ABSTRACT
While emergency care units must be integrated into a healthcare network to increase their effectiveness, operational strategies must be adopted to improve efficiency. We developed a simulation model and evaluated patient queues and staffing levels to assess the efficiency of clinical and pediatric care at a public health unit. Our results suggest that the public health unit is efficient, with 80% to 97% utilization of bottleneck resources; however, there are resource imbalances. The scenarios indicate that the level of effectiveness of the UPA can be increased by 24% if future investment prioritizes hiring a general practitioner, a screening nurse, and a secretary in this sequence. Conversely, the reduction of any of these three functions has a significant negative impact on system efficiency. The approach developed in open source can be applied and adjusted to other UPAs of SUS, the Brazilian Unified Health System.
Keywords:
health care planning; efficiency analysis; discrete event simulation
1 INTRODUCTION
Emergency care units (UPA, Portuguese acronym) are integrated into a healthcare system, comprising hierarchical health services operated by professionals, resources, and institutions that fund and regulate health units to improve or maintain health, which is believed to be one of the most crucial aspects of life 36); (41. Decisions in healthcare are hierarchical and classified as strategic, tactical, and operational according to a taxonomy 13. The process of determining the number of resources, professionals, or equipment in health units to achieve effectiveness and efficiency is a tactical decision, commonly referred to as capacity planning. The presence of queues on such systems increases the complexity of capacity planning 33, which requires the use of sophisticated methods, such as discrete-event simulation (DES) 19. However, researchers often face barriers to accessing detailed methodologies and modeling strategies. In this context, a pertinent research question arises: How can open-source discrete event simulation modeling, such as SimPy and similar frameworks, validate and predict resource utilization and efficiency in Brazilian UPA for achieving Manchester Triage System waiting time targets?
This study develops a generic model for public UPA, illustrated in Figure 1, with its validity examined through a case study in Contagem, Minas Gerais (MG), based on the operational guidelines of the National Emergency Care Policy 21.
Overview of the public Emergency Care Unit (UPA) located in Contagem, Minas Gerais, Brazil, illustrating its main structural characteristics and performance indicators.
According to 7, the efficiency level of health units in the micro-regions of MG is high, and the Belo Horizonte micro-region, where the case study UPA is located, is a reference for other units. However, general nursing staff often perceive that the UPA lacks adequate materials, standardized procedures, sufficient human resources, and training. In addition, they reveal the incorrect way that the population uses the health service, which hinders the work process 29. The proposed discrete-event simulation (DES) model reinforces the need for standardization of routine tasks and contributes to its capacity planning by assessing the UPA efficiency and proposing strategies to improve its effectiveness.
DES has been successfully applied in health care systems, such as on the evaluation of admission and discharge policies on Intensive Care Units performance 10, in evaluating medical testing equipment for diagnostic services 22, on sizing triage system for reducing laboratory queues 3 or on improving operating theater efficiency 11. However, according to the literature review in Section 2, few studies are developing open-source DES solutions for emergency care units. Most studies use commercial software, and few use strong testing methods. There is also little evidence on cost-effectiveness comparisons.
Therefore, we propose an open-source DES model to validate and predict resource use and efficiency in UPA to meet Manchester Triage System waiting time targets. The conceptual model is represented by an Activity Cycle Diagram (ACD), and DES algorithms are implemented in SimPy, Python. This approach contributes to identifying bottleneck resources in UPA, developing a decision-making framework for resource allocation, and evaluating performance metrics to enhance capacity planning in public health units and bolster efforts to improve their productivity. The ACD notation is a foundational and visual notation created for DES models originally proposed between the 1970s-1980s 38); (16); (14); (2. It represents a UPA at the operational level of detail to be implemented as a discrete-event simulation using a generic programming language, such as SimPy.
SimPy is a Python discrete-event simulation framework in Python 31); (34); (40. It allows users to simulate queues, resource contention, and represent capacity use dynamics with Python generator functions. The environment is the simulation clock that keeps track of time and manages events. Processes are Python generator functions that yield events, which are active components of the system, such as patients arriving at a queue. The events represent activities that are yielded, or delayed within a process, with pauses until the event completion. The contention of entities occurs in Resources. SimPy supports the modeling of various resource types, such as classical resources, priority-based resources, and containers, each with limited processing capacity to accurately represent real-world systems. We model the behavior of patients, the use of equipment, and of healthcare professionals with processes. All processes are within the UPA environment. Patients interact with the environment, resources, and with each other via events.
In the following sections, we describe this research. In Section 3, we develop the theoretical framework where the state of the art is systematically reviewed and analyzed. In Section 3, we introduce the conceptual model, proposed algorithms, and data used in the DES model. Section 4 presents the results, scenarios, and discusses practical implementation suitability. Finally, in Section 5, we conclude the study, presenting its limitations, future developments, and research directions.
2 LITERATURE REVIEW
In this section, we systematically review the state of the art of literature and follow official PRISMA standards (24) to answer the following research question: How has open-source discrete event simulation, such as SimPy and similar frameworks, been applied in emergency care unit modeling? The objective is to review and analyze the application of DES to Emergency Care units.
The inclusion criteria are (i) studies in English, published between 2014-2025 (inclusive); (ii) in Peer-reviewed journals and conference proceedings; (iii) focusing on emergency care units; (iv) using open-source DES tools, such as Simpy, SimJulia, Simmer, Ciw, etc. The exclusion criteria are (i) studies with proprietary simulation software, such as Arena, AnyLogic, Simul8, Flexsim; (ii) purely theoretical models without healthcare context; (iii) review articles; (iv) studies on non-emergency healthcare; (v) studies using only System Dynamics or Monte Carlo simulation, or Agent-Based Modeling without Discrete Event Simulation components.
The search strategy included multiple databases (Scopus; Web of Science; PubMed / Medline; IEEE Xplore; ACM Digital Library; ScienceDirect) using boolean queries with time filter 2014-2025, combining: (i) Open-source simulation terms: “SimPy”, “SimJulia”, “Simmer”, “Ciw”, “Salabim”, “open-source simulation”; (ii) Discrete event simulation terms: “discrete event simulation”, “DES”, “event-driven simulation”, “process-based simulation”; and (iii) Emergency care terms: “emergency department”, “emergency room”, “ER”, “ED”, “emergency care”, “emergency unit”. The resulting identification stage selected 361 documents.
The screening stage encompassed a variety of documentation, including records, books, chapters, journal articles, technical reports, and theses. In this stage, 356 documents were excluded for the following reasons: 185 documents demonstrated an absence of explicit reporting regarding open-source tools or the explicit utilization of proprietary DES software; 89 papers were excluded from the study because they do not report results from the ED application; 47 papers were review and open-source packages tutorial of DES open-source use, such as SimPy (https://simpy.readthedocs.io/en/latest/), Simmer (https://r-simmer.org/), Ciw (https://ciw.readthedocs.io/en/latest/), SimJulia (https://simjuliajl.readthedocs.io/en/stable/welcome.html), and 35 documents did not use simulation methodology.
In the eligibility stage, a set of five applied ED studies remained eligible for full-text review because they either explicitly matched the ED focus using a simulation tool. The studies describe 1 the use of DES to study ED operational changes during COVID-19 27; 2 a modeling strategy for acute stroke treatment using DES with proposal of operations improvement 17; 3 a cloud web app for automated input data management for DES in an ED context 23; a simulation-based optimization method applied to ED management 9 and; 5 the design/development of an ED model implemented via the R simmer package 28. Following, in the inclusion stage, seven documents were included in a qualitative synthesis. Such studies were identified with mentions of open-source DES libraries, including workflow papers, and some applied reports on ED; however, many applied ED studies did not specify software. The PRISMA flowchart is illustrated in Figure 2.
The principal open-source tools cited were: (i) SimPy on tutorials and usability reports, indicating these tools are advocated for health-service DES 25; instructional material shows ED arrivals and resources modeling 26; (ii) Simmer (R) with a tutorial for DES in R and an ED design/development 4), (28; (iii) open-source optimization libraries for simulation-optimization workflows 9; and (iv) general tooling note, i.e., method papers recommending packaging DES models with web apps or cloud services for usability 25.
Studies with DES applications on emergency care include: (i) redesigning operations during the pandemic 27, (ii) evaluating surge capacity during disaster/peak arrival scenarios 5, (iii) reducing time-sensitive stroke workflows at comprehensive centers 17, (iv) planning for ED expansion 8, and (v) using digital tools for real-time input data and workflows. Each application type has distinct data, validation, and bias considerations 23); (15.
The number of methodological tutorials on open-source DES tooling has increased from 2019 to 2023, with frequently applied ED studies from 2017 to 2024 showing a trend. These studies’ locations include Brazil 6, Italy 5, Canada 8, Colombia 23, and Vietnam 28. However, methodological approaches for replication and validation practices vary and are often incompletely reported. These studies include DES modeling 8); (17, scenario analysis and DoE 8, DES-based digital twins 15, and simulation-optimization workflows 9. Validation often relied on face-to-face meetings with ED managers or comparisons to historical performance metrics. However, the level of statistical validation differs across studies.
3 METHOD AND DATA
The conceptual modeling of UPA operations was conceived by interviewing professionals who work in the system. The proposed model, the code, and the data that support the findings are available at Github (https://github.com/otaviomvasc/ProjetoUPA) repository. The ACD describes the entities’ flow, activities, and queues. The process is described as follows: patients arrive at the secretariat for the registry, undergo a screening process, and are classified according to five types of prioritization (1 to 5) according to Manchester Triage System 39); (30 (emergency, very urgent, urgent, less serious, and mild cases) which sets the maximum waiting time of 0, 10, 50, 120, or 240 minutes to start a consultation.
The selected UPA has three General Practitioners (GPs) and two pediatricians. After the consultation, patients leave the system or experience one of the four types of examination (X-ray, electrocardiogram, urine, and blood test) or take medication. After medication, a patient can leave the system, return to the physician with higher priority care, or undergo tests. A patient must return to the physician with the exam before leaving the system. X-ray and electrocardiogram results are immediate, but blood and urine tests require waiting for the exam results. During this interval, the patient can undergo further examinations.
The scope of the study is limited to medical care and examinations at the UPA. Furthermore, we adopted some simplifying assumptions, such as patients can perform all exams, each patient performs an exam only once, and after returning to the physician, patients leave the system. The process is illustrated in Figure 3 and further detailed in Algorithms 1-5.
Activity Cycle Diagram of the UPA unit. On-line access (https://www.yworks.com/yed-live/?file=https://gist.githubusercontent.com/joaoflavioufmg/51b87daf55c3255000ba906d3ff23792/raw/ed2f8426d1458d6aef51512e66623fbdcd8dc224/DCA-UPA)
Algorithm 1 starts the simulation. DES, a powerful statistical tool, creates a set of replications to produce robust metrics of the UPA system. Users, such as healthcare managers or UPA decision-makers, can set the simulation time, warm-up, and the number of replications in the STAR SIMULATION function, which runs the simulation. This function creates a simulation object that calls a RUN REPLICATIONS method.
The Simulation class, defined by the Algorithm 2, runs the replications, computes output statistics with replication data, and produces charts. Each iteration of the RUN REPLICATIONS function creates an object of the Replication class, described in Algorithm 5, which starts the process through the CREATE ARRIVALS method. Algorithms 3 and 4 are Entity and Resources classes that create Patient objects and the resources that patient entities perform activities.
Algorithm 5 is the Replication class. Replication objects create resources and patient arrivals. The CREATE ARRIVALS function creates Patient objects from the Entity class and calls PROCESS ENTITY method. This method receives a patient and its route, allocates it in a queue, and checks its service priority before occupying the resource, described in function REQUEST RESOURCE, which allocates the required resource for performing the service, performs function WAIT OPERATION TIME, counts queuing time and number of patients, and computes Resource Usage. At the end of the activity, the resource is released in the method RELEASES RESOURCE. Following a method COMPUTE PATIENT CYCLE saves patients’ and resources data, such as time and number of patients in queue, time and number of patients in process, which is used to produce statistics at the end of the simulation. Therefore, the PROCESS ENTITY method requests the required types of resources listed in Table S2, process operations which times are described in Table S1, release resources, and DECIDE NEXT PROCESS of patients, according to the conceptual model described in the ACD 3, in a discrete event schema. The method DECIDE NEXT PROCESS receives the patient, and its current process, and decides the patient’s flow based on method SEARCH NEXT PROCESS, which evaluates its current process, a condition, or a probabilistic decision, according to ACD in Figure 3. Being a conditional or probabilistic decision, the probability distributions are evaluated in Appendix 5, Table S3.
In the case of returning to GPs or pediatricians, the patient priority parameter is increased. If the decision is to wait for the exam results, it is necessary to process the waiting time. The PROCESS ENTITY method checks whether the following process is the system output, closing the general patient cycle and computing its statistics, or calling the following process.
3.1 Data
Data on intervals between arrivals were obtained indirectly by evaluating indicators of four months of operation at the UPA in 2023. Records indicate 11,7% of patients have priority 1, 15% 2, 70% 3, 0,01% 4, and 3,3% 5. We collected time samples that enable processes and activities to be represented with statistical significance. However, expert knowledge that holds a detailed understanding of processes was also considered. The simulation results were validated with the UPA managerial reports of monthly production. Current data is described in Appendix 5, Table S1. The number of resources, and the processes in which they are allocated, is described in Appendix 5, Table S2. The historical flow of patients sets probabilistic branches, presented in Appendix 5, Table S3.
The model verification consisted of checking the computational results of cycles and flows of each patient. Although several combinations of flows are possible, all flows occurred according to the rule in the UPA and in Figure 3. In the validation phase, we compared the UPA’s sample of patient records queue times with such metrics on simulation. The values in Table 1 were presented to the UPA team, who validated the results. Emergency patients, which is color red in Manchester Triage System, are directly taken to UPA beds, which is out of scope of our conceptual model, while mild case patients, which color is blue in Manchester Triage System, are less numerous, some patients give up staying in queue, leaving the system after long waiting times, and they were not tracked on this health unit. On running the simulation model, we visually set the warm-up period for five days for the average queue time of a very urgent patient (priority 1), as illustrated in Figure 4.
We model the UPA system in which replications are independently identically distributed (iid). Therefore, the subsequent study stage is sizing replications to increase the robustness of the metric (average queue of urgent patients). After five replications of the UPA’s clinical and pediatric care, we observe an average of 20.35 ± 7.5 min (CI 95%) of time in queue for urgent patients.
For reaching a desired precision with CI 95%, the simulation is sized to n ∗ replications, estimated in , where , is the metric sample average, h the precision, i.e., half-width of confidence interval, µ the population mean, the number of replications n, the sample standard deviation s, and t n−1,1−α/2 as the t-student distribution. The average queue time of urgent patients is 20,35 minutes. We set a desired precision (h ∗) of 15% of the mean, i.e., 3 min for urgent patients; therefore, P(17 ≤ µ ≤ 23) = 0, 95, consequently, the validated simulation experiment was sized to n ∗ = 55 replications. Additionally, we validate the simulation bottleneck resources utilization against actual UPA data, and expert knowledge, which describes which professionals in UPA are mostly busy, and which activities produce larger queues in practice. Observation of longer queues and reports about the UPA system reveal “Blood test” and “Apply medication” as bottleneck resources. Such activities performance include nursing technicians, which are the most used resources in UPA.
4 RESULTS AND DISCUSSION
After analyzing the current key performance indicators and the results of the simulations, we proposed the scenarios that would improve the effectiveness and efficiency of the UPA with the least increase in resources, in line with the Ministry of Health’s policy. The values presented in Table 1 validate the results and are supplemented to better describe the UPA’s current operations. The simulation reveals a highly efficient public health unit. However, the target of maximum waiting time of very urgent patients is not reached, and the most used resources, i.e., GP, nurse, and secretary, represent a bottleneck for the overall UPA system. Therefore, future investments in increasing resource capacity should prioritize such resources. Simulating the UPA system, considering the removal of one GP, a screening nurse, or a secretary would yield an unstable system with average arrival rates higher than server rates. In practice, such a strategy could be tragic.
In an iterative process of simulation, analysis of results, and hypothesis generation, we describe four additional scenarios. The current situation is described as “As Is”, and additional scenarios are described as “To Be”. On Scenario To Be 1, the number of secretaries is reduced from two to one, and registry time is reduced 50% due to investments in process redesign. In this scenario, the average queue time is reduced by 1.47 minutes, from 8.34 to 6.87. Scenario To Be 2 equipment capacity is doubled, presenting 2 X-rays, 2 MRIs, 4 electrocardiograms, and 16 nurses’ assistance. Average resource utilization is reduced; however, average high-priority patient time is slightly increased. Scenario To Be 3 increases capacity from two secretary and nurse screenings to three professionals. Results show a considerable reduction in results average utilization; however, GP utilization is not reduced. Finally, Scenario To Be 4 considers an additional investment in another GP. Resources’ average utilization and queue time are presented in Figures 5 and 6.
Discrete event simulation models are often implemented using commercial software, such as ArenaTM AnyLogic, and Simio. Despite their advantages, such as graphical interfaces and robust analytical capabilities, the licensing costs can be prohibitive for many public healthcare organizations, particularly in developing countries like Brazil, where UPAs operate under severe budget constraints. Although open-source simulation frameworks have recently emerged 35); (18, the literature on open-source simulation models for healthcare remains scarce.
Our SimPy-based approach addresses three critical limitations of commercial solutions in health-care operations research. First is cost-effectiveness: the proposed framework eliminates licensing barriers while maintaining analytical rigor, making sophisticated capacity planning accessible to resource-limited healthcare systems. Second is transferability. The modular design enables rapid adaptation to different UPA configurations across Brazil’s diverse healthcare landscape. Our parameterized approach allows healthcare managers to modify patient flow, resource configurations, and service time distributions with simple updates, facilitating SUS network deployment without additional software investments. Third, our approach promotes reproducibility and transparency. The open-source nature of the model enables end-users to review modeling assumptions, validation of algorithmic implementations, and replication of results. These are critical requirements for evidence-based healthcare policy.
Even though our proposed simulation framework can be improved in future work. The models’ activities can be further aggregated for simplifying analysis 32. Moreover, data frameworks can be modeled and exported to standardized spreadsheets including similar performance indicators following best practices presented in commercial simulation softwares, such as ArenaTM. Relevant improvements concern (i) improving staffing sizing and scheduling by combining the proposed DES framework with stochastic programming features (20), and (ii) developing a graphical interface for improving visualizing the DES model. For such, we suggest Casymda 12 for Business Process Modeling Notation (BPMN) interface like Arena, Salabin, and Kalasim 37); (1, as alternatives for a graphical interface in Python for DES.
5 CONCLUSION
In this paper, we proposed a discrete-event simulation model to assess the efficiency of a public UPA contributing to operations research for health care. The model enabled the analysis of the current practice and different configurations of patient and resource flows in the health unit, grouped into optimistic and pessimistic scenarios. The results suggest that the public UPA is efficient. Even though the overall system utilization can be further improved by 24% if future investment prioritizes hiring a GP, a screening nurse, and a secretary.
We propose a healthcare simulation framework designed to model the operations of Emergency Care Units (UPAs). Built using a generic SymPy-based model, the framework is easily transferable and adaptable to different UPAs. Key components of patient flow are incorporated, including arrival, triage using the Manchester Triage System, queuing for medical attention from general practitioners and specialists, access to diagnostic and treatment resources such as X-rays, and the final disposition process (discharge, hospitalization, or referral).
All elements of the system can be parameterized via databases, enabling more intuitive and flexible input configuration. The model produces performance metrics such as the average time patients spend in the system by severity level, utilization rates of healthcare professionals and diagnostic equipment, queue lengths, and the total time from arrival to discharge. Users can adjust parameters such as patient arrival rates, service time distributions, and resource throughput times to apply this framework to different UPAs.
Although we provided a detailed model of the UPA health unit, the study has some limitations. Data quality can be improved by digitizing data collections in operations and queues, which would imply changing distributions, the required numbers of replications, and improving the quality of outcome statistics. Another issue is the scope of the study. It was limited to clinical and pediatric care activities and did not include the flow of emergency patients. Consequently, this is an avenue for future work.
Alternative strategies, such as increasing working hours, or referring to other units and granting vouchers for patients who reach a waiting time limit, were adopted in Spain, and in Portugal, respectively, for mitigating excessive queues of elective surgery 33. Although these are temporary strategies, these scenarios can also be simulated in future studies.
Data availability
The simulation model code and the data that support the findings are available at Github (https://github.com/otaviomvasc/ProjetoUPA) repository. The Activity Cycle Diagram of the UPA unit (https://www.yworks.com/yed-live/?file=https://gist.githubusercontent.com/joaoflavioufmg/51b87daf55c3255000ba906d3ff23792/raw/ed2f8426d1458d6aef51512e66623fbdcd8dc224/DCA-UPA) is available for on-line access. Complementary original data supporting this study are in the text and in the Appendix.
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FUNDING.
The authors acknowledge the support of the Brazilian Society of Operational Research (SOBRAPO), as well as the financial support from the Coordination for the Improvement of Higher Education Personnel (CAPES) - Funding Code 001, and the National Council for Scientific and Technological Development (CNPq) - Project Code 444452/2023-0, for their support of this research.
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Use of AI-assisted technologies
Artificial intelligence tools were used for bibliographic semantic search and organization, and to improve readability and language. After using this tool/service, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the publication’s content.
APPENDIX: SUPPLEMENTARY DATA
Case study data on process time distributions, number of resources and corresponding process, and processes probabilistic branches.
























