Analysis of nonpreemptive priority queues with service disciplines depending on the number of waiting messages

This paper presents analyses of nonpreemptive priority queues with single server and walking process. The queues are priority queue with probabilitisc discipline for low priority, threshold for the number of waiting messages, persistent wait for high priority and persistent wait. For the queues, probabilities for the number of messages at the beginning of the service and mean waiting times of message are derived. For low priority level, it is shown that the mean waiting time can be obtained by using a root of the denominator of generating function. In some of the numerical examples given, the mean waiting times are compared with that of a nonpreemptive priority queue with one-limited discipline and then characteristics of the mean waiting time are considered.