Queuing Theory & Discrete Simulation as a Tool to Improve Medicine Deliver Center Service Levels
DOI:
https://doi.org/10.2298/YJOR240316015TKeywords:
Queuing theory, discrete simulation, waiting timeAbstract
The increasing demand for medical services and supplies as medicine delivery has been found in applied mathematical models, such as queuing theory, a tool to analyze and improve medical processes. However, these models often assume specific arrival intervals and demands without real variability and uncertainty demand. This research proposes a methodology in real systems, considering queuing theory and discrete simulation. The goal is to provide reliable scenarios and facilitate the decision-making process in medical centers. The data were collected in drug dispensing centers in Colombia as service times, service level and users’ arrival. The data were processed in a simulation model by Flexsim with multiple scenarios. The results revealed a 50% reduction in average waiting time, identified staff constraints and critical processes, and improved resource allocation. This applied case demonstrated that the queue theory and simulation integration become a valuable tool for managing variability in this medical service delivery system.References
S. Ghosh and R. Hassin, “Inefficiency in stochastic queueing systems with strategic customers,” European Journal of Operational Research, vol. 295, no. 1, pp. 1–11, Nov. 2021. doi: 10.1016/j.ejor.2021.03.065.
N. G. Micheal Mathavavisakan and K. Indhira, “A literature review on retrial queueing system with Bernoulli vacation,” Yugoslav Journal of Operations Research, vol. 34, no. 1, pp. 109–134, 2024. doi: 10.2298/YJOR230415020M.
M. A. Cohen et al., “Bespoke Supply Chain Resilience: The Gap between Theory and Practice,” Journal of Operations Management, vol. 68, no. 5, pp. 515-531, 2022. doi: 10.1002/joom.1184.
N. T. Mai and D. M. Cuong, “The Application of Queueing Theory in the Parking Lot: a Literature Review,” in Proceedings of the International Conference on Emerging Challenges: Business Transformation and Circular Economy (ICECH 2021), Hanoi, Vietnam, 2021, pp. 190–203. doi: 10.2991/aebmr.k.211119.020.
Dr. A. Adeniran, M. Sani Burodo, and Dr. S. Suleiman, “Application of Queuing Theory and Management of Waiting Time Using Multiple Server Model: Empirical Evidence From Ahmadu Bello University Teaching Hospital, Zaria, Kaduna State, Nigeria,” International Journal of Scientific and Management Research, vol. 5, no. 4, pp. 159–174, 2022, doi: 10.37502/ijsmr.2022.5412.
G.A.Gir´on-Restrepo, S. Tena-Monferrer, and J. C. Fandos-Roig, ”A review of the Colombian healthcare system: challenges and opportunities,” in Modern Healthcare Marketing in the Digital Era, K. Djakeli, Ed. Hershey, PA: IGI Global, 2024, pp. 150–163. doi: 10.4018/9798-3693-0679-6.ch009
Equipo Directivo de Superintendencia de notariado y registro, “Informe general rendici´on de cuentas Superintendencia Notariado y Registro,” 2019, [Online]. Available: https://servicios.supernotariado.gov.co/files/portal/portal-informe rdc20192020.pdf.
M. C. Ram´ırez, “El tiempo de espera es el tal´on de Aquiles de las entidades bancarias,” Revista el Tiempo, 2016, [Online]. Available: https://www.larepublica.co/consumo/el-tiempode-espera-es-el-talon-de-aquiles-de-las-entidades-bancarias-2354506.
D. Pab´on Guerrero, Y. I. Mu˜noz Silva, J. P. Mu˜noz Valencia, and S. A. Noguera Mu˜noz, “Barreras de acceso en la prestaci´on de los servicios de salud para los usuarios de la IPS Totoguampa del Municipio de Silvia en el Departamento del Cauca, 2022,” Universidad Cat´olica de Manizales, 2022. [Online]. Available: https://repositorio.ucm.edu.co/handle/10839/4072.
D. A. Collo Burbano et al., “Retos de la farmacovigilancia con la venta, comercializaci´on y dispensaci´on adecuada de medicamentos homeop´aticos y medicamentos tradicionales a base de plantas en un establecimiento farmac´eutico,” Universidad Nacional abierta y a distancia, May 2023. [Online]. Available: http://repository.unad.edu.co/handle/10596/57613
Ministerio de salud y Protecci´on social, “Informe global del proceso de consulta p´ublica del documento completo de An´alisis de Impacto Normativo (AIN) en la tem´atica de alimentos para prop´ositos m´edicos especiales (APME) en Colombia.,” 2023. [Online]. Available: https://www.minsalud.gov.co/Normativa/Paginas/analisis-de-impacto-normativo.aspx.
Ministerio de salud y Protecci´on social, “Perfil farmac´eutico de la Rep´ublica de Colombia,” 2012.[Online].
X. Wang and S. M. Disney, “The bullwhip effect: Progress, trends and directions,” European Journal of Operational Research, vol. 250, no. 3, pp. 691–701, May 2016, doi: 10.1016/J.EJOR.2015.07.022.
D. A. Figueredo De P´erez and I. Vargas-Chaves, “El acceso a medicamentos en Colombia y los contornos de un derecho y una pol´ıtica farmac´eutica a medio camino,” Justicia, vol. 25, no. 37, pp. 125–150, Jun. 2020, doi: 10.17081/just.25.37.3528.
D. Worthington, M. Utley, and D. Suen, “Infinite-server queueing models of demand in healthcare: A review of applications and ideas for further work,” Journal of the Operational Research Society, vol. 71, no. 8, pp. 1145–1160, Aug. 2020, doi: 10.1080/01605682.2019.1609878.
W. F. Angeles Bachet, “An´alisis de la demora y las salidas ineficaces del proceso desde un enfoque de sistemas y de Teor´ıa de colas. Una revisi´on sistem´atica,”Revista de Climatolog´ıa, vol. 23, pp. 1104–1113, Jul. 2023, doi: 10.59427/RCLI/2023/V23CS.1104-1113.
M. M. Hamdi, H. F. Mahdi, M. S. Abood, R. Q. Mohammed, A. D. Abbas, and A. H. Mohammed, “A review on Queue Management Algorithms in Large Networks,” IOP Conference Series: Materials Science and Engineering, vol. 1076, no. 1, p. 012034, Feb. 2021, doi: 10.1088/1757-899X/1076/1/012034.
H. Attar, M. R. Khosravi, S. S. Igorovich, K. N. Georgievan, and M. Alhihi, “Review and performance evaluation of FIFO, PQ, CQ, FQ, and WFQ algorithms in multimedia wireless sensor networks,” International Journal of Distributed Sensor Networks, vol. 16, no. 6, p. 155014772091323, Jun. 2020, doi: 10.1177/1550147720913233.
F. F. Galimulina and N. V. Barsegyan, “Application of Mass Service Theory to Economic Systems Optimization Problems—A Review,” Mathematics, vol. 12, no. 3, p. 403, Jan. 2024, doi: 10.3390/MATH12030403.
R. Renteria, M. Chong, I. de Brito Junior, A. Luna, and R. Quiliche, “An entropy-based approach for disaster risk assessment and humanitarian logistics operations planning in Colombia,” Journal of Humanitarian Logistics and Supply Chain Management, vol. 11, no. 3, pp. 428–456, Jul. 2021, doi: 10.1108/JHLSCM-03-2020-0018.
R. Delgado de la Torre, “Recordando a Erlang: Un breve paseo (sin esperas) por la Teor´ıa de Colas,” Materials matem`atics, pp. 0001–0033, 2009. https://ddd.uab.cat/record/97914
J. Linares-Cos, J. A. Vilalta Alonso, and R. Garza R´ıos, “Concepciones te´oricas sobre la calidad en la gesti´on de los servicios y su efectividad desde la teor´ıa de colas,” Revista Cubana de Administraci´on P´ublica y Empresarial, vol. 4, no. 1, pp. 128–143, 2020.
E. L´opez and L. G. Joa, “Queueing theory applied to the study of the service system of a pharmacy,” Revista Cubana de Inform´atica M´edica, vol. 10, no. 1, pp. 3–15, 2018.
J. M. Izar Landeta, C. B. Ynzunza Cort´es, and J. Garnica Gonz´alez, “An´alisis y optimizaci´on de dos sistemas de l´ıneas de espera de empresas de log´ıstica y transporte de los Estados de Quer´etaro y Colima,” Investigaci´on administrativa, vol. 47, no. 121, pp. 1–20, 2018,
S. Adhikari et al., “Analysis of average waiting time and server utilization factor using queueing theory in cloud computing environment,” International Journal of Nonlinear Analysis and Applications, vol. 12, no. Special Issue, pp. 1259–1267, Dec. 2021, doi: 10.22075/ijnaa.2021.5636.
N. S. Alejandro P´erez, S. Hern´andez Gonz´alez, J. A. Jim´enez Garc´ıa, and V. Figueroa Fern´andez, “An´alisis de un sistema de servicio con Teor´ıa de colas y simulaci´on,” Pistas Educativas, vol. 41, no. 135, 2020.
G. P. Loor Alc´ıvar, S. M. Rodr´ıguez Merch´an, O. B. Santos V´asquez, and B. J. Loor Alc´ıvar, “Teor´ıa de colas y optimizaci´on de proceso de atenci´on al usuario,” AlfaPublicaciones, vol. 4, no. 3, pp. 22–38, Jul. 2022, doi: 10.33262/ap.v4i3.221.
M. A. Kalwar, H. Bux Marri, M. A. Khan, and S. A. Khaskheli, “Applications of Queuing Theory and Discrete Event Simulation in Health Care Units of Pakistan,” International Journal of Science and Engineering Investigations, vol. 10, no 109, p. 6-18, 2021
R.A.Memon,J.P.Li,andJ.Ahmed,“SimulationModelforBlockchainSystemsUsingQueuing Theory,” Electronics , vol. 8, no. 2, p. 234, Feb. 2019, doi: 10.3390/electronics8020234.
P. Amalia and N. Cahyati, “Queue analysis of public healthcare system to reduce waiting time using flexsim 6.0 software,” International Journal of Industrial Optimization,vol. 1, no. 2, pp. 101–110, 2020.
W. M. Salazar Gallardo, “Modelo de teor´ıa de colas y simulaci´on para la asignaci´on del recurso humano en un sistema operativo de servicios.,” Escuela Polit´ecnico Nacional, Quito, 2022. [Online]. Available: http://bibdigital.epn.edu.ec/handle/15000/22795
A. Elalouf and G. Wachtel, “Queueing Problems in Emergency Departments: A Review of Practical Approaches and Research Methodologies,” Operations Research Forum, vol. 3, no. 1, pp. 1–46, Mar. 2022, doi: 10.1007/S43069-021-00114-8.
J. E. T´avara Pacheco, “Aplicaci´on de la teor´ıa de colas para proponer mejoras en la atenci´on del paciente en el servicio de farmacia del Hospital III Jos´e Cayetano Heredia-Piura,” Universidad Nacional de Piura, 2019. [Online]. Available: https://repositorio.unp.edu.pe/handle/UNP/1873
C.ChenandL.K.Tiong, “Usingqueuing theory and simulated annealing to design the facility layout in an AGV-based modular manufacturing system,” International Journal of Production Research, vol. 57, no. 17, pp. 5538–5555, 2019, doi: 10.1080/00207543.2018.1533654.
P. O. Peter and R. Sivasamy, “Queueing theory techniques and its real applications to health care systems– Outpatient visits,” International Journal of Healthcare Management, vol. 14, no. 1, pp. 114–122, 2021, doi: 10.1080/20479700.2019.1616890.
A. Zhang, X. Zhu, Q. Lu, and R. Zhang, “Impact of Prioritization on the Outpatient Queuing System in the Emergency Department with Limited Medical Resources,” Symmetry, vol. 11, no. 6, p. 796, Jun. 2019, doi: 10.3390/SYM11060796.
L. A. Velasquez Silva, “An´alisis del impacto de la aplicaci´on de la teor´ıa de colas en la reducci´on de tiempos y la satisfacci´on de clientes en el rubro de alimentos, en los ´ultimos 5 a˜nos: una revisi´on de la literatura cient´ıfica,” Universidad Privada del Norte, Lima, 2020. [Online]. Available: https://hdl.handle.net/11537/24858
J. Deng, “Resource Management in FlexSim Modelling: Addressing Drawbacks and Improving Accuracy,” Applied Sciences, vol. 13, no. 9, p. 5760, May 2023, doi: 10.3390/app13095760.
K. Akin and H. & Ordu, “A novel Simulation-Based Two-Stage optimization approach for nurse planning,” International Journal of Simulation Modelling, vol. 20, no. 4, pp. 591–602, Dec. 2022, doi: 10.2507/ijsimm21-4-618.
M. Ordu, E. Demir, C. Tofallis, and M. M. Gunal, “A comprehensive and integrated hospital decision support system for efficient and effective healthcare services delivery using discrete event simulation,” Healthcare Analytics, vol. 4, p. 100248, Dec. 2023, doi: 10.1016/j.health.2023.100248.
S. W. Akuamoah, D. Lu, and D. Yaro, “Application of Queueing Theory in Dispensation of Resources and Optimization in Teleconsultation,” International Journal of Applied and Computational Mathematics, vol. 6, no. 4, pp. 1–17, Aug. 2020, doi: 10.1007/S40819-02000851-0.
Y. A.-W. Nawusu, A. A. A. Danaa, and S. Ismail, “Queue Management during Health Pandemics: A Queuing Theory Perspective,” Asian Journal of Research in Computer Science, vol. 6, n. 4, pp. 18–26, Dec. 2020, doi: 10.9734/ajrcos/2020/v6I430164.
F. Lenin, V. Satama, M. L. Bernal, and D. I. Montenegro G´alvez, “Teor´ıa de colas y l´ıneas de espera, un reto empresarial en el mejoramiento continuo de los servicios,” Ciencia Latina Revista Cient´ıfica Multidisciplinar, vol. 5, no. 5, pp. 8418–8440, Oct. 2021, doi: 10.37811/cl rcm.v5i5.933.
W. A. Massey and J. Pender, “Dynamic rate Erlang-A queues,” Queueing System, vol. 89, no. 1–2, pp. 127–164, Jun. 2018, doi: 10.1007/s11134-018-9581-2.
M. Demircioglu, H. Bruneel, and S. Wittevrongel, “Analysis of a Discrete-Time Queueing Model with Disasters,” Mathematics, vol. 9, no. 24, p. 3283, Dec. 2021, doi: 10.3390/math9243283.
R. Rathore, “A Review on Study of application of queueing models in Hospital sector,” International Journal for Global Academic & Scientific Research, vol. 1, no. 2, pp. 01–05, Jun. 2022, doi: 10.55938/ijgasr.v1i2.11.
W. Qu, T. Tao, B. Xie, and Y. Qi, “A State-Dependent Approximation Method for Estimating Truck Queue Length at Marine Terminals,” Sustainability, vol. 13, no. 5, p. 2917, Mar. 2021, doi: 10.3390/su13052917.
G. Ascione, N. Leonenko, and E. Pirozzi, “Fractional Erlang queues,” Stochastic Processes and their Applications, vol. 130, no. 6, pp. 3249–3276, Jun. 2020, doi: 10.1016/j.spa.2019.09.012.
J. W. S. de Lima, G. Callou, and E. Andrade, “Queueing Theory and Stochastic Petri Net: A tutorial,” Research, Society and Development, vol. 10, no. 3, pp. e2810312826, Mar. 2021, doi: 10.33448/rsd-v10i3.12826.
C. Blondia, “Evaluation of the Waiting Time in a Finite Capacity Queue with Bursty Input and a Generalized Push-Out Strategy,” Mathematics, vol. 10, no. 24, p. 4771, Dec. 2022, doi: 10.3390/math10244771.
I. Cruz Dom´ınguez and E. Garc´ıa Jim´enez, “Recolecci´on y An´alisis de Datos del Sistema de l´ınea de espera del Instituto Soledad Acevedo De Los Reyes,” Anuario de Investigaci´on UM, vol. 1, no. 1, pp. 35–48, Aug. 2020.
W.Q.Duan, Z.Khan, M.Gulistan, and A. Khurshid, “Neutrosophic Exponential Distribution: Modeling and Applications for Complex Data Analysis,” Complexity, vol. 2021, no. 1, p. 5970613, Jan. 2021, doi: 10.1155/2021/5970613.
D. L. Rizzini, F. Galasso, and S. Caselli, “Geometric Relation Distribution for Place Recognition,” IEEE Robot Autom Lett, vol. 4, no. 2, pp. 523–529, Apr. 2019, doi: 10.1109/lra.2019.2891432.
S. A. Afolalu, O. M. Ikumapayi, A. Abdulkareem, M. E. Emetere, and O. Adejumo, “A short review on queuing theory as a deterministic tool in sustainable telecommunication system,” Materials Today: Proceedings, vol. 44, pp. 2884–2888, Jan. 2021, doi: 10.1016/j.matpr.2021.01.092.
Y. Perwej, S. Qamar Abbas, J. P. Dixit, D. N. Akhtar, and A. K. Jaiswal, “A Systematic Literature Review on the Cyber Security,” International Journal of Scientific Research and Management, vol. 9, no. 12, pp. 669–710, Dec. 2021, doi: 10.18535/ijsrm/v9i12.ec04.
E. Jafarnejad Ghomi, A. M. Rahmani, and N. N. Qader, “Applying queue theory for modeling of cloud computing: A systematic review,” Concurrency and Computation: Practice and Experience, vol. 31, no. 17, p. e5186, Sep. 2019, doi: 10.1002/cpe.5186.
A. Dudin, O. Dudina, S. Dudin, and K. Samouylov, “Analysis of Multi-Server Queue with Self-Sustained Servers,” Mathematics, vol. 9, no. 17, p. 2134, Sep. 2021, doi: 10.3390/math9172134.
T. M. V. Anuruddhika, S. Prasanth, and R. M. K. T. Rathnayaka, “The Approaches Utilized in Queuing Modeling: A Systematic Literature Review,” Asian Journal For Convergence In Technology, vol. 8, no. 2, pp. 24–30, Aug. 2022, doi: 10.33130/ajct.2022v08i02.006.
L. Fratta, M. Gerla, and L. Kleinrock, “Flow Deviation: 40 years of incremental flows for packets, waves, cars and tunnels,” Computer Networks, vol. 66, pp. 18–31, Jun. 2014, doi: 10.1016/j.comnet.2014.04.001.
M. J. Blesa and A. Fern´andez Anta, “Maria Serna’s contributions to adversarial queuing theory,” Computer Science Review, vol. 39, p. 100348, Feb. 2021, doi: 10.1016/j.cosrev.2020.100348.
P. W. Glynn and H. Lam, “Constructing simulation output intervals under input uncertainty via data sectioning,” Simulation Winter Conference, vol. 2018-December, pp. 1551–1562, Jul. 2018, doi: 10.1109/wsc.2018.8632450.
I. J. B. F. Adan, B. D’Auria, and O. Kella, “Special volume on ‘Recent Developments in Queueing Theory’ of the third ECQT conference,” Queueing Systems, vol. 93, no. 1, pp. 1–2, Sep. 2019, doi: 10.1007/s11134-019-09630-1.
I. de Brito, M. H. C. Cunha, L. A. Tozi, L. A. Franzese, L. da S. Fraz˜ao M´arcia, and A. Bressane, “Managing funerary systems in the pandemic: lessons learned and an application of a scenario simulation in S˜ao Paulo City, Brazil,” Journal of Humanitarian Logistics and Supply Chain Management, vol. 11, no. 3, pp. 481–492, 2021, doi: 10.1108/jhlscm-09-20200078.
S. M. Ulam and S. Higuera De Frutos, “Aventuras de un matem´atico. Memorias de Stanislaw M. Ulam,” Pensamiento Matem´atico, vol. 7, no. 1, pp. 199–202, 2017.
P. A. C. Raats and J. H. Knight, “The contributions of Lewis Fry Richardson to drainage theory, soil physics, and the soil-plant-atmosphere continuum,” Frontiers in Environmental Science, vol. 6, no. APR, p. 346275, Apr. 2018, doi: 10.3389/fenvs.2018.00013.
H. John, “Holland, Adaptation in natural and artificial systems,” Ann Arbor MI University of Michigan Press, vol. Ann Arbor, pp. 1-200?, 1992.
U. Farooq and M A. Ahmad, ”Finite Element Approach To Reinforced Concrete Using Ansys.” National conference on sustainable infrastructure development, At Chandigarh, India. 2014.
B. J. Alder and T. E. Wainwright, “Studies in Molecular Dynamics. I. General Method,” The Journal of Chemical Physics, vol. 31, no. 2, pp. 459–466, Aug. 1959, doi: 10.1063/1.1730376.
System simulation, 2nd. ed. New Jersey, 1987. https://bib.ubp.edu.ar/cgi-bin/koha/opacdetail.pl?biblionumber=16647.
J. A. Barra Montevechi, A. T. Campos, G. T. Gabriel, and C. H. dos Santos, “Input Data Modeling: An Approach Using Generative Adversarial Networks,” Winter Simulation Conference, IEEE, pp. 1–12, Dec. 2021. doi: 10.1109/WSC52266.2021.9715407.
Y. Anacona-Mopan, J. Segura-Dorado, and H. Paz-Orozco, “Optimizaci´on de la distribuci´on en planta con formulaci´on QAP y simulaci´on de eventos discretos,” Informador T´ecnico, vol. 87, no. 1, pp. 13–28, Sep. 2023, doi: 10.23850/22565035.4814.
J. Gonz´alez C, D. Galvis S, and L. Hurtado T, “La distribuci´on Beta Generalizada como un modelo de sobrevivencia para analizar la evasi´on universitaria,” Estudios pedag´ogicos (Valdivia), vol. 40, no. 1, pp. 133–144, 2014, doi: 10.4067/s0718-07052014000100008.
S. V. Prasad, P. S. K. Patra, R. Donthi, and M. K. Challa, “The optimization of the health care system by M/M/S queueing model,” AIP Conference Proceedings, vol. 2707, no. 1, May 2023, doi: 10.1063/5.0148445/2889666.
Y. D. V. Torres, Y. D. V. Torres, P. L. Alfonzo, and S. I. Mari˜no, “Teor´ı¬a de colas. Propuesta de un simulador did´actico,” Revista Publicando, vol. 4, no. 13 (2), pp. 1–20, Dec. 2017.
R. Poloczek and B. Oleksiak, “Modeling and simulating production processes with the use of the FLEXSIM method,” Metalurgija, vol. 62, no. 3–4, pp. 484–487, Jul. 2023.
C. E. Mendoza-Mac´ıas and Y. I. Ramos-Alfonso, “Evaluaci´on de la calidad del servicio con la utilizaci´on de indicadores cualitativos y cuantitativos en el sector bancario,” Dominio de las Ciencias, vol. 6, no. 3, pp. 950–966, Jul. 2020, doi: 10.23857/dc.v6i3.1327.
M. M. Kembe, E. S. Onah, and Iorkegh, “A study of waiting and service costs of a MultiServer Queuing model in a specialist Hospital,” International Journal of Scientific & Technology Research, vol. 1, n. 8, pp. 19–23, 2012.
M. Mohammadi and M. Shamohammadi, “Queuing Analytic Theory Using WITNESS Simulation in Hospital Pharmacy,” International Journal of Engineering & Technology, vol. 12, no. 6, pp. 20–27, 2012.
M. Bahadori, S. M. Mohammadnejhad, R. Ravangard, and E. Teymourzadeh, “Using queuing theory and simulation model to optimize hospital pharmacy performance,” Iranian Red Crescent medical journal, vol. 16, no. 3, 2014, doi: 10.5812/ircmj.16807.
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