Application of Queuing Theory Models in Managing Patient Waiting Time: A Case Study of General Hospital Wudil, Kano State, Nigeria

Abstract

This study examined the application of queuing theory to manage patient waiting times at General Hospital Wudil, Kano State, Nigeria. The goal was to identify service inefficiencies and propose strategies for improving healthcare delivery. Primary data on patient arrivals, waiting times, and service durations were collected and analyzed using both  (single-server) and  (multi-server) queuing models. Preliminary model assumption checks, conducted through graphical plots, confirmed that both patient inter-arrival and service times follow exponential distributions. This supports the use of Poisson arrivals and exponential service times in the models. Furthermore, a Kolmogorov-Smirnov test indicates that both arrival and service times are indeed exponentially distributed, as the p-value is below the 5% significance level. The findings from the operating characteristics measures indicated that the single-server model resulted in high congestion, with a utilization rate of approximately 86%, an average queue length of about 5 patients, and a mean waiting time of nearly 14 minutes. This situation led to significant patient dissatisfaction and delays. In contrast, the multiple-server model exhibited improved performance, with utilization reduced to 77%, the average queue length decreasing to just 2 patients, and the average waiting time dropping to about 6 minutes. The study concludes that patient waiting time is strongly influenced by server capacity. Increasing the number of service points substantially reduces congestion and enhances efficiency. It recommends that hospital management adopt flexible staffing, expand service points, and implement queue management systems to optimize resource use and improve patient satisfaction.