Computer Simulation Everywhere: Mapping Fifteen Years Evolutionary Expansion of Discrete-Event Simulation and Integration with Digital Twin and Generative Artificial Intelligence

Abstract

Discrete-event simulation (DES) as an operations research (OR) technique has continued to evolve since its inception in the 1950s. DES evolution mirrors the advances in computer science (hardware and software, processing speed, and advanced information visualization capabilities). DES overcame the initial usability obstacles and lack of efficacy challenges in the early 2000s to remain a popular OR tool of “last resort.” Using bibliographic data from SCOPUS, this study undertakes a science mapping of the DES literature and evaluates its evolution and expansion in the past fifteen years. The results show asymmetrical but positive yearly literature output; broadened DES adoption in diverse fields; and sustained relevance as a potent OR method for tackling old, new, and emerging operations and production issues. The thematic analysis identifies DES as an essential tool that integrates and enhances digital twin technology in Industry 4.0, playing a central role in enabling digital transformation processes that have swept the industrial space in manufacturing, logistics, healthcare, and other sectors. DES integration with generative/artificial intelligence (GenAI/AI) provides a great potential to revolutionize modeling and simulation activities, tasks, and processes. Future studies will explore more ways to integrate GenAI tools in DES.

1. Introduction

Computer simulation is an operations/operational research (OR) technique often deployed to model complex, dynamic, and non-linear systems with interactions among several stochastic elements and components. Over six and a half decades ago, John Harling [1], while evaluating the launch of simulation in 1957/1958, nicknamed it a tool of “last resort” [1,2], so-called because simulation is often adopted as a problem-solving or decision support system when other OR techniques cannot produce an optimal solution [1,2,3,4]. In those circumstances, mathematical models and other OR techniques cannot model systems behavior accurately, or it is difficult to break down complex systems into simpler, manageable, analytical constructs [1,3]. Another reason for preferring the simulation method occurs when experimenting with the actual system is impossible or unsafe [3,5]. On the other hand, the complexity and costs associated with developing simulation studies can be complicated, making it a tool of “last resort” when other OR methods fail [3,6]. Further, simulation as an analytical tool can be complex, putting the developers/experts and other stakeholders involved in the simulation and modeling project in a puzzling situation [3,5,6,7]. On occasions when simulation experts have little or no background in the application domain, any “aha moments” (moments of insight) become the only means of achieving breakthroughs [3,7,8]. Similarly, the potential users of simulation techniques for decision making (e.g., managers and decision makers) who are familiar with the application domains can also find it difficult to relate to the technical model and need to generate ideas or discover knowledge to enhance their understanding of the model and simulation [6,7,8].

Simulation can be classified as discrete event or continuous based on how the state variables change during model run or experimentation [9,10]. In a continuous simulation, variables change continuously, usually through a function in which time is a variable. Its state changes all the time, not just at the time of some discrete events [3,9]. For example, the water level in a reservoir with given inflows and outflows may change continuously. In such cases, “continuous simulation” is more appropriate, although discrete-event simulation (DES) can serve as an approximation [3,5,10]. Conversely, DES explains the state variables that change instantaneously at distinct points in time. Its events occur at intervals, and the number of events is finite [3,5,11]. Discrete simulation models address what happens to the individual elements in the system and proceed to the succeeding interacting components [3,11]. For instance, in a road traffic problem, car arrivals and departures from traffic points occur at distinct points in time, referred to as events. Nothing happens between two consecutive events, which makes the arrival and departure events discrete [3,11]. The events refer to an occurrence at a time that changes the state of the system, e.g., the arrival of a customer at the service point [12]. The DES process often involves experimentation on a computer-based model that depicts a replica of a real system, with the model acting as a vehicle for experimentation, often in a trial-and-error manner [13,14]. This study focuses on the evolution and expansion of DES.

DES growth has not been without challenges. Starting in the mid-2000s, the simulation community began to raise concerns about the future of DES practice as demonstrated in several studies (e.g., “Simulation modeling is 50, do we need a reality check?” [15], “DES, where to next?” [16], and more). By 2010, a panel discussion entitled “DES is dead, long live agent-based simulation!” (ABS) was held during the annual OR society simulation workshop in Worchester, UK [17]. This concern was re-echoed at a panel presentation during the 2011 Winter Simulation Conference [18]. The general notion from these debates considered DES to have outlived its usefulness while welcoming the “new bride,” ABS [17]. ABS’s key strengths center on the ability to capture the “complexity arising from individual actions and interactions” that mimic the real world [17,19]. However, these ABS features that captured the interests of practitioners and researchers in OR and other disciplines, including mathematics and computer science, sociology, and psychology, are also available in DES [19]. Although few voices rose to defend DES’s continuous relevance [19], the discussion against it appeared louder until a third option arose, proposing a “holy matrimony” between ABS and DES [20,21], or with other methods, such as systems dynamics [22,23], to combine two methods to create a hybrid model [20,21,22,23] as the only survival technique.

In the end, DES survived the obstacles and the scare of having outlived its usefulness to remain a popular OR method used to solve diverse problems in several industries. In the winter of 2017, simulation experts in academia and industry assembled at Red Rock Casino Resort and Spa, Las Vegas, USA, during the Winter Simulation Conference (WSC), entitled “WSC turns 50: Simulation everywhere” [24], pointing to the continuous expansion of the simulation method. In 2020 when the coronavirus disease 2019 (COVID-19) broke out, DES became a potent OR tool in addressing diverse disease infection problems, including making spread forecasts, assigning and optimizing intensive care unit beds, initiating and testing healthcare management control strategies, and making critical decisions regarding COVID-19 vaccination problems [25,26,27,28].

Recently, to further enhance the evolution and expansion of DES and improve model and simulation tasks, activities, and processes, researchers and industry practitioners are integrating artificial intelligence (AI)/generative artificial intelligence (GenAI) into DES processes to enhance simulation and modeling capabilities. Reviewing the transformative capabilities of AI/GenAI and large language models (LLMs) technology to improve productivity and efficiency raises questions about the potential for AI technologies to enhance similar benefits in DES.

This study extends the discourse on the continued evolution, expansion, and recent integration of new technologies over the past decade and a half. Specifically, the study addresses the following five research objectives:

• RO1. Assess the evolutionary expansion of DES research.
• RO2. Analyze the research landscape to uncover the thematic structure, applications, and evolution.
• RO3. Evaluate the intellectual structure to highlight the impacts of documents and sources’ citations and impact.
• RO4. Analyze the social structures of DES research and identify authors’ and countries’ collaborations.
• RO5. Examine the recent developments involving DES integration with digital twin (DT) and AI/GenAI technologies.

The rest of the paper is organized as follows: Section 2 presents DES modeling processes, activities, and tasks. Section 3 addresses the materials and methods, including the bibliometric analysis framework, data collection processes and procedures, and analysis techniques. Section 4 presents and discusses the results. The final part, Section 5, concludes the paper and identifies the potential future research areas.

2. Background and Overview of Discrete-Event Simulation and Modeling Processes

2.1. Overview of Discrete-Event Simulation

DES processes involve designing real or imaginary operations models to analyze complex systems and behavior through experimentation. Understanding the systems’ behavior by conducting experiments with a simulation model helps to evaluate strategies for improving operational outcomes and decision making [29]. Assumptions are often made about the systems and transformed into mathematical algorithms and relationships to reveal operational functionality and performance [3,29,30]. This section presents the modeling and simulation processes, activities, and tasks.

2.2. Modeling Activities, Tasks, and Processes

DES as an OR technique is used to solve complex dynamic problems where exact analytic and mathematical methods are problematic or not feasible [3,30,31]. It often involves “experimentation on a computer-based model” of a replica system, the model acting as a “vehicle for experimentation” based on a “what if” scenario and other statistical design techniques [3,5,31]. Figure 1 presents DES modeling activities, tasks, and processes.

The first step in the simulation and modeling process involves problem definition or formulation. It involves analyzing the system layout and requirements, setting the objectives of the simulation study, and defining the process flow [3,5]. Other activities include preparing a list of problems to address, identifying a set of assumptions, and determining the questions the project seeks to answer based on data availability [3,30,32].

In the second step, the analyst creates a conceptual model, which is an abstract or logical representation of a proposed or imaginary operational system based on some problem specifications. The model can be represented by a diagram or pictorial sketches showing the system’s process flow or layout. The analyst can also supplement the conceptual model with text or pictures [5,30,33,34]. When the conceptual modeling process employs a visual display technique, the model elements and the system’s components use graphic symbols, sketches, or block diagrams supplemented by text. Further discussions about conceptual modeling activities in DES are available elsewhere [30].

Model development is the next step in the DES modeling process. This step involves implementing the conceptual model using a computer program or by “drag and drop” of elements utilizing modeling and simulation software [3,35]. Most DES modeling and simulation efforts today use commercial software, making it possible to build models without recourse to extensive programming. Graphical images can employ 2D or 3D graphics. The parameters are also defined by using drop-down menus and command of the DES software. Examples of model-building and simulation applications today include WITNESS/VR, FlexSim, Simul8, Arena, and more [36,37].

The fourth step involves model validation. This is a process of determining whether a simulation model accurately represents the system based on set objectives [38,39,40]. The activities include checking and correcting errors in the model, such as logic, routing, wrong component combinations, or systems errors [12,39,41]. Validation helps to ensure that the simulation model accurately mimics the real-world system. The validation process also includes designing and effecting appropriate correction mechanisms. On the other hand, model verification is concerned with determining whether the model of the system of interest has implemented the conceptual model accurately together with the assumptions [34,40]. Recent studies have emphasized using 3D visualization to validate DES models. Visualizing modeled operations in 3D helps to generate insight and offers substantial help to the analyst in debugging simulation models and verifying that the model accurately represents the modeled system [39]. The visual display also enables all stakeholders to be involved in the validation and verification process, as they can observe the model behavior visually and provide feedback on how well it matches the existing system [42].

Experimentation and analysis are the next steps in the DES process. They involve investigating alternative courses of action to arrive at a preferred solution to improve the system of interest. The simulation analyst can observe the model behavior at runtime and alter parameters to examine alternatives. Other important activities include collecting output statistics, undertaking multiple replications, and undertaking statistical analysis [3,5,43]. Most experimentation and analysis also involve optimizers [5,28,43], which help to obtain optimal solutions. Like the validation process, visualizing the model, preferably using a 3D display, can be beneficial during experimentation and analysis. Proponents posit that using 3D visualization during experimentation enhances ease of analysis and generates ideas about the modeled system. Visualizing the model at runtime and in real-time using 3D/VR during experimentation reveals the entities’ actual and dynamic positions [39]. It provides true-to-scale graphics and animation, making simulation models easy to understand and invaluable for communicating new ideas and alternatives [39,41].

After experimentation comes the presentation of results and communication with clients or project owners. Visual simulation is quite effective for presenting simulation outcomes and communication with clients. Using 3D graphics and VR for these tasks can simplify the presentation and interpretation of simulation results to the users, especially to the managers and other decision makers who typically have little knowledge of statistics and computer simulation. The 3D/VR model can communicate accurate physical details, making simulation models easy to understand [36,44]. Further, using 3D graphics can simplify the presentation of the results for technical and non-technical stakeholders and decision makers. Visualizing the model offers immense benefits in conveying ideas to senior management and the board [36]. Viewing all aspects of an operation in a 3D animated model can improve users’ understanding, increasing the sense of participation and involvement of managers and other stakeholders.

2.3. Limitations of Simulation

DES, like other simulation methods, has several limitations. Sometimes it is challenging to create simulation models that accurately replicate the actual system due to the unavailability of data to describe the system’s behavior. It is common for a model to require input data that is limited or unavailable. This issue must be addressed prior to the design of the model to minimize its impact once the model is completed. Further, computer simulation can prove too expensive and time consuming to implement. A DES model is often implemented as a computer program or as some input into simulator software. Producing an efficient and workable computer program may take surprisingly long and can be complicated to implement [3]. Although general-purpose simulation software can reduce the time to produce simulation models/programs, it can be expensive to obtain.

3. Materials and Methods

3.1. Bibliometric Analysis

This study employs quantitative bibliometric analysis method incorporating performance analysis and science mapping of DES research using bibliographic data. The performance measures incorporate quantitative evaluation of the scientific research relating to productivity or publications output and a citation impact analysis of the published document, authors, institutions, and countries [45]. The science mapping components assess the thematic structure, trends, and co-occurrence of themes over time [45,46]. It also undertakes an assessment of the evolutionary trends in research to reveal theme dynamics over time, demonstrated through text analytics and mapping using keywords as the unit of analysis [47,48,49].

Another aspect the bibliometric analyses highlight relationships, social interactions, and collaborations among publications, authors, institutional affiliations, and countries [48,49]. In this study, the aspect involving recent developments utilizes qualitative analysis to evaluate the potential impact of recent technologies on the DES modeling activities and processes identified in Figure 1 in the previous section.

3.2. Data Collection

The data used in this study came from peer-reviewed journal articles, conference proceedings, and book chapters published between the period of 2010 and 2024 and indexed in the SCOPUS bibliographic database. The rationale for using SCOPUS as the data source is that it indexes a wide coverage of literature from nearly all disciplines from quality sources [50,51,52]. A query string (

Table 1. Literature survey and data collection process: search and retrieval, filtering, screening, and selection criteria of the published documents.

Activities/Focus	Criteria
Data Source(s)	SCOPUS Bibliographic Database search.
Search Criteria	((“discret*”) AND (“simulat*” OR “model*”)) AND PUBYEAR: 2010–2024. The search generated 187,727 published documents.
	Documents Filtering, Screening, and Selection
Filtering	Removed: Books: 409, Erratum: 122, Retracted: 113, Letter: 78, Note: 71; Editorial: 67; Short survey: 38, Data paper: 32 [187,727–930] = 186,797 documents. Removed through SCOPUS filtering platform: Non ((“Discrete-Event Simulation”) AND (“Artificial Intelligence” OR “digital twin”)): 187,797 − 184,666 = 2131
Screening	Screened out 9 Irrelevant Documents as follows: Literature not addressing the topic of interest: 2131 − 54 = 2077
Final Documents Selection	2077 publications from SCOPUS published between 2010 and 2024 (during COVID-19). Documents retrieved in text formats (.txt and .csv files) for analysis.

) was created using relevant keywords on DES and applications. The use of wildcards (*) ensured that all application documents were retrieved, which were subjected to stringent filtering processes. The database survey and data collection occurred in December 2024.

The bibliographic database interface offers the option to extract as plain text (.txt), Excel (.xlsx), or comma-separated value (.csv) files. The extracted data in the comma-separated file format went through further filtering, screening, and selection processes. During the screening process, non-peer-reviewed publications, duplicate entries, and irrelevant titles were removed, leaving 2077 screened publications. Table 1 shows the query string created using the search keywords and the filtering and selection criteria. Metadata was then extracted from the screened documents and exported as .csv files for processing and analysis.

3.3. Data Analytics Tools and Techniques

Recent advances in big data analytics and the availability of software solutions (including open-source software) offer more effective and efficient ways to carry out data analysis. This study employed VOSviewer_1.6.20 [53,54] and the BIBLIOMETRIX R package 5.1.0, a bibliographic analysis software library embedded in the R-Studio environment [55].

The above two applications help to produce quantitative bibliometric outputs, network analysis, and visualization [53,54,55]. Quantitative data analytics includes statistical evaluation of publications, trends, and performances and mapping the relationships among the published documents [56,57]. Network analysis and visualization can also enrich result presentation from bibliometric analyses [53,54]. The performance measures include publication trends, citation impacts, and collaboration indexes [51]. The science mapping and evaluation offers co-citation analysis and co-occurrence of keywords analysis to identify the research streams and themes. Bibliometric coupling and co-authorship analyses highlight relationships and social interactions among publications, authors, affiliations, and countries [55,56]. These techniques help to analyze the conceptual, intellectual, and social structures of the scientific literature produced on DES.

4. Results

4.1. Sample Description and Preliminary Results

Table 2. Descriptive statistics of the sample and preliminary results.

Variable Description	Results	Variable Description Contd.	Results
Years of publication	2010–2024	Documents contents:
Sources (journals, proceedings, book chapters)	947	Keywords plus (ID)	10,575
Documents information:		Author’s keywords (DE)	4121
Articles	885 (42.6%)	Authors and collaboration:
Book chapters	60 (2.9%)	Authors	5629
Conference papers	1132 (54.5%)	Authors of single-authored docs	36
Annual publication growth rate:	2.03%	Single-authored docs	124
Average citations per doc	9.5	Co-authors per doc	3.62
References	50,886	International co-authorships %	19.31

presents the summary statistics analyzed using the bibliographic metadata extracted from the 2077 SCPs (journal articles: 885 or 42.6%; conference proceedings: 1132 or 54.5%; book chapters: 60 or 2.9%). The results also highlight 19.3% international cooperation among co-authors across several regions, showing that DES topics attract a global audience among researchers and practitioners and affirm that simulation is everywhere. Also, the published documents appeared in 947 sources authored/co-authored by 5627 researchers from 89 countries. The analysis of results in Section 4 helps answer the research questions (RO1 to RO4) presented earlier in Section 1.

4.2. Scientific Literature Production Trend on DES

This section examines the first research objective (RO1) about the evolutionary expansion of DES research evidenced by scientific literature production (SLP). The analysis of SLP identifies the yearly publications covering the past fifteen years (2010 to 2024), as shown in Figure 2a. The results show an annual average SLP of 138.5. There were more conference proceedings than journal articles by about 12%. However, this is not unusual in the technology fields, where initial innovations are often presented at international conferences before appearing in journals. While the SLP in the first three years was at or slightly below the annual average, the subsequent years recorded above-average annual SLPs. The highest number of publications for any single year occurred in 2020, during the outbreak of COVID-19, when scientists utilized DES as a potent tool to analyze various pandemic-related problems [25,26]. Overall, the analysis using R-Bibliometrics shows an annual productivity trend of 2.03% (Table 2).

Figure 2b presents a scatter plot of the SLP for the same period to visualize the literature productivity trend, which fits a linear trend. While the SLP is at the mean for some years, others are slightly above or below it. The linear model produced the regression equation y = 2.232x + 120.61, where x is the nth year, and y is the total SLP. The coefficient of determination (R² = 0.40) indicates that time predicts about 40% of the variation in SLP (annual increases). The model is appropriate for this dataset because the trend of the SLP over time exhibits growth.

4.3. Domains of Discrete-Event Simulation Research and Practice

The second research objective (RO2) analyzes the research landscape to uncover the thematic structure of DES, its applications, and evolution. This section evaluates the DES application domains.

DES as an OR technique can be utilized to solve problems in several sectors and fields of endeavor and to support decision making in operations and production activities. The SCOPUS bibliographic data identifies enormous application areas (over 100). However, we collapsed and merged related areas (e.g., computer science theory, applications, and more) into one category named “computer science.” Figure 3 presents the summary of the identified domains, some of which include computer sciences (26%), engineering (21%), mathematics, business management and decision sciences (20), medical and health sciences, computer science and engineering, business and economics, and arts and humanities. Figure 3 shows twelve disciplines where DES plays a significant role in problem solving, especially systems optimization.

4.4. Thematic Structure of DES Research and Evolution

This section analyzes the thematic structure and evolutionary trends through a science mapping of DES research and practice. The preliminary results of the text analytics using R-Bibliometrix identified 4121 unique but unstemmed author keywords with a total word frequency of 7501 extracted from 2077 SLPs.

The basis for using authors’ keywords as an approximation to the thematic structure of research is established in the literature [50,51,52,53,54]. To ensure exhaustive thematic analytics, the sample is stratified into three categories based on word frequency (f), which explains the number of times each keyword re-occurs in the dataset. The categorizations are as follows:

• Prominent themes, defined by prominent keywords with a frequency (f) of 10 or more, (f ≥ 10);
• Emerging themes, having keyword frequencies between 4 and 9 (4 ≤ f < 10);
• Least frequent themes (f < 4) and evolutionary trends during the period (2010–2024).

The classification of keywords as prominent, emerging, and least frequent themes (f ≥ 10; 4–9; f < 4, respectively) is based on convenience and to ensure an exhaustive analysis rather than following any statistical method.

4.4.1. Prominent Themes

The text analytics using R-Bibliometrix highlight the most popular research themes on DES in the past fifteen years (from the period of the threat of DES extinction [discussed in the introduction] to the period of “simulation everywhere”). The results identify 53 unstemmed author keywords with a total word frequency of 1991 (f = 1991) or 26.5%. These terms, which represent the research themes on DES and modeling, went through a “stemming” process. Word “stemming” is a text analytics process involving merging terms with different spellings but the same meaning or synonyms, e.g., “modeling/modelling” [57]. The stemming process reduced the themes from 53 to 44 (

Table 3. Analysis of eminent keywords and research themes trends.

Keywords	Stemmed Co-Words	Link Strength	Keywords Contd.	Stemmed Co-Words	Link Strength
Discrete-Event Simulation	973	494	Waiting Time	14	18
Simulation	213	176	Productivity	13	25
Parallel Discrete-Event Simulation (DES)	71	42	Operations Research	13	20
Optimization	61	90	Digital Twin	13	15
Modeling	55	83	Performance Evaluation	13	13
Healthcare	35	52	Time Warp	13	12
Logistics	31	37	Maintenance	12	22
Emergency Department	29	42	Patient Flow	12	18
Industry 4.0	27	33	Plant Simulation	12	18
Devs	24	13	Machine Learning	12	14
System Dynamics	23	32	Cost-Effectiveness	12	11
Manufacturing	22	33	Resource Allocation	11	18
Simulation Modeling	20	22	Supply Chain Management	11	17
Performance	19	20	Construction Management	11	13
Arena	18	29	Efficiency	11	13
Supply Chain	18	26	Discrete Event Systems	11	6
Discrete-Event	18	21	Queuing Theory	10	16
COVID-19	17	28	Process Improvement	10	12
Scheduling	17	24	Synchronization	10	11
Computer Simulation	17	10	Discrete Event	10	8
Simulation Optimization	15	11	Process Mining	10	7
Design Of Experiments	14	21	Simulation Model	10	7

). The three most popular themes other than “DES,” “simulation,” or “modeling” included “optimization,” “healthcare,” and “logistics,” appearing 61, 35, and 31 times, respectively. This result shows that DES continues to tackle problems in core OR/management sciences areas.

Similarly, terms such as “industry 4.0,” “digital twin” (DT), and “COVID-19” being among the prominent themes indicates the continuous relevance of DES in tackling problems in emerging fields and technologies in the fourth industrial revolution and disease outbreak, such as the “SARS coronavirus-2” (SARS-CoV-2) [58].

4.4.2. Emerging Themes

This section analyzes the emerging themes based on author keywords that occurred between four and nine times (4 ≤ f < 10). The text analytics results using the R-Bibliometrix show 160 emerging themes with a total frequency of 869 times (f = 869 or 11.6% of the total word frequencies). Also, using the VOSviewer application, we created a network map and visualization of the thematic structure of DES and applications scientific literature landscape. The text analytics solution offers the functionality to remove nugatory and non-connected nodes and words that do not convey contextual meanings, leaving 148 terms. The text mining algorithm stratified the themes into thirteen (13) color-coded clusters. The nodes with the same color belonged to the same cluster throughout the network (Figure 4).

The cluster categorization contains some random elements. Removing a theme with several connected edges in the network can lead to a reclassification of the clusters. The identified research themes are more significant than the cluster where the terms are listed. The network visualization highlights the thirteen clusters as follows:

Cluster #1: (“discrete-event system,” “design of experiment,” and “experimentation.” Others are “evaluation” and “performance analysis”). These terms point to conducting simulation experiments to analyze designs and systems’ behavior or complex processes through what-if scenarios.

Cluster #2: (“modeling and simulation,” “conceptual modeling,” “validation,” and “model checking”) point to two crucial “modeling and simulation” activities: developing the conceptual model and checking errors in the programmed model, often carried out during experimentation explained above.

Cluster #3: The third cluster deals with “healthcare simulation” for “outpatient clinic” to determine “patient waiting time” and “appointment scheduling,” a vital area of DES applications.

Cluster #4: (“operational research,” “decision support systems,” “artificial intelligence,” “production planning and control”);

Cluster #5: (“cost-effectiveness analysis,” “multi-objective optimization,” “colorectal cancer”). These keywords point to model optimization, systems evaluation, and cancer diagnoses in healthcare.

Cluster #6: The cluster focuses on the use of “hybrid simulation” and “data envelopment analysis” to analyze “hospital” operations, “healthcare management,” and other “healthcare” issues.

Cluster #7: (“production scheduling,” “routing,” “transport”). DES plays key roles in efficient work scheduling, vehicle routing, and product scheduling.

Cluster #8: (“operations management,” “production planning,” “lean manufacturing,” and “manufacturing systems”). These themes show another aspect where DES is utilized to streamline operations.

Cluster #9: (“decision Support system,” “prediction,” “design”). The themes in this cluster relate to DES’s role as a tool for aiding decision making in facility design and making predictions.

Cluster #10: (“energy efficiency,” “sustainable manufacturing,” and “resource management”).

Cluster #11: (“production,” “reverse logistics,” “sustainability”). DES plays an important role as a tool to enhance sustainable and efficient production.

Cluster #12: (“emergency medical services,” “cost,” and “cloud computing”). Modeling and simulation of emergency services in healthcare and operations cost reduction forms a significant area of DES application.

Cluster #13: (“discrete-event system,” “queuing system,” and “Internet of Things”). The thirteenth cluster examines the DES application to evaluate queuing systems and the Internet of Things in Industry 4.0.

Cluster #14: (“discrete simulation” and “forecasting”). The two themes address the use of DES to make forecasts. Figure 4 presents the social network map showing the themes as labeled.

4.4.3. Least Frequent Themes and Trends

The least frequent themes category contains terms with word frequencies less than four (f < 4). The dataset contains 3908 terms, making up 95% (3908/4121) of the themes. In terms of word frequencies, it represents 4641 or 62% of the 7501 total keyword frequencies. The keywords are unstemmed, meaning that in the text analytics algorithm, words with similar meanings that are spelled differently are considered unique (e.g., “AI” and “artificial intelligence” are considered unique terms). The text analytics algorithm categorizes the keywords into color-coded clusters on a network map. The circles (nodes) with the same color belong to the same cluster. Also, in the legend (Figure 5), the node labels represent the research themes under focus in each period segment mapped to the period of occurrence or year of publication (pre-2014, that is, 2010 to 2014; 2014–2016; 2016–2018; 2018–2020; 2020–2024), as explained below.

The network map contains three categories of themes: DES theory, modeling and simulation processes, tasks and activities, and the diverse application areas. The clusters and the themes in each period segment are as follows:

• Pre-2014: (“testing,” “data integration,” “queuing model,” “healthcare modeling,” “bed management,” “breast cancer,” and more).
• 2014–2016: (“formal verification,” “work sampling,” “diagnoses,” “car sharing,” and more).
• 2016–2018: (“layout design,” “artificial intelligence,” “automation,” “object-oriented modeling,” and more).
• 2018–2020: (“core manufacturing simulation,” “manufacturing planning,” “fast-moving consumer goods,” “traffic congestion,” and more).
• 2020–2022: (“supply chain planning,” “capacity analysis,” “virtual reality,” “crowd management,” “underground mining,” “artificial neural network”).
• 2022–2024: (“mass vaccination,” “capacity analysis,” “load sharing,” “ambulance deployment,” and more).
• post-2024: (“management science,” “sales operations planning,” “decomposition,” “artificial intelligence,” “additive manufacturing,” “collaborative networks,” and more).

The theme dynamics (pre-2014 to 2022–2024 and beyond) highlight the trends and evolution in the application of DES to solve diverse problems in several domains in the different period segments identified above. For example, in pre-2014 (2010–2014), themes such as “testing” point to model testing as one of the stages in the DES processes. Also, “data integration” represents one of the tasks during model experimentation where real-life or imaginary data can be integrated with a simulation model to investigate a “what-if” scenario. Other terms such as “healthcare modeling,” “breast cancer,” and “bed management” point to the application of DES to evaluate cancer diagnoses, hospital bed allocation, and utilization scenarios. Figure 4 shows the complete themes under this category.

The period segments of 2022–2024 and post-2024 identify themes such as “mass vaccination,” “capacity analysis,” and “ambulance deployment,” pointing to the use of DES to model and simulate critical health issues around COVID-19 vaccination. The current period (2024 and beyond) mirrors technological trends using DS methods, such as machine learning methodology and “generative adversarial networks” (Figure 5). The entire period (2010–2024) provides the evolutionary trends that highlight the continuous application of DES in research and problem solving in real-life issues over the years.

4.5. Intellectual Structure of DES Research

This section evaluates the intellectual structure of DES research based on a citation analysis in the era of “simulation everywhere” [24] and focuses on the impact of citations on documents and sources. The results help to address the third research objective (RO3). The preliminary results (Table 2) show an average of 9.5 citations per document (Table 2) and a total of 19,731 from 2010 to 2024 based on SCOPUS bibliographic data. The Google Scholar (scholar.google.com) citation count can be greater than the number of records in SCOPUS.

The citation structure analysis using the R-based Bibliometrix application (

Table 4. The citation structure of research publications on DES.

Year	≥300	≥200	≥100	≥50	≥30	≥10	≥1	NC	TP	% Cited
2010	0	0	4	7	6	18	56	20	111	82%
2011	0	1	0	11	4	22	56	26	120	78%
2012	1	0	3	5	8	33	60	27	137	80%
2013	0	0	0	3	10	38	67	6	124	95%
2014	0	0	2	5	8	32	56	17	120	86%
2015	0	0	0	4	8	38	69	16	135	88%
2016	0	0	1	5	12	35	89	18	160	89%
2017	0	0	0	4	6	41	79	25	155	84%
2018	0	0	1	3	6	38	68	9	125	93%
2019	0	0	0	2	6	31	83	26	148	82%
2020	0	0	0	6	0	37	94	26	163	84%
2021	0	0	0	3	4	27	86	27	147	82%
2022	0	0	0	0	2	25	87	30	144	79%
2023	0	0	0	0	0	11	76	54	141	62%
2024	0	0	0	0	0	1	51	95	147	35%
Total Pubs	1	1	11	58	80	427	1077	422	2077

NC: no citation (publications that did not earn any citations as of 31 December 2024), TP: total publications per year.

) shows that about 80% of the articles earned at least one or more citations, with the four highest citation impacts occurring in 2013 (95%), 2018 (93%), 2016 (89%), and 2015 (88%). Also, 35% of the current year publications with zero citable years received at least one citation. Table 4 presents the complete citation structure of the publications.

4.5.1. Most Cited Documents

Table 5. Ten most cited documents on the use of DES to solve COVID-19 problems.

Rank	Paper	Focus	Sources	TC	AC P/Year	Citable Years
1	[58]	DES and system dynamics in the logistics and supply chain context	Decision Support Systems	347	24.79	14
2	[59]	Applications of simulation within the healthcare context	Journal of the Operational Research Society	211	17.58	12
3	[60]	The application of DES in a health care setting	Medical Decision Making	187	13.36	14
4	[61]	SimLean: Utilising simulation in the implementation of lean-in healthcare	European Journal of Operational Research	184	14.15	13
5	[62]	A review of DES applications in healthcare.	BMC Health Services Research	171	21.38	8
6	[63]	Current and future trends of DES and virtual reality use in industry	IEEE Transaction on Human-Machine System	169	16.9	10
7	[22]	Combining system dynamics and discrete-event simulation in healthcare	Proc. Winter Simulation Conf.	129	8.6	15
8	[64]	Comparing agent-based simulation with DES in modeling emergency behaviors	Proc. Winter Simulation Conf.	115	7.7	15
9	[40]	DES method in construction engineering and management	Journalof Construction Engineering Management	110	7.33	15
10	[23]	Comparing DES and systems dynamics application in healthcare	European Journal of Operational Research	108	9	12

TC: total citations based on SCOPUS bibliographic data; AC P/Year: average citation per year.

presents the top ten most cited publications. The results show that the article examining “DES and system dynamics in the logistics and supply chain context” [58] recorded the highest citation count. Table 5 presents the complete list of research focus, sources, and citations. Fifty percent of the ten most cited articles or conference papers had near maximum citable years. This result implies that citable years accounted for the high citation impacts, among other factors, such as the article title or the sources in which it appears. The most cited article appeared in some of the most popular sources (“Decision Support Systems” and “Journal of Operational Research Society”).

4.5.2. Eminent Sources

The 2077 documents analyzed in this study were published in 947 sources, giving an average of 2.2% publications per source. The analysis of eminent sources shows that the top twenty journals and proceedings published 23.3% of the documents and earned 7635 (38.7%) citations out of 19,731. Most of the journals and conference proceedings were core sources in OR, while others are sources in the application domains. Examples are Proceedings—Winter Simulation Conference, Simulation, and Journal of Simulation. These three sources published 205, 29, and 23 articles and proceeding papers and earned citation counts of 1667, 304, and 430. Others are Simulation Modelling Practice and Theory, European Journal of Operational Research, and Journal of the Operational Research Society. Sources in the application domains include Medical Decision Making, Health Care Management Science (healthcare), and Automation in Construction (engineering and construction).

Table 6. The top 20 sources with most eminent sources and citation impacts.

Rank	Sources	NP	TC	AVTC	Pub_Start_Yr.
1	Proceedings—Winter Simulation Conference	205	1667	8.1	2010
2	Simulation	23	430	18.7	2010
3	Journal of Simulation	29	304	10.5	2010
4	Simulation Modelling Practice and Theory	17	621	36.5	2011
5	European Journal of Operational Research	12	622	51.8	2010
6	Computers and Industrial Engineering	11	330	30.0	2014
7	Journal of the Operational Research Society	14	386	27.6	2010
8	Medical Decision Making	16	449	28.1	2010
9	Procedia CIRP	20	217	10.9	2014
10	Value In Health	13	429	33.0	2010
11	IFAC-Papers Online	16	166	10.4	2015
12	ACM Transactions on Modeling and Comp. Simulation	19	181	9.5	2011
13	Automation in Construction	9	342	38.0	2012
14	BMC Health Services Research	9	317	35.2	2011
15	Health Care Management Science	7	288	41.1	2011
16	International Journal of Advanced Manufacturing Technology	9	155	17.2	2011
17	Lecture Notes in Comp Science; Subseries Lecture Notes in Artificial Intelligence; Lecture Notes in Bioinformatics	28	158	5.6	2010
18	PLOS ONE	11	186	16.9	2011
19	Proceedings of the 2013 Winter Simulation Conference—Simulation: Making Decisions in A Complex World	12	107	8.9	2013
20	Journal of Construction Engineering and Management	6	280	46.7	2010

NP: no. of Publications; TC: total citations; AVTC: average TC per document; Pub Yr.: publication start year.

presents the complete list of the top most eminent sources.

4.6. Social Structure of Publications

Countries’ Publications and Impact

The final part of the analysis examines the social structure of publications on DES research, which addresses the fourth research objective (RO4). Recently, the simulation community began paying attention to “simulation around the world,” which has become a track at conferences, such as the Winter Simulation Conference [65]. The results help to answer questions regarding collaboration among countries where the authors are domiciled as another measure of the social structure of publications in science mapping studies [50,51,53].

The results show 1968 unique authors from 89 countries that published articles used in this study, with a total frequency of 5429, as some authors published more than one articles. The international collaboration index results show a moderate association of 19.03% among the authors’ affiliated countries and international co-authorship.

Table 7. Countries with international collaborations on publications in two categories, SCP and MCP, and impact.

Country	Publications	SCP	MCP	TC	ATC (Pub)
United States	200	165	35	2517	12.59
United Kingdom	98	76	22	2315	23.62
China	79	70	9	703	8.9
Germany	73	60	13	995	13.63
Italy	62	47	15	693	11.18
Canada	60	52	8	1214	20.23
Brazil	44	36	8	530	12.05
Sweden	36	23	13	470	13.06
France	33	23	10	198	6
Australia	30	19	11	746	24.87
India	29	25	4	118	4.07
Korea	24	22	2	267	11.13
Malaysia	24	20	4	147	6.13
Turkey	24	15	9	285	11.88
Indonesia	22	20	2	57	2.59

SCP: collaboration as non-corresponding author; MCP: contributions as corresponding author; TC: total citations; ATC (Pub): average total citation per publication.

shows the USA, the UK, China, Germany, and Italy as the five most dominant countries in literature publications on DES and applications. The table shows a complete list of the top ten countries. The analysis also highlights the countries where the corresponding authors are domiciled, which follow a similar pattern as literature publications led by USA, the UK, and Italy. The USA published the highest number of articles (200, including 35 as corresponding authorship) through collaborations, the UK came second with 98 documents through global collaborations but had 22 corresponding authorships. The USA and UK also earned the most citations (2517 and 2315, respectively). Table 6 shows the complete list of the top 10 countries where the authors/co-authors are domiciled.

4.7. DES Integration with Digital Twin in Industry 4.0 and Artificial Intelligence

Since the inception of DES in the 1950s, developments in discrete-event modeling and simulation have often paralleled technological advances in computer science (hardware and software) and other related fields [66,67]. The analysis of the thematic evolution in this study identifies two key technologies that occurred in recent years, namely, “digital twin” (DT) listed in Table 3 and “artificial intelligence” (AI), identified in Figure 5. While DES has contributed towards the advancement or enabling DT technology in Industry 4.0 on the one hand, GenAI possesses demonstrable capability to transform DES and modeling activities, tasks performance, and processes. This section employs descriptive bibliometric analysis to analyze the integration of DES with DT and AI, which addresses the fifth research objective (RO5).

4.7.1. The Role of DES in Enhancing Digital Twin in Industry 4.0

In Table 3, DT is identified as one of the emerging themes in this study. While DT technology is generally considered a groundbreaking development in industry operations and processes, DES has contributed significantly to enhancing the advancement and smooth functioning of this technology since the advent of Industry 4.0 [66,67,68]. By definition, DT is a virtual system that forms a replica of a real physical system or process [69]. The virtual (DT) dynamic system updates in real time with data from its physical replica (twin), allowing for its predictive analysis, monitoring, and maintenance [66,69].

As identified in several studies reviewed in this article, e.g., [70,71], computer simulation, particularly DES and continuous simulation, provides the underlying black box, logical models, and the engine that enables the modeling and simulation of the virtual replica (DT) system that mimics the real physical counterpart. It helps the simulated twin system respond to the real-time data inputs. For example, in a DT of an assembly plant [72], a DES model simulates the flow of components, the operation of machines, the movement of workers, and the impact of breakdowns or delays. Similarly, DES has been utilized to simulate DTs for several other operations and processes (warehouse logistics [71]; production and manufacturing systems [73,74]; critical care delivery and healthcare workflow [75,76]). Integrating DES and using real-time data from the real physical systems (manufacturing, operations, logistics, and healthcare) enhances the predictive and diagnostic power of DT in the context of Industry 4.0 [77,78], particularly in complex, event-driven systems, thereby overcoming disruptions and inaccurate predictions for informed decision making.

4.7.2. DES Integration with Artificial Intelligence/Generative Artificial Intelligence

The attempt to integrate AI in DES to further transform computer modeling and simulation has been ongoing for quite some time. However, recent efforts in this direction are now yielding results, especially as AI applications in industry become increasingly ubiquitous, with AI integration with other systems and platforms to solving problems in operations and production activities and processes now common. Integrating AI (e.g., artificial neural networks [79], machine learning [80,81], and deep learning [82]) with DES offers a hybrid architecture that brings additional intelligence, adaptability, and learning capabilities, reinforcing the predictive capacity, optimization, and intelligent decision making of computer simulation [80,83].

Recently, the emergence of GenAI presents significant potential for rapid transformation in DES. GenAI is a subset of artificial intelligence (AI) that leverages large language models (LLMs), generative adversarial networks (GANs), and multimodal frameworks to create new content, including text, images, audio, code, and video [84,85,86]. For DES, the benefits of GenAI span several aspects of modeling and simulation activities and processes, from idea generation to formulating a simulation project proposal and defining DES project objectives to the actual creation of the simulation model and coding, model optimization, and results presentation. The DES literature also presents the significance of AI integration in solving problems in operations and production activities and processes. Integrating AI technologies (e.g., artificial neural networks [79], machine learning [80,81], and deep learning [82]) with DES offers a hybrid architecture that brings additional intelligence, adaptability, and learning capabilities, reinforcing the predictive capacity, optimization, and intelligent decision making of computer simulation [80,83].

Further, the emergence of GenAI presents significant potential for rapid transformation in DES. GenAI as a subset of AI leverages large language models (LLMs), generative adversarial networks (GANs), and multimodal frameworks to create new content, including text, images, audio, code, and video [84,85,86]. For DES, the benefits of GenAI cut across several aspects of modeling and simulation activities and processes, from idea generation to formulating a simulation project proposal and defining the DES project objectives to the actual creation of the simulation model, model optimization, results presentation, and enhancing the overall model usability [84,85,86,87,88].

Several studies reviewed in this article demonstrate the application of AI and GenAI in DES, highlighting significant promise for problem solving in various domains, as evidenced by real-world use cases. Ortiz-Barrios et al. [89] integrated DES and AI for “shortening bed waiting times” and “capacity management of intensive care units during the COVID-19 pandemic” [90], both in hospital operations. Others [84,85,86,87,91] identified the benefits of GenAI in creating the DES model from text descriptions by issuing prompts (text commands or instructions), which enables the GenAI tool (e.g., ChapGPT or others) to create a conceptual/graphical model. Furthermore, several GenAI tools demonstrate significant capacity to develop computer program codes for the DES model of systems and processes [84,85,86,87,89,91]. This development enables non-simulation experts and managers to write text prompts for the GenAI tool, thereby creating or developing DES models, which increases its efficacy, simulation, and modeling accessibility and improves usability [84,85,86,87,88,90,91]. This will further increase the use of DES as an OR technique, thus making computer simulation and modeling available everywhere.

Despite the above benefits, several limitations and drawbacks exist when using GenAI. Regarding the capacity of GenAI to generate synthetic data for simulation, such data sometimes fails to mimic real-world trends and may also contain false information, otherwise known as hallucinations [88,92,93,94]. Several other studies have also raised concerns about ethical issues, privacy violations, and intellectual property infringement by using data or information from unauthorized sources [85,88,92,93].

5. Conclusions

This study successfully analyzed the evolutionary expansion of DES as an OR technique, highlighting key development trends in simulation and modeling research and practice. Within the past fifteen years (2010–2024), DES scientific literature production has continued to expand, indicating increased usage, not only during the COVID-19 period [25,26] but also beyond. This study, therefore, extends the initial arguments that not only is DES “well and kicking” [19] or “alive and strong” [25] but continues to expand. Thus, DES has outlived the doom prediction of becoming obsolete [15,16,17], instead witnessing extensive expansion and popularity as an OR technique, hence the motif, “simulation everywhere.” Thus, DES enjoys continuous usage to solve diverse problems across several fields of endeavor. For example, DES remained an essential OR tool in tackling COVID-19-related problems [25] and has remained at the center of digital transformation that has swept across the industrial space, from manufacturing to healthcare and the service industry in recent years, therefore providing evidence of its continuous relevance. The DES publications analyzed in this study were published in several high-quality sources and generated citation impacts with high collaboration among institutions and countries, which further provides evidence about “simulation everywhere.”

Another notable highlight in DES evolution is the continuous adoption and integration of new technologies to improve simulation and modeling activities, tasks, and processes. During the period of 2010–2024, the key technologies integrated with DES included DT, AI, and GenAI. DES lends a hand in enhancing DT to realize its purpose of virtually simulating a replica of a real physical asset, monitoring its performance, making predictions, and making decisions about the maintenance and performance improvement of the real physical assets. As the simulated DT (virtual replica system) utilizes real data, it enables continuous feedback loops, predictive diagnostics, and synchronized system optimization.

The third contribution of this study examines the integration of AI in DES, including machine learning, artificial neural networks, and deep learning, which has further transformed the simulation landscape. The integration of AI with DES provides a hybrid architecture that enhances intelligence, adaptability, and learning capabilities. The incorporated intelligent components enable the DES model to adapt, learn from historical and streaming data, and autonomously enhance its predictive analytic capabilities. Similarly, the ongoing integration with GenAI brings the possibility of generating simulation models from text prompts. The development of GenAI adoption is significant as the technology becomes ubiquitous. Several industries, including healthcare, manufacturing, logistics, and smart cities, are increasingly adopting these integrated systems, thereby enhancing modeling and simulation experience and improving accessibility and usability.

Future work will continue to explore the integration of GenAI in every aspect of the DES processes, which is capable of further transforming the simulation and modeling experience and streamlining DES tasks and activities.