Queuing with Nonpreemptive and Preemptive-Resume Priorities

This paper considers a special queue situation, one in which a single facility serves two major priority classes of customers. Within each class, there are several levels of priorities. The first class has the higher priority. On arrival, a customer of the first class immediately replaces any customer of lower priority being served. The second class has the lower priority, as compared to the first class. On its arrival, a customer of the second class cannot interrupt the current service of a lower priority customer in the system; it must wait until the service is completed. The first class is the preemptive priority, and the second class is the nonpreemptive priority. This paper formulates a theoretical solution for this queuing system, which has a wide range of application in the computer industry. The real-time control program under the multiprogramming environment is an analog of this priority queuing model.