On priority queues with priority jumps

In this paper, we investigate a simplified head-of-the-line with priority jumps (HOL-PJ) scheduling discipline. Therefore, we consider a discrete-time single-server queueing system with two priority queues of infinite capacity and with a newly introduced HOL-PJ priority scheme. We derive expressions for the probability generating function of the system contents and the packet delay. Some performance measures (such as mean and variance) of these quantities are derived and are used to illustrate the impact and significance of the HOL-PJ priority scheduling discipline in an output queueing switch. We compare this dynamic priority scheduling discipline with a first-in, first-out (FIFO) scheduling and a static priority scheduling (HOL) and we investigate the influence of the different parameters of the simplified HOL-PJ scheduling discipline.