We experience service or provide service in various forms in our daily life. Usually the service follows the first-come, first-served discipline. However, situations commonly occur that a service facility provides service for multi-class of units. These units may be distinguished according to some measures such as patience, time sensitivity, importance etc. In this case, the priority service system allows customers of varied classes to receive different quality of service from a single server. This dissertation is devoted to study three priority service systems: MAP/PH/1 queue with discretionary priority, M/G/1 queue with discretionary priority and a priority queueing system with inventory management. In the MAP/PH/1 queue with discretionary priority, by treating the highpriority queue as bounded, the steady-state probability vector for the system can be expressed in a matrix-geometric form. We obtain the sojourn time distribution of the high and low priority customers. By comparing the discretionary priority rule with the preemptive and nonpreemptive disciplines numerically, the effect of the discretionary priority rule is demonstrated. In the M/G/1 queue with discretionary priority, the service time distributions are non-exponential, and the Markov model does not work directly. We construct an imbedded Markov model for specific time points on the time axis. By investigating the embedded Markov chain, we figure out the stationary distribution and other performance measures of the original system. Lastly, for the priority queueing system with inventory management, we find a priority service rule to minimize the long-run expected waiting cost by dynamic programming method and obtain the necessary and sufficient condition for the system being stable. Formulating the model as a level-dependent quasi-birthand-death (LDQBD) process, we get the steady state probability distribution. Useful analytical properties for the cost function are identified and extensive computations are conducted to examine the impact of parameters to the system performance measures. Keywords priority queue, discretionary discipline, inventory management, matrix analytic method