Applications of Queue Models to Enhance Effective Healthcare Delivery in Government Hospitals in Nigeria

Abstract

The need to develop queue models which could guide hospital management personnel in making policies which enhance prompt healthcare delivery in order to sustain patients’ interest and patronage cannot be over-emphasized. Problem of stampede leading to loss of lives in palliative distribution centers has been very frequent in recent times. Traffic congestion is a common phenomenon that occurs when patients’ arrival rate surpasses the rate of service in any service providing facilities such as hospitals and clinics. In this research, we present two queuing models with the aim of applying them to solve the problem of long queues in hospitals. In model 1, we apply the queue discipline approach of first-come first-served to derive the distribution probability that governs the numbers of patients’ arrival and departure in any given time interval of a single-server queuing system. We observe that the expected inter-arrival and expected treatment times of a patient is a continuous density function similar to that of a renewal process. In model 2, we used the method of Kolmogorov linear differential equations for each value of $P_n(T)$ to derive the transient solution. The values of $P_n(T)$ is also examined as time $T$ tends to infinity ($\infty$) and we observed that the queue system can reach its statistical equilibrium state, if $P_n(T)$ tends to a limit $P_n$, and $E[n]$ is a finite value for the distribution limit. The results from the numerical illustration show that the time spent in the queue, the number of patients, and the line length all increase rapidly as the traffic intensity $\rho$ increases. It is also observed that for the queue system to attain a steady-state equilibrium for sufficiently large $\rho < 1$, it will take a long time. Our proposed models have an advantage over the existing ones in that they contain mathematical formulas which could guide hospital management personnel to make policies which enhance prompt services, sustainability of patients’ interest and patronage.