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 FIFO scheduling and a static priority scheduling (HOL) and we investigate the influence of the different parameters of the simplified HOL-PJ scheduling discipline.

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 and cons of each jumping scheme.

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In this paper, we introduce and analyze a modified HOL (head-of-the-line) priority scheduling discipline. The modification is incorporated to cope with the so-called starvation problem of regular HOL priority queues. We consider a discrete-time single-server queueing system with two priority queues of infinite capacity and with the introduced priority scheme. We show that the use of probability generating functions is suitable for analyzing the system contents and the packet delay. Some performance measures (such as means and variances) of these stochastic quantities will be derived. Furthermore, approximate expressions of the tail probabilities are obtained from the probability generating functions, by means of the dominant-singularity method. These expressions, together with their characteristics, constitute one of the main contributions of this paper. Finally, the impact and significance of the m-HOL (modified HOL) priority scheduling on these performance measures is illustrated by some numerical examples.

Recently, numerous studies have shown that human dynamics cannot be described accurately by exponential laws. For instance, Barabási [Nature (London) 435, 207 (2005)] demonstrates that waiting times of tasks to be performed by a human are more suitably modeled by power laws. He presumes that these power laws are caused by a priority selection mechanism among the tasks. Priority models are well-developed in queueing theory (e.g., for telecommunication applications), and this paper demonstrates the (quasi-)immediate applicability of such a stochastic priority model to human dynamics. By calculating generating functions and by studying them in their dominant singularity, we prove that nonexponential tails result naturally. Contrary to popular belief, however, these are not necessarily triggered by the priority selection mechanism.