Effectiveness of Mathematical and Simulation Models for Improving Quality of Care in Emergency Departments: A Systematic Literature Review

Abstract

Objectives

The purpose of this systematic literature review is to critically evaluate the use of mathematical and simulation models within emergency departments (EDs) and assess their potential to improve the quality of care. This review emphasizes the critical need for quality enhancement in health care systems, with a specific focus on EDs.

Methods

This review incorporates studies that have investigated the quality of care provided in ED settings, employing assorted mathematical and simulation models for adult populations. Based on the selected studies, a narrative approach was used to synthesize the findings, focusing on outcome classification, simulation, and modelling. There are six outcome dimensions: safety, effectiveness, patient-centeredness, timeliness, efficiency, and equity.

Results

This review analyzed 112 studies, uncovering a distinct focus on a set of key performance measures within ED operations, accounting for 222 instances across these studies. Measures assessing timeliness were most frequent, occurring 111 times, indicative of a strong emphasis on operational efficiency aspects such as waiting times and patient flow. A total of 75 examinations were conducted on efficiency-related measures, with a specific focus on identifying and addressing operational bottlenecks and optimizing resource utilization. On the other hand, safety, patient-centeredness, and effectiveness were not as commonly represented, with only 3, 4, and 29 instances, respectively.

Conclusion

This review highlights the considerable potential of mathematical and simulation models to enhance ED operations, particularly regarding timeliness and efficiency. However, aspects such as patient safety, effectiveness, and patient-centeredness were underrepresented, while equity was absent across the studies, indicating a clear need for further research. These findings emphasize the importance of adopting a more thorough approach to evaluating and improving the quality of emergency care. Future research should also concentrate on refining data management practices, incorporating observational studies, and exploring various simulation tools to develop a more balanced and inclusive understanding of these models' applications.

Keywords

quality of care - health care improvement - emergency department - simulation techniques - modelling techniques - clinical decision support systems - data analytics in health care

Protection of Human and Animal Subjects

This study did not involve human subjects; it is a systematic literature review based solely on previously published research.

Publikationsverlauf

Eingereicht: 07. Dezember 2024

Angenommen: 17. April 2025

Accepted Manuscript online:
21. April 2025

Artikel online veröffentlicht:
22. August 2025

• References

• 1 Wolfe A. Institute of Medicine Report. Crossing the Quality Chasm: A New Health Care System for the 21st Century. Policy Politics Nurs Pract 2001; 2: 233-235
• 2 Hyrkäs K, Lehti K. Continuous quality improvement through team supervision supported by continuous self-monitoring of work and systematic patient feedback. J Nurs Manag 2003; 11 (03) 177-188
• 3 Donabedian A. Explorations in Quality Assessment and Monitoring: The Definition of Quality and Approaches to its Assessment. 1980 . Accessed October 27, 2022 at: https://philpapers.org/rec/DONEIQ
• 4 World Health Organisation. Quality of Care. A Process for Making Strategic Choices in Health Systems. 2006 . Accessed October 27, 2022 at: https://apps.who.int/iris/bitstream/handle/10665/43470/?sequence=1
• 5 Department of Health. High Quality Care for All. NHS Next Stage Review Final Report. 2008 . Accessed October 27, 2022 at: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/228836/7432.pdf
• 6 NHS England. Major plan to recover urgent and emergency care services. January 30, 2023. Accessed May 11, 2023 at: https://www.england.nhs.uk/2023/01/major-plan-to-recover-urgent-and-emergency-care-services/
• 7 The King's Fund. Accident and emergency (A&E) waiting times. February 17, 2023. Accessed May 11, 2023 at: https://www.kingsfund.org.uk/projects/nhs-in-a-nutshell/waiting-times
• 8 NHS England. Delivery Plan for Recovering Urgent and Emergency Care Services. January 2023. Accessed May 11, 2023 at: https://www.england.nhs.uk/wp-content/uploads/2023/01/B2034-delivery-plan-for-recovering-urgent-and-emergency-care-services.pdf
• 9 Schweigler LM, Desmond JS, McCarthy ML, Bukowski KJ, Ionides EL, Younger JG. Forecasting models of emergency department crowding. Acad Emerg Med 2009; 16 (04) 301-308
• 10 Chan SSW, Cheung NK, Graham CA, Rainer TH. Strategies and solutions to alleviate access block and overcrowding in emergency departments. Hong Kong Med J 2015; 21 (04) 345-352
• 11 Angelo SA, Arruda EF, Goldwasser R, Lobo MSC, Salles A, Silva JRL. Demand forecast and optimal planning of intensive care unit (ICU) capacity. Pesqui Oper 2017; 37 (02) 229-245
• 12 Keeling MJ, Rohani P. Modeling infectious diseases in humans and animals. Clin Infect Dis 2008; 47: 864-870
• 13 Dundar S, Gokkurt B, Soylu Y. Mathematical modelling at a glance: A theoretical study. Procedia Soc Behav Sci 2012; 46: 3465-3470
• 14 Gaba DM. The future vision of simulation in health care. Qual Saf Health Care 2004; 13 (Suppl. 01) i2-i10
• 15 Gilbert N, Troitzsch K. Simulation for The Social Scientist. 2nd ed.. Open University Press; 2005
• 16 Breuer DJ, Kapadia S, Lahrichi N, Benneyan JC. Joint robust optimization of bed capacity, nurse staffing, and care access under uncertainty. Ann Oper Res 2022; 312 (02) 673-68
• 17 Zhang B, Murali P, Dessouky MM, Belson D. A mixed integer programming approach for allocating operating room capacity. J Oper Res Soc 2017; 60 (05) 663-673
• 18 Oddoye JP, Jones DF, Tamiz M, Schmidt P. Combining simulation and goal programming for healthcare planning in a medical assessment unit. Eur J Oper Res 2009; 193 (01) 250-26
• 19 Farahi S, Salimifard K. A simulation–optimization approach for measuring emergency department resilience in times of crisis. Oper Res Health Care 2021; 31: 100326
• 20 Box GEP. Robustness in the strategy of scientific model building. Robustness in Statistics 1979; 201-236
• 21 Moher D, Liberati A, Tetzlaff J, Altman DG. PRISMA Group. Preferred reporting items for systematic reviews and meta-analyses: the PRISMA statement. PLoS Med 2009; 6 (07) e1000097
• 22 Ahmed MA, Alkhamis TM. Simulation optimization for an emergency department healthcare unit in Kuwait. Eur J Oper Res 2009; 198 (03) 936-942
• 23 Oh C, Novotny AM, Carter PL, Ready RK, Campbell DD, Leckie MC. Use of a simulation-based decision support tool to improve emergency department throughput. Oper Res Health Care 2016; 9: 29-39
• 24 Mandahawi N, Shurrab M, Al-Shihabi S, Abdallah AA, Alfarah YM. Utilizing six sigma to improve the processing time: a simulation study at an emergency department. J Ind Prod Eng 2017; 34 (07) 495-503
• 25 Komashie A, Mousavi A. Modeling emergency departments using discrete event simulation techniques. Proc Winter Simul Conf 2005; 2005: 2681-2685
• 26 Hoot NR, LeBlanc LJ, Jones I. et al. Forecasting emergency department crowding: a discrete event simulation. Ann Emerg Med 2008; 52 (02) 116-125
• 27 Wang J, Li J, Tussey K, Ross K. Reducing length of stay in emergency department: A simulation study at a community hospital. IEEE Trans Syst Man Cybern A Syst Hum 2012; 42 (06) 1314-1322
• 28 Tsai JCH, Weng SJ, Liu SC. et al. Adjusting daily inpatient bed allocation to smooth emergency department occupancy variation. Healthcare (Basel) 2020; 8 (02) 78
• 29 Hurwitz JE, Lee JA, Lopiano KK, McKinley SA, Keesling J, Tyndall JA. A flexible simulation platform to quantify and manage emergency department crowding. BMC Med Inform Decis Mak 2014; 14: 50
• 30 Lim ME, Worster A, Goeree R, Tarride JÉ. Simulating an emergency department: the importance of modeling the interactions between physicians and delegates in a discrete event simulation. BMC Med Inform Decis Mak 2013; 13 (01) 59
• 31 De Boeck K, Carmen R, Vandaele N. Needy boarding patients in emergency departments: An exploratory case study using discrete-event simulation. Oper Res Health Care 2019; 21: 19-31
• 32 Mould G, Bowers J, Dewar C, McGugan E. Assessing the impact of systems modeling in the redesign of an emergency department. Health Syst (Basingstoke) 2013; 2 (01) 3-10
• 33 Baril C, Gascon V, Vadeboncoeur D. Discrete-event simulation and design of experiments to study ambulatory patient waiting time in an emergency department. J Oper Res Soc 2019; 70 (12) 2019-2038
• 34 Atalan A, Dönmez CC. Optimizing experimental simulation design for the emergency departments. Braz J Oper Prod Manag 2020; 17 (04) 1-13
• 35 Peng Q, Yang J, Strome T, Weldon E, Chochinov A. Evaluation of physician in triage impact on overcrowding in emergency department using discrete-event simulation. J Proj Manag 2020; 5: 211-226
• 36 Gül M, Guneri AF, Gul M. A computer simulation model to reduce patient length of stay and to improve resource utilization rate in an emergency department service system. Int J Ind Eng Theory Appl Pract 2012; 19: 221-231 . Accessed April 25, 2025 at: https://www.researchgate.net/publication/266787725
• 37 Zeinali F, Mahootchi M, Sepehri MM. Resource planning in the emergency departments: A simulation-based metamodeling approach. Simul Model Pract Theory 2015; 53: 123-138
• 38 Coughlan J, Eatock J, Patel N. Simulating the use of re-prioritisation as a wait-reduction strategy in an emergency department. Emerg Med J 2011; 28 (12) 1013-1018
• 39 Stainsby H, Taboada M, Luque E. Towards an agent-based simulation of hospital emergency departments. Paper presented at: 2009 IEEE International Conference on Services Computing, Bangalore, India; 2009: 536-539
• 40 Yousefi M, Ferreira RPM. An agent-based simulation combined with group decision-making technique for improving the performance of an emergency department. Braz J Med Biol Res 2017; 50 (05) e5955
• 41 Lee SR, Shin SD, Ro YS, Lee H, Yoon JY. Multimodal quality improvement intervention with dedicated patient flow manager to reduce emergency department length of stay and occupancy: Interrupted time series analysis. J Emerg Nurs 2022; 48 (02) 211-223.e3
• 42 Yeh JY, Lin WS. Using simulation technique and genetic algorithm to improve the quality care of a hospital emergency department. Expert Syst Appl 2007; 32 (04) 1073-1083
• 43 Uriarte AG, Zúñiga ER, Moris MU, Ng AHC. System design and improvement of an emergency department using Simulation-Based Multi-Objective Optimization. J Phys Conf Ser 2015; 616: 012015 . Institute of Physics Publishing
• 44 Amissah M, Lahiri S. Modelling granular process flow information to reduce bottlenecks in the emergency department. Healthcare (Basel) 2022; 10 (05) 942
• 45 Memari H, Rahimi S, Gupta B, Sinha K, Debnath N. Towards patient flow optimization in emergency departments using genetic algorithms. Paper presented at: 2016 IEEE 14th International Conference on Industrial Informatics (INDIN), Poitiers, France; 2016: 843-850
• 46 Gunal MM, Pidd M. Interconnected DES models of emergency, outpatient, and inpatient departments of a hospital. Paper presented at: Winter Simulation Conference, Washington, DC; 2007: 1461-1466
• 47 Zhang XL, Zhu T, Luo L, He CZ, Cao Y, Shi YK. Forecasting emergency department patient flow using Markov chain. Paper presented at: 2013 10th International Conference on Service Systems and Service Management, Hong Kong, China; 2013: 278-282
• 48 Jones SS, Evans RS, Allen TL. et al. A multivariate time series approach to modeling and forecasting demand in the emergency department. J Biomed Inform 2009; 42 (01) 123-139
• 49 Girishan Prabhu V, Taaffe K, Pirrallo RG, Jackson W, Ramsay M. Overlapping shifts to improve patient safety and patient flow in emergency departments. Simulation 2022; 98 (11) 961-978
• 50 Green LV, Soares J, Giglio JF, Green RA. Using queueing theory to increase the effectiveness of emergency department provider staffing. Acad Emerg Med 2006; 13 (01) 61-68
• 51 Ricciardi C, Ponsiglione AM, Converso G, Santalucia I, Triassi M, Improta G. Implementation and validation of a new method to model voluntary departures from emergency departments. Running Title: Modeling Voluntary departures from emergency departments. Math Biosci Eng 2020; 18 (01) 253-273
• 52 Cochran JK, Broyles JR. Developing nonlinear queuing regressions to increase emergency department patient safety: Approximating reneging with balking. Comput Ind Eng 2010; 59 (03) 378-386
• 53 Ortiz-Barrios M, Alfaro-Saiz JJ. An integrated approach for designing in-time and economically sustainable emergency care networks: A case study in the public sector. PLoS ONE 2020; 15 (06) e0234984
• 54 Ahalt V, Argon NT, Ziya S, Strickler J, Mehrotra A. Comparison of emergency department crowding scores: a discrete-event simulation approach. Health Care Manag Sci 2018; 21 (01) 144-155
• 55 Gabriel GT, Campos AT, Magacho AL. et al. Lean thinking by integrating with discrete event simulation and design of experiments: an emergency department expansion. PeerJ Comput Sci 2020; 6: e284
• 56 Ashour OM, Okudan Kremer GE. A simulation analysis of the impact of FAHP–MAUT triage algorithm on the Emergency Department performance measures. Expert Syst Appl 2013; 40 (01) 177-187
• 57 Harper A, Mustafee N. A hybrid modelling approach using forecasting and real-time simulation to prevent emergency department overcrowding. Paper presented at: 2019 Winter Simulation Conference (WSC), National Harbor, MD; 2019: 1208-1219
• 58 Kaushal A, Zhao Y, Peng Q. et al. Evaluation of fast track strategies using agent-based simulation modeling to reduce waiting time in a hospital emergency department. Socioecon Plann Sci 2015; 50: 18-31
• 59 Choi D, Noh Y, Rha JS. Work pressure and burnout effects on emergency room operations: a system dynamics simulation approach. Serv Bus 2019; 13 (03) 433-456
• 60 Choon OH, Dali Z, Beng PT, Magdalene CPY. Uncovering effective process improvement strategies in an emergency department using discrete event simulation. Health Syst (Basingstoke) 2014; 3 (02) 93-104
• 61 Vile JL, Allkins E, Frankish J, Garland S, Mizen P, Williams JE. Modelling patient flow in an emergency department to better understand demand management strategies. J Simul 2017; 11 (02) 115-127
• 62 Konrad R, DeSotto K, Grocela A. et al. Modeling the impact of changing patient flow processes in an emergency department: Insights from a computer simulation study. Oper Res Health Care 2013; 2 (04) 66-74
• 63 Castanheira-Pinto A, Gonçalves BS, Lima RM, Dinis-Carvalho J. Modeling, assessment and design of an emergency department of a public hospital through discrete-event simulation. Appl Sci (Basel) 2021; 11 (02) 805
• 64 Conte R, Gilbert N, Bonelli G. et al. Manifesto of computational social science. Eur Phys J Spec Top 2012; 214: 325-346
• 65 Hutchinson CL, Curtis K, McCloughen A, Qian S, Yu P, Fethney J. Predictors and outcomes of patients that return unplanned to the Emergency Department and require critical care admission: A multicenter study. Australas Emerg Care 2022; 25 (01) 88-97
• 66 Bouda Abdulai AS, Mukhtar F, Ehrlich M. United States' performance on emergency department throughput, 2006 to 2016. Ann Emerg Med 2021; 78 (01) 174-190
• 67 Hajjarsaraei H, Shirazi B, Rezaeian J. Scenario-based analysis of fast track strategy optimization on emergency department using integrated safety simulation. Saf Sci 2018; 107: 9-21
• 68 Günal MM, Pidd M. Understanding target-driven action in emergency department performance using simulation. Emerg Med J 2009; 26 (10) 724-727
• 69 Cabrera E, Taboada M, Iglesias ML, Epelde F, Luque E. Simulation optimization for healthcare emergency departments. Procedia Comput Sci 2012; 9: 1464-1473
• 70 Dunn R. Reduced access block causes shorter emergency department waiting times: An historical control observational study. Emerg Med (Fremantle) 2003; 15 (03) 232-238
• 71 Cabrera E, Taboada M, Iglesias ML, Epelde F, Luque E. Optimization of healthcare emergency departments by agent-based simulation. Procedia Comput Sci 2011; 4: 1880-1889
• 72 England T, Brailsford S, Evenden D. et al. Examining the effect of interventions in emergency care for older people using a system dynamics decision support tool. Age Ageing 2023; 52 (01) afac336
• 73 Coats TJ, Michalis S. Mathematical modelling of patients flow through an accident and emergency department. Emerg Med J 2001; 18 (03) 190-192
• 74 Goienetxea Uriarte A, Ruiz Zúñiga E, Urenda Moris M, Ng AHC. How can decision makers be supported in the improvement of an emergency department? A simulation, optimization and data mining approach. Oper Res Health Care 2017; 15: 102-122
• 75 Miller MJ, Ferrin DM, Szymanski JM. Simulating six sigma improvement ideas for a hospital emergency department. Paper presented at: Proceedings of the IEEE Winter Simulation Conference, New Orleans, December 7–10, 2003 1926-1929
• 76 Zhao Y, Peng Q, Strome T, Weldon E, Zhang M, Chochinov A. Bottleneck detection for improvement of emergency department efficiency. Bus Process Manag J 2015; 21 (03) 564-585
• 77 Kuo YH, Chan NB, Leung JMY. et al. An integrated approach of machine learning and systems thinking for waiting time prediction in an emergency department. Int J Med Inform 2020; 139: 104143
• 78 Taboada M, Cabrera E, Epelde F, Iglesias ML, Luque E. Agent-based emergency decision-making aid for hospital emergency departments. Emergencias 2012; 24 (03) 189-195 . Accessed May 23, 2023 at: https://portalrecerca.uab.cat/en/publications/agent-based-emergency-decision-making-aid-for-hospital-emergency
• 79 Kim S, Kim S. Differentiated waiting time management according to patient class in an emergency care center using an open Jackson network integrated with pooling and prioritizing. Ann Oper Res 2015; 230 (01) 35-55