This thesis analyzes single server queueing models with finite capacity, specifically focusing on analyzing the stationary probabilities for M/G/1/K, G/M/1/K, and G/G/1/K queues. For M/G/1/K and G/M/1/K, stationary probabilities are computed analytically through recursive formulations to validate the simulation results. Additionally, a simulated-based sensitivity analysis is also conducted on the G/G/1/K queue to investigate how traffic intensity and buffer size affect critical performance measures, including average waiting time, queue length, and blocking probabilities. This analysis considers a wide range of interarrival and service distributions, including deterministic, exponential, gamma, geometric, hyperexponential, lognormal, truncated normal, uniform, and Weibull distributions.