Healthcare facilities in most part of the world experience high influx of patients needing clinical service; this creates the issue of long waiting queue, long waiting time of patients and overutilization of medical personnel. The study examined the service quality in consonance with the patience waiting time in order to strike an economic balance between the cost of service and the cost associated with the waiting for the services. The study applies the queuing models waiting time to compare the performance of multi-servers to determine the optimal balance between the cost of patients waiting for clinical services and the cost of providing the services in a specialized clinic. On sorting to access the perception of patients on six (6) dimensions of service, the result shows the optimum balance was achieved between the cost of patients waiting for services and the cost of providing the service.The healthcare managers should assess the impact of not serving potential patients appropriately against the capacity cost of the servers so as to balance the cost of keeping patients waiting with the cost of adding more servers.