Application of \(G_k/G_d/1\) Queuing Model to Patient Flow at Hospital - Pandey, Manish Kumar; Gangeshwer, D. K.; Verma, Thaneshwar Lal (Communications in Mathematics and Applications, 2021)
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.