Application of \(G_k/G_d/1\) Queuing Model to Patient Flow at Hospital

Authors

  • Manish Kumar Pandey Department of Applied Mathematics, Chhattisgarh Swami Vivekanand Technical University, Bhilai
  • D. K. Gangeshwer Department of Applied Mathematics, Chhattisgarh Swami Vivekanand Technical University, Bhilai
  • Thaneshwar Lal Verma Department of Applied Mathematics, Chhattisgarh Swami Vivekanand Technical University, Bhilai

DOI:

https://doi.org/10.26713/cma.v12i3.1530

Keywords:

Queuing theory, \(G_k/G_d/1\) model, Appointment probability

Abstract

The health systems should have an ability to deliver efficient and smooth and safe services to the patients. Now-a-day, in hospitals, to get timely appointments to doctors, is a very difficult task, for most of patients long wait for appointments, that means demand and supply are imbalanced in a queue. Queuing theory is the branch of operations research in applied mathematics and deals with the phenomenon of waiting lines. Therefore, the present paper deals with the application of \(G_k/G_d/1\) queuing model to patient flow at hospital namely Raipur, India. The arrival process is measured by exponential distribution and the service process is measured by Poisson distribution. Finally, appointment probabilities of waiting time of patients have been derived, and also expected queue length, waiting time for the patients in the model have been shown.\ It has also been observed that waiting time for patients can be reduced by using multiple servers instead of a single server queued model. Lastly, a numerical illustration of the model has been provided. The proposed result would be useful for academic literature, queuing scientists, and practitioners.

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References

D. Ben-Tovim, J. Filar, P. Hakendorf, S. Qin, C. Thompson and D. Ward, Hospital event simulation model: Arrivals to discharge–design, development and application, Simulation Modeling Practice and Theory 68 (2016), 80 – 94, DOI: 10.1016/j.simpat.2016.07.004.

P. Bhattacharjee and P. K. Ray, Simulation modeling and analysis of appointment system performance for multiple classes of patients in a hospital: a case study, Operations Research for Health Care 8 (2016), 71 – 84, DOI: 10.1016/j.orhc.2015.07.005.

S. C. Brailsford, P. R. Harper, B. Patel and M. Pitt, An analysis of the academic literature on simulation and modeling in health care, Journal of Simulation 3(3) (2009), 130 – 140, DOI: 10.1057/jos.2009.10.

D. Cocchi, F. Frosini, E. Ciagli, P. Tortoli, C. Carpini, D. Cirone and A. Belardinelli, Discrete event simulation model for the analysis of centralized front office service in a regional hub hospital, in World Congress on Medical Physics and Biomedical Engineering (2018), pp. 559 – 562, Springer, Singapore, DOI: 10.1007/978-981-10-9035-6_103.

M. M. Günal and M. Pidd, Discrete event simulation for performance modeling in health care: a review of the literature, Journal of Simulation 4(1) (2010), 42 – 51, DOI: 10.1057/jos.2009.25.

X. Hu, S. Barnes and B. Golden, Applying queueing theory to the study of emergency department operations: a survey and a discussion of comparable simulation studies, International Transactions in Operational Research 25(1) (2018), 7 – 49, DOI: 10.1111/itor.12400.

H. Jiang, M. Wang and Y. Mao, MRI allocation analysis of regional hospitals based on queuing simulation model, China Medical Equipment 13(6) (2016), 101 – 103.

Y. H. Kuo, O. Rado, B. Lupia, J. M. Leung and C. A. Graham, Improving the efficiency of a hospital emergency department: a simulation study with indirectly imputed service-time distributions, Flexible Services and Manufacturing Journal 28(1-2) (2016), 120 – 147, DOI: 10.1007/s10696-014-9198-7.

D. C. Lane, C. Monefeldt and E. Husemann, Client involvement in simulation model building: hints and insights from a case study in a London hospital, Health Care Management Science 6(2) (2003), 105 – 116, DOI: 10.1023/A:1023385019514.

M .K. Pandey and D. K. Gangeshwer, A queuing model with heterogeneous servers for specific service on health sector, International Journal of Applied Mathematics & Statistics 58(1) (2019), 28 – 35, URL: http://www.ceser.in/ceserp/index.php/ijamas/article/view/5991.

L. R. Pinto, P. M. S. Silva and T. P. Young, A generic method to develop simulation models for ambulance systems, Simulation Modeling Practice and Theory 51 (2015), 170 – 183, DOI: 10.1016/j.simpat.2014.12.001.

F. Rodrigues, G. S. Zaric and D. A. Stanford, Discrete event simulation model for planning Level 2 "step-down” bed needs using NEMS, Operations Research for Health Care 17 (2018), 42 – 54, DOI: 10.1016/j.orhc.2017.10.001.

M. Saima and S. Nisha, A comparison of single server and multiple server queuing models in different departments of hospitals, Punjab University Journal of Mathematics 47(1) (2015), http://journals.pu.edu.pk/journals/index.php/pujm/article/viewArticle/3598.

N. Sharma, Analysis of Simulation for Queuing Models, Ph.D Thesis, Department of Statistics, Maharshi Dayanand University Rohtak, Haryana, India (2011), URL: http://hdl.handle.net/10603/7835.

J. Shi, E. Erdem, Y. Peng, P. Woodbridge and C. Masek, Performance analysis and improvement of a typical telephone response system of VA hospitals: a discrete event simulation study, International Journal of Operations & Production Management 35(8) (2015), 1098 – 1124, DOI: 10.1108/IJOPM-01-2014-0016.

G. Vassilacopoulos, A simulation model for bed allocation to hospital inpatient departments, Simulation 45(5) (1985), 233 – 241, DOI: 10.1177%2F003754978504500502.

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Published

30-09-2021
CITATION

How to Cite

Pandey, M. K., Gangeshwer, D. K., & Verma, T. L. (2021). Application of \(G_k/G_d/1\) Queuing Model to Patient Flow at Hospital. Communications in Mathematics and Applications, 12(3), 645–653. https://doi.org/10.26713/cma.v12i3.1530

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Research Article