Optimality Test for Multi-Sever Queuing Model with Homogenous Server in the Out-Patient Department (OPD) of Nigeria Teaching Hospitals

Full Text (PDF, 586KB), PP.9-17

Views: 0 Downloads: 0

Author(s)

Tochukwu A. Ikwunne 1,* Moses O. Onyesolu 2

1. Department of Mathematics/Computer Science/Informatics/Statistics, Federal University, Ndufu Alike Ikwo, Abakiliki, Nigeria

2. Department of Computer Science, Nnamdi Azikiwe University, Awka, Nigeria

* Corresponding author.

DOI: https://doi.org/10.5815/ijmecs.2016.04.02

Received: 6 Dec. 2015 / Revised: 23 Jan. 2016 / Accepted: 2 Mar. 2016 / Published: 8 Apr. 2016

Index Terms

Multi-Server, Out-patient, Total Cost, Trade-off, Utilization factor

Abstract

Queuing by patients in the out-patients department to access hospital services in Nigeria teaching hospitals is a teething concern to most healthcare providers. This causes inconvenience to patients and economic costs to the hospitals. Patients waiting for minutes, hours, days or months to receive medical services could result in waiting costs to them. Providing too much service could result in excessive costs. Also not providing adequate services could result in excessive waiting and costs. This study sought to determine an optimal server level and at a minimum total cost which include waiting and service costs in homogenous servers in order to reduce patients’ congestions in the hospital as low as reasonably practicable. The queuing characteristics in all the twenty-three (23) teaching hospitals in Nigeria were analysed using a Multi-server Queuing Model and the waiting and service costs determined with a view to ascertaining the optimal service level. The data for this study were collected through observations and interviews. The data was analysed using Quantitative Methods, Production and Operations Management (POM QM) and Queuing Theory Calculator Software as well as using descriptive analysis. The results of the analysis demonstrated that average queue length, waiting time of patients as well as over utilization of specialist doctors at the teaching hospitals could be reduced at an optimal server level and at a minimum total cost as against their present server level with high total cost which include waiting and service costs. Therefore, this call for refocusing so as to improve the overall patient care in our cultural context and meet the patient needs in our environment.

Cite This Paper

Tochukwu A. Ikwunne, Moses O. Onyesolu, "Optimality Test for Multi-Sever Queuing Model with Homogenous Server in the Out-Patient Department (OPD) of Nigeria Teaching Hospitals", International Journal of Modern Education and Computer Science(IJMECS), Vol.8, No.4, pp.9-17, 2016. DOI:10.5815/ijmecs.2016.04.02

Reference

[1]Kandemir-Cavas, C., Cavas, L, “Application of Queuing Theory to the Relationships between Insulin Level and Number of Insulin Receptors,” Turkish Journal of Biochemistry, 32 (1): 32-38 (2007).
[2]Osorio and Bielaire, Describing Network Congestion with an Analytic Queuing to Network Model, Swiss Transport Research Conference, 2007.
[3]Costa, A. X., Riddely, S. A., Shahani, A. K., Harper, P.R., Desenna, V., and Nielsen, M,S., Mathematical Modelliing and Simulation for Planning Critical Care Capacity, Anaesthesia; 2003, 58, (1), 320-329.
[4]Bagust, A, place, M. and Posnett, J.W., Dynamics of Bed use in Accommodating Emergency Admissions; Stochastic Simulation Model. BMJ, 1999, 329: 155-163.
[5]Bitran, G., and Tirupat, D., Multi-product Queuing Networks with Deterministic Routing: Decomposition Approach and the Notion Interference, Management Science, 1988, Volume 34, PP 75-100.
[6]Koizumi, N., Kuno E and Smith, E. T., A Queuing Network Model with blocking: Analysis of Congested Patient Flow in Mental Health System, Health Care Management Science, 2002, 8(1): 49-60.
[7]Tutumi Y. and Newlands, D., Hospital Bed Capacity and Mix Problem for State Supported Public and Fee Paying Private Wards, Economic and Management, IESEG, School of Management, 2009, CNRS-LEM (UME 8129)
[8]Smith, D., and Mayhew, L., Using Queuing Theory to Analyze Governments Completion Time Target in Accident and Emergency Departments, Health Care Management Science, 2008, 11:11-21.
[9]Stakutis C., Boyle T., “Your Health, Your Way: Human enabled Health Care. CA Emerging Technologies,” 2009, pp. 1-10.
[10]Chambers, Chester, and Panagiotis Kouvelis, “Modeling and Managing the Percentage of Satisfied Customers in Hidden and Revealed Waiting Line Systems”. Production and Operations Management, 15(1), 103-116 (2006).
[11]Institute for Healthcare Improvement, Going Lean in Health Care. IHI Innovation Series.2005 Available at: www.IHI.org - See more at: http://www.centrallogic.com/resources/patient-flow-journal/scholarship-recipient-strategies-to-enhance-patient-flow#sthash.MdZVDEW7.dpuf
[12]Adeleke, A.R., Adebiyi, C.E. and Akinyemi, O., “Application of Queuing Theory to Omega Bank PLC, Ado Ekiti,” International Journal of Numerical Mathematics, I(122):129 (2005)
[13]Klassen, R. D. and L. J. Menor., “The process management triangle: An empirical investigation of process trade- offs,” Journal of Operations Management 25, 1015–1034 (2007).
[14]Foster E Michael, Hosking Michael R and Ziya Serhan , “A Spoonful of Math helps the medicine Go Down : An Illustration of How Healthcare benefit from mathematical modeling and analysis”, BMC Medical Research Methodology 2010, 10:60 http://www.biomedcentral.com/1471-2288/10/60.
[15]Singh Vikas , “Use of Queueing Models in Health Care” 2006, www.scansims.org/sims2008/02.pdf.
[16]Fomundam Samuel, Herrmann Jeffery, “A Survey of Queuing theory Applications in Healthcare” 2007, drum.lib.umd.edu/bitstream/1903/7222/1/tr_2007-24.pdf.
[17]Wilson MJ, Nguyen K., Bursting at the Seams: Improving Patient Flow to Help America’s Emergency Departments. Urgent Matters ⁄ George Washington University Medical Center, 2004. Available at http://urgentmatters.org/media/file/reports_UM_WhitePaper_ BurstingAtTheSeams.pdf. –
[18]Green L.V., “Using Operational Research to reduce Delays for Healthcare,” In tutorials in Operational Research (Z,-L. Chen and S. Raghavan eds), 2008, 1-16. INFORMS.
[19]Green L., Soares J., Giulio J., and Green R., Using Queueing Theory to Increase the Effectiveness of Physician Staffing in the Emergency Department. Academic Emergency Medicine (January), 2006, 61–68.
[20]Georgievskiy igor, Georgievskiy Zhanna, Pinney William, “Using Analysis and Computer Simulation Modeling to Reduce Wating Time in the Hospital Admitting Department”, 2002, http://www.flexsim.com/products/healthcare/docs/Reduce_Admissions_wait_times.pdf
[21]Royston Geoff , “Meeting global health challenges through operational research and management science”, Bull World Health Organ 2011;89:683–688 | doi:10.2471/BLT.11.086066, Submitted: 19 January 2011 – Revised version received: 26 April 2011 – Accepted: 23 May 2011 – Published online: 5 July 2011.
[22]Mehandiratta Reetu, “Application of Queueing theory in Health Care”, International Journal of Computing and Business Research, ISSN (online): 2229-6166, May 2011.
[23]Martha Hostetter and Sarah Klein , “In Focus: Improving Patient Flow—In and Out of Hospitals and Beyond: Commonwealth fund newsletters,” 2013 , available at http://www.commonwealthfund.org/publications/newsletters/quality-matters/2013/october-november/in-focus-improving-patient-flow
[24]Hall, R. W., ed., Patient Flow: Reducing Delay in Healthcare Delivery. Springer, 2006, 1-44.
[25]Fink Ross and Gillett John, “Queuing Theory and the Taguchi Loss Function: The Cost of Customer Dissatisfaction in Waiting Lines”, International Journal of Strategic Cost Management. Spring, 2006.
[26]Bolch, G.; Greiner, S.; de Meer, H.; Trivedi, K. S, Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications. John Wiley & Sons, 2001, pp. 209–262.
[27]Barbeau, Michel; Kranakis, Evangelos (2007, Principles of Ad-hoc Networking, John Wiley & Sons, 2007 pp. 42
[28]Kembe, M. M, Onah, E. S, Iorkegh, S. (2012). A Study of Waiting and Service Costs of a Multi-Server Queuing Model in a Specialist Hospital. Int. J. of Scientific & Tech. Research; 2012, 8:3.
[29]Naasir K., Saleh R., "Impact of Information Technology in Medicinal Research Evidence based Planning ", IJITCS, vol.15, no.1, pp.2091-1610, 2014.