In this paper, we consider several discrete-time priority queues with priority jumps. In a priority scheduling scheme with priority jumps, real-time and non-real-time packets arrive in separate queues, i.e., the high- and low-priority queue respectively. In order to deal with possibly excessive delays however, non-real-time packets in the low-priority queue can in the course of time jump to the high-priority queue. These packets are then treated in the high-priority queue as if they were real-time packets. Many criteria can be used to decide when packets of the low-priority queue jump to the high-priority queue. Some criteria have already been introduced in the literature, and we first overview this literature. Secondly, we propose and analyse a new priority scheme with priority jumps. Finally, we extensively compare all cited schemes. The schemes all differ in their jumping mechanism, based on a certain jumping criterion, and thus all have a different performance. We show the pros an...