State Probabilities of M/M/1 Priority Queues

This paper considers a preemptive priority and a nonpreemptive priority queuing model in the steady state. Each model assumes two priority levels, a single-service channel, no queue-length limit, and negative exponential interarrival-time and service-time distributions. The paper develops a set of computationally efficient recursion formulas that allow exact calculation of the state probabilities. In the nonpreemptive-priority case, this is the first time that a complete solution for the equilibrium-state probabilities has been obtained.