A queuing analysis of a preemptive, priority-driven, time-sliced dispatcher algorithm, typical of those found in many time-sharing systems, is presented. A distinctive feature of the system being modeled is that a preempted task, when readmitted to the dispatcher, is reallocated a full time slice rather than the residual. The combination of preemption, time-slice renewal and class-dependent arrival and service rates places the analysis beyond that of the well-known FBN algorithms. The model is used to predict the behavior of the dispatcher algorithm under various workloads. The model reveals that, at high arrival rates, the time-slice renewal policy prevents processor bound tasks from being relegated to the lower priority queues, thereby severely degrading the throughput of tasks with short processor requirements.