Delays and avoidable waiting in hospitals is a major concern for providers and patients. This article explains how Queueing model can be applied to reduce unwanted delays in providing quality services in an eye hospital using bottleneck analysis. A process map was developed and 1413 samples were included in this study. The entry and exit time at each process was measured and using queuing theory server utilization rates were calculated. The study revealed significant bottlenecks. Using mathematical simulations, appropriate solutions were also developed.