A preemptive priority queue with impatient customers and multiple vacations

The article established a queue model of a preemptive priority queue with impatient customers and multiple vacations. The first class customers have preemptive priority. Both two-class customers can renege because of impatience. First, we obtain State transition equations. Then we derive the probability distribution of the two-class customers, and respectively calculated the expected number of the two-class customers, the average reneging rate and other queue indices. Finally, we perform analysis by numerical examples.