This paper analyzes a queueing system consisting of a single server which dispenses service to jobs of K≥1 priority classes. Jobs are assumed to arrive to the queue according to a Poisson point process with a class dependent rate and to have class dependent service demands that are generally distributed. A linear priority function of the time spent in the system is specified for each job class and is used to schedule jobs. Specifically, the server, when available for service, nonpreemptively selects the job having the highest priority value to be the next job scheduled. Previous work in analyzing a system of this type has concentrated on providing bounds on the expected class response time. The paper extends these results by providing a closed form expression for the mean class response time and an expression for the ratio of expected response times in the limiting case of heavy traffic. It also provides a closed form expression for the mean class response time under certain light load conditions.
