the process logs [70], [71]. This belongs to the complexity of dynamic process execution and is a trend that has developed in recent years.

V. DISCUSSION OF EXECUTION RESULTS
Based on 63 relevant studies retrieved on process complexity, 92 process complexity metrics were extracted. The results of the analysis are discussed in detail below to answer the specific research questions.

A. WHAT ARE THE THEORETICAL FOUNDATION AND DOMAIN BACKGROUND OF EACH METRIC (RQ1)?
The theoretical foundation and domain background of each complexity metric were determined based on descriptions provided in the literature. For some studies, the theoretical foundation of their metrics was not explicitly described, and in cases where the relevant theoretical foundation could not be found, they were classified as unclassified. Table 4 presents the theoretical foundation and domain background for each metric source.
The concept of complexity measurement first appeared in the field of software engineering and later gradually extended to the field of process management. Early process complexity metrics were mostly extended from software complexity metrics. As shown in Table 4, 37 (40.2%) metrics were developed  in the context of software complexity, whereas 55 (59.8%) were developed in the context of process complexity. Among the 92 metrics, 60 (65.2%) were the source metrics initially defined in the process field, and 32 (34.8%) were derived based on existing metrics. Among the 32 derived metrics, 20 metrics were extended from software complexity metrics, 11 metrics were extended from process complexity metrics (including various compounded or combined process complexity metrics), and the remaining 1 metric was a composite of multiple software and process complexity metrics. Fig.3 shows the relationships between these metrics. The metrics indicated by the arrows were extended from the metrics at the tail of the arrows. The dashed boxes represent software complexity metrics and the solid boxes represent the process complexity metrics. The dotted arrows link two complexity metrics from different domains, whereas the solid arrows link the two metrics applied in the process domain.
A process model is a visual representation of a process that is typically constructed using various graphical modeling languages. Therefore, most metrics were defined based on the basic form of a graph. As shown in Fig.4, the majority of these metrics (45.7%) have a theoretical basis in the graph theory. Thirty metrics (32.6%) were defined based on graphical symbol elements. Four metrics (4.3%) were based on cognitive load theory, and there were three metrics each (3.3%) based on Petri nets and Shannon information entropy theory. There were two metrics (2.2%) based on number theory, one metric (1.1%) based on graph entropy, and the remaining seven metrics (7.6%) did not find their theoretical basis.

B. WHICH ASPECTS OF PROCESS COMPLEXITY ARE MEASURED BY EACH METRIC (RQ2)?
The process complexity is reflected in more than one aspect. To comprehensively measure the complexity of a process, multiple metrics are needed to comprehensively assess the 47950 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  process complexity [18]. Based on the extracted data, the angle of each metric to analyze the complexity of the process was determined, and then the degree to which it covered the overall complexity of the process was evaluated, that is, the comprehensiveness of measuring the overall complexity of the process. Currently, complexity metrics focus on four aspects: activity complexity (A), control-flow complexity (CF), data-flow complexity (DF), and resource complexity (R). Different complexity metrics can consider more than one type of complexity. Based on the coverage of different aspects of complexity by each metric, metrics that cover the same aspect of complexity were grouped together. Table 5 shows the degree to which each metric covers the overall complexity of the process, where the numbers (6, 21, 54, etc.) correspond to the respective metric numbers in Table 3, and B-J represents the set of metrics with the same degree of coverage. B = {3, 7, 10, 34, 35, 56}; C = {9, 13,1617,18,20,22,23,24,25,26,29,30,31,32,33,36,43,45,46,47,48,49,50,51,52,53 Among the 92 process complexity metrics, each is specifically designed to measure one or more aspects of process complexity. When considering the process complexity, these metrics can be classified As shown in Fig.5, only two metrics (2.2%) covered all four types of complexity, three metrics (3.3%) considered three types of complexity (activity, control-flow, and dataflow) simultaneously, and one metric (1.1%) considered three types of complexity (activity, data flow, and resource). 29 metrics (31.5%) considered activity and control-flow complexity, five metrics (5.4%) considered activity and resource complexity, and two metrics (2.2%) considered data flow and resource complexity. One metric (1.1%) covered activity and data flow complexity, control flow and data flow complexity, and control flow and resource complexity. In contrast, there were six (6.5%), 31 (33.6%), eight (8.7%), and two (2.2%) metrics that measured only one type of complexity: activity, control flow, data flow, and resource complexity, respectively. Fig.6 illustrates the inclusion of the four types of complexity among the 92 metrics. Specifically, 47 metrics (51.1%) included activity complexity, 67 metrics (72.8%) included control-flow complexity, 18 metrics (19.6%) included dataflow complexity, and 13 metrics (14.1%) included resource complexity.
In summary, only a small number of metrics (6.5%) covered complexity in more than two aspects of the process,   while most metrics (93.5%) only considered one or two aspects of process complexity. It is difficult to develop a metric that covers all aspects of process complexity, and even if all aspects are covered, the effectiveness of measuring overall process complexity remains to be validated. In addition, most metrics focus on activity and control-flow complexity, with only a few metrics considering data flow and resource complexity.

C. WHETHER EACH METRIC HAS BEEN VALIDATED (RQ3)?
Theoretical and empirical validations were used to evaluate the rationality and effectiveness of metrics for measuring process complexity [4]. Table 6 shows the validation status of each metric, where B represents the set of metrics validated by both theoretical and empirical methods, C represents the set of metrics validated only by theoretical methods, D represents the set of metrics validated only by empirical methods, and E represents the set of metrics validated by any method. The numbers in each set correspond to the metric IDs listed in Table 3   It can be observed that the theoretical validation of the metrics is more difficult than empirical validation. Among the validated metrics, only a few (14.1%) passed theoretical validation, and more than half (54.3%) passed empirical validation without reasonable theoretical support. Of the 13 metrics that passed theoretical validation, nine used Wuyuker's theoretical properties for validation. This indicates that empirical validation is currently the main method of validation, and most studies have used it to demonstrate the validity of the proposed metrics. The validity and effectiveness of metrics that were not validated are questionable. Among the six metrics that have passed double validation, only the CFC metric has undergone multiple rounds of theoretical and empirical validation, and its validity and effectiveness in measuring process complexity are relatively high. This section aims to comprehensively evaluate the process complexity metrics and identify the metrics with better overall performance. To achieve this, we utilized five quality questions that were previously defined to thoroughly analyze and discuss each metric. Table 3 presents the quality scores (out of six) obtained for each metric, and Fig.8 displays the quality score ratios. There are 26 metrics (28.3%) that received a composite score of 2.00 or lower, indicating lower overall quality. Eleven metrics (12.0%), including TS, TNG, ACD, MCD, CH, MM, , CNC, cohesion metrics, coupling metrics, and CFC, received a composite score of 4.00 or higher, indicating higher overall quality. Fig.9 shows how often process complexity metrics are utilized for improvement, composition, or combination into new metrics. The numbers in set B correspond to the metric IDs listed in Table 3. 6, 7, 11, 12, 32, 45, 48, 49, 50, 51, 52, 53, 57, 58, 59, 64, 65, 67} Metrics used more frequently in measuring process complexity include CFC (six times) and NOA (four times). The NOA and CFC metrics are extensions of the LOC and MCC metrics, respectively, which are complexity metrics from the software domain. LOC counts the number of lines of code in a software program, whereas MCC counts the number of linearly independent paths in a software program, indicating the control flow complexity of a program module. Because of the similarity between the software and business process domains, these two metrics were extended to the process domain in the early stages of developing process complexity metrics, and seven process complexity metrics were developed based on NOA and CFC.
Overall, the CFC is currently the most widely used and highly regarded metric of the process complexity. It has been used the most to extend new metrics and has the highest overall quality score. If a metric is not developed with an appropriate measurement tool, that is, if it cannot automatically measure the complexity of a process, the metric is of no practical significance [14]. As shown in Table 7, among the 92 identified metrics, only 27 (29.3%) mentioned the corresponding automation software in the literature, and most metrics did not have tool support. Measurement tools can automate the calculation of process complexity and reduce the cost of human resources in process design, optimization, and reengineering.

VI. CONCLUSION
Complexity measurement has a significant impact on the operation, maintenance, and optimization of processes. Over the past few decades, with the increasing importance of business processes in enterprises, researchers have started using complexity metrics to analyze the complexity of business processes. Complexity metrics can provide guidance to process designers, optimize processes, improve process execution efficiency, and enhance organizational competitiveness in constantly changing environments.
Currently, the complexity of a process is mainly obtained by analyzing the complex relationships in the business process model. Existing metrics describe the process model complexity from different perspectives, reflecting certain aspects' complexity of the process. However, it is difficult to fully evaluate the complexity of the entire process model. Most metrics have no theoretical basis, which raises questions about the validity of their measurement results, and they lack support from measurement tools.
There is no absolute best metric, and future research should propose process complexity metrics that are more adaptable VOLUME 11, 2023 to specific application scenarios and requirements. New complexity metrics need to be validated by both theoretical and empirical means so that their measurement results are persuasive. In addition, it is necessary to develop corresponding tools to support automated measurement, which can reduce process management costs and promote the development of intelligent process management.