Predictions and Application of Queueing Analysis: A Case of Regional Hospital Limbe, Cameroon
DOI:
https://doi.org/10.7494/dmms.2024.18.6442Abstract
In this work, we apply queue analysis and the prediction of waiting time at the Regional Hospital Limbe (RHL). The main purpose of the work was to be able to make mathematical sense of a real-life scenario concerning queues (waiting lines) and to try to come up with models for performance measurement and improvement. This can be achieved using queueing theory concepts, composed of queueing models that provide some operational insights because of their analytical nature. The observations included studying patient arrival and waiting times, together with doctor service times. The results show the busy departments in the hospital, busy days, and busy times. Long waiting times were found to exist mainly in general practitioner (GP) and specialist consultations. The queueing concept was applied to only one service segment, GP consultation. Although strong scientific conclusions cannot be made on the queuing models obtained due to inefficient data, the value of this work lies mainly in the methodology and proposal of different operating systems that can be adopted. Furthermore, some predictions were made using machine learning to see how long a patient can wait in a queue for service, the model predicting with an average of 10 minutes and 53 seconds of error.
References
Abdulkareem N.M. & Abdulazeez A.M. (2021). Science and business. International Journal, 5(2), pp. 128–142. DOI: https://doi.org/10.1186/s12913-022-07502-8.
Adeniran D.A., Burodo M.S. & Suleiman, S. (2022). Application of Qeuing 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, 5(4), pp. 159–174. DOI: https://doi.org/10.37502/IJSMR.2022.5412.
Almusawi M.A., Radwan N.M., Mahmoud N.E., Haji A.M. & Alabdulkareem, K.I. (2023). Patient waiting time at primary healthcare centers in Riyadh Region, Saudi Arabia: A cross-sectional study. Dr. Sulaiman Al Habib Medical Journal, 5, pp. 65–69. DOI: https://doi.org/10.1007/s44229-023-00032-3.
Benevento E., Aloini D. & Squicciarini N. (2023). Towards a real-time prediction of waiting times in emergency departments: A comparative analysis of machine learning techniques. International Journal of Forecasting, 39(1), pp. 192–208. DOI: https://doi.org/10.1016/j.ijforecast.2021.10.006.
Biya M., Gezahagn M., Birhanu B., Yitbarek K., Getachew N. & Beyene W. (2022). Waiting time and its associated factors in patients presenting to outpatient departments at Public Hospitals of Jimma Zone, Southwest Ethiopia. BMC Health Services Research, 22, 107. DOI: https://doi.org/10.1186/s12913-022-07502-8.
Boukas E.-K., Zhang Q. & Yin G. (1995). Robust production and maintenance planning in stochastic manufacturing systems. IEEE Transactions on Automatic Control, 40(6), pp. 1098–1102. DOI: https://doi.org/10.1109/9.388692.
Brockmeyer E., Halstrøm H. & Jensen A. (1948). The life and works of A.K. Erlang. Copenhagen: Copenhagen Telephone Comp.
Chakka R., Van Do T. & Pandi Z. (2022). A generalized Markovian queue and its applications to performance analysis in telecommunications networks. In: Performance Modelling and Analysis of Heterogeneous Networks. River Publishers, pp. 371–387. DOI: https://doi.org/10.1201/9781003339052-23.
Cooper R.B. (1981). Queueing theory. In: Proceedings of the ACM’81 conference (1981), pp. 119–122.
Ding S. (2023). Analysis and application of computer queueing theory. In: P. Kar, J. Li & Y. Qiu (Eds.), Proceedings of the 2023 International Conference on Image, Algorithms and Artificial Intelligence (ICIAAI 2023). Amsterdam: Atlantis Press, pp. 447–453. DOI: https://doi.org/10.2991/978-94-6463-300-9_45.
Dshalalow J.H. (Ed.) (2023). Advances in Queueing Theory, Methods, and Open Problems. CRC Press. DOI: https://doi.org/10.1201/9781003418283.
Elalouf A. & Wachtel G. (2021). Queueing problems in emergency departments: a review of practical approaches and research methodologies. Operations Research Forum, 3, 2. DOI: https://doi.org/10.1007/s43069-021-00114-8.
Erlang A.K. (1909). The theory of probabilities and telephone conversations. Nyt Tidsskrift for Matematik B, 20, pp. 33–39.
Fun W.H., Tan E.H., Khalid R., Sararaks S., Tang K.F., Ab Rahim I., Md. Sharif S., Jawahir S., Sibert R.M.Y. & Nawawi M.K.M. (2022). Applying discrete event simulation to reduce patient wait times and crowding: The case of a specialist outpatient clinic with dual practice system. Healthcare, 10(2), 189. DOI: https://doi.org/10.3390/healthcare10020189.
Garcia-Corchero J.D. & Jimenez-Rubio D. (2022). Waiting times in healthcare: equal treatment for equal need? International Journal for Equity in Health, 21(1), 184. DOI: https://doi.org/10.1186/s12939-022-01799-x.
Green L. (2013). Queueing analysis in health care. In: R. Hall (Ed.) Patient flow: reducing delay in healthcare delivery, Springer, pp. 361–384. DOI: https://doi.org/10.1007/978-1-4614-9512-3.
Harchol-Balter M. (2013). Performance modeling and design of computer systems: queueing theory in action. Cambridge: Cambridge University Press. DOI: https://doi.org/10.1017/CBO9781139226424.
Harki N.A. (2024). Multi-level feedback queue scheduling technique. Cihan University-Erbil Scientific Journal, 8(2), pp. 36–42. DOI: https://doi.org/10.24086/cuesj.v8n2y2024.pp36-42.
Ji J. (2023). Application of queuing theory in public service counters. In: P. Kar J., Li & Y. Qiu (Eds.), Proceedings of International Conference on Image, Algorithms and Artificial Intelligence (ICIAAI 2023), Amsterdam: Atlantis Press, pp. 509–517. DOI: https://doi.org/10.2991/978-94-6463-300-9_52.
Johnston A., Lang E. & Innes G. (2022). The waiting game: managing flow by applying queuing theory in Canadian emergency departments. Canadian Journal of Emergency Medicine, 24(4), pp. 355–356. DOI: https://doi.org/10.1007/s43678-022-00318-9.
Joseph J., Senith S., Kirubaraj A.A. & Ramson J.S. (2022). Machine learning for prediction of wait times in outpatient clinic. Procedia Computer Science, 215, pp. 230–239. DOI: https://doi.org/10.1016/j.procs.2022.12.026.
Kalwar M.A., Marri H.B., Khan M.A. & Khaskheli S.A. (2021). Applications of queuing theory and discrete event simulation in health care units of Pakistan. International Journal of Science and Engineering Investigations, 10(109), pp. 6–18. URL: https://www.researchgate.net/publication/356980604.
Kendall D.G. (1953). Stochastic Processes Occurring in the Theory of Queues and Their Analysis by the Method Of The Imbedded Markov Chain. The Annals of Mathematical Statistics, 24(3), pp. 338–354.
Koole G. (2013). Call center optimization. MG books. Lakatos L., Szeidl L. & Telek M. (2019). Queuing Networks, In: Introduction to Queueing Systems with Telecommunication Applications, Springer, pp.285–297. DOI: 10.1007/978-3-030-15142-3.
Lakatos L., Szeidl L. & Telek M. (2019). Queuing networks, In: L. Lakatos, L. Szeidl, M. Telek, Introduction to Queueing Systems with Telecommunication Applications, Second Edition, Springer, pp. 421–444. DOI: https://doi.org/10.1007/978-
-030-15142-3_10.
Le D.X., Do H.T., Bui K.T., Hoang T.Q., Nguyen G.H., Nguyen A.V., Nguyen Q.T., Gorgui-Naguib H. & Naguib RG.N. (2021). Lean management for improving hospital waiting times – Case study of a Vietnamese public/general hospital emergency department. The International Journal of Health Planning and Management, 37(1), pp. 156–170. DOI: https://doi.org/10.1002/hpm.3310.
Li X. (2024). Performance evaluation of M | M | 1 queueing models in cloud computing environments. Highlights in Science, Engineering and Technology, 85, pp. 841–848. DOI: https://doi.org/10.54097/1xcw8y74.
Liberopoulos G., Papadopoulos C.T., Tan B., Smith J. & Gershwin S.B. (2006). Stochastic modeling of manufacturing systems. Springer. DOI: https://doi.org/10.1007/3-540-29057-5.
Machangara D.T. (2018) Predictions and Application of Queuing Analysis at Regional Hospital Limbe. MSc thesis, African Institute for Mathematical Sciences (AIMS), Cameroune, December 2018. URL: https://library.nexteinstein.org/wp-content/
uploads/2023/01/Daphne-Essay-Template-en-2017-2018.tex_.pdf [1.10.2024].
Mbwogge M., Astbury N., Nkumbe H.E., Bunce C. & Bascaran C. (2022). Waiting time and patient satisfaction in a subspecialty eye hospital using a mobile data collection kit: pre-post quality improvement intervention. JMIRx Med 3(3),
e34263. DOI: https://doi.org/10.2196/34263.
Mohammadi T., Roshanaei G., Faradmal J., Sadeghifar M., Manafi B. & Mahjub H. (2022). Improving service efficiency and throughput of cardiac surgery patients using Monte Carlo simulation: a queueing setting. Scientific Reports, 12(1), 21217. DOI: https://doi.org/10.1038/s41598-022-25689-y.
Nair A.M., Sreelatha K. & Ushakumari P. (2021). Application of queuing theory to a railway ticket window. In: 2021 International Conference on Innovative Practices in Technology and Management (ICIPTM), Noida, India, pp. 154–158. DOI: https://doi.org/10.1109/ICIPTM52218.2021.9388368.
Newell C. (2013). Applications of queueing theory. Vol. 4. Springer Science & Business Media. DOI: https://doi.org/10.1007/978-94-009-5970-5.
O’Malley M.S., Fletcher S.W., Fletcher R.H. & Earp J.A. (1983). Measuring patient waiting time in a practice setting: A comparison of methods. The Journal of Ambulatory Care Management, 6(3), pp. 20–27. DOI: https://doi.org/10.1097/00004479-198308000-00006.
Palm C. (1943). Intensity fluctuations in telephone traffic. Ericsson Technics, vol. 44.
Palomo S., Pender J.J., Massey W.A. & Hampshire R.C. (2023). Flattening the curve: Insights from queueing theory. PLoS ONE, 18(6), e0286501. DOI: https://doi.org/10.1371/journal.pone.0286501.
Peter P.O. & Sivasamy R. (2021). Queueing theory techniques and its real applications to health care systems – outpatient visits. International Journal of Healthcare Management, 14(1), pp. 114–122. DOI: https://doi.org/10.1080/20479700.
1616890.
Proudlove N. (2022). Use and misuse of queueing theory for hospital capacity decisions. In: J. Vissers, S. Elkhuizen, N. Proudlovve (Eds.) Operations Management for Healthcare. Routledge, pp. 197–216. DOI: https://doi.org/10.4324/9781003020011.
Rema V. & Sikdar K. (2021). Optimizing patient waiting time in the outpatient department of a multi-specialty Indian hospital: The role of technology adoption and queue-based Monte Carlo simulation. SN Computer Science, 2, 200. DOI:
https://doi.org/10.1007/s42979-021-00595-8.
Saastamoinen K., Rissanen A., Suni J., Hyttinen J., Paakkunainen P. & Liakka A. (2023). Simulation of the queuing situation of patients at a health center. Engineering Proceedings, 39(1), 72. DOI: https://doi.org/10.3390/engproc2023039072.
Saaty T.L. (1957). Résumé of useful formulas in queuing theory. Operations Research, 5(2), pp. 161–200.
Shortle J.F., Thompson J.M., Gross D. & Harris C.M. (2018). Fundamentals of queueing theory, Fifth Edition. Hoboken: John Wiley & Sons.
Suleiman S., Burodo M.S. & Ahmed Z. (2022). An application of single and multi-server exponential queuing model in some selected hospitals of the North-Western Nigeria. Asian journal of probability and statistics, 16(2), AJPAS.82945, pp. 1–9. DOI: https://doi.org/10.9734/ajpas/2022/v16i230396.
Walker K., Jiarpakdee J., Loupis A., Tantithamthavorn C., Joe K., Ben-Meir M., Akhlaghi H., Hutton J., Wang W., Stephenson M., Blecher G., Buntine P., Sweeny A. & Burak T. (2022). Emergency medicine patient wait time multivariable prediction models: a multicentre derivation and validation study. Emergency Medicine Journal, 39(5), pp. 386–393. DOI: https://doi.org/10.1136/emermed-2020-211000.
Xiong Y. (2023). Research and application analysis of the basic theory of queuing theory. In: P. Kar, J. Li & Y. Qiu (Eds.), Proceedings of the 2023 International Conference on Image, Algorithms and Artificial Intelligence (ICIAAI 2023), Amsterdam: Atlantis Press, pp. 454–463. DOI: https://doi.org/10.2991/978-94-6463-300-9_46.
Yao D.D. (Ed.) (1994). Stochastic modeling and analysis of manufacturing systems. Springer Science & Business Media. DOI: https://doi.org/10.1007/978-1-4612-2670-3.
Zavanella L., Zanoni S., Ferretti I. & Mazzoldi L. (2015). Energy demand in production systems: A queuing theory perspective. International Journal of Production Economics 170(B), pp. 393–400. DOI: https://doi.org/10.1016/j.ijpe.2015.06.019.
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