On priority queues with priority jumps

Maertens, Tom; Walraevens, Joris; Bruneel, Herwig

doi:10.1016/j.peva.2005.12.003

Cited by 31 publications

(44 citation statements)

References 12 publications

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“…A model where the tasks with the shortest execution times are selected first is called the shortest job first selection or the variant shortest remaining processing time (see [21]). Yet another interesting complication could be modeling the evolution of the priority level of waiting tasks: the priority level of tasks might, for instance, increase during their time in the queue (see, e.g., [22,23]). The pure priority selection mechanism can also be altered, e.g., to a hybrid priority-FCFS or priority-random selection mechanism.…”

Section: Discussionmentioning

confidence: 99%

Stochastic queueing-theory approach to human dynamics

et al. 2012

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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.

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Section: Discussionmentioning

confidence: 99%

Stochastic queueing-theory approach to human dynamics

et al. 2012

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“…In other words, only when the high-priority queue is empty, packets of the low-priority queue can be served. This priority queueing system has been analyzed in [18] and the pgf of the class-2 packet delay is found to be…”

Section: Preliminariesmentioning

confidence: 99%

Priority queueing systems: from probability generating functions to tail probabilities

2006

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Obtaining (tail) probabilities from a transform function is an important topic in queueing theory. To obtain these probabilities in discrete-time queueing systems, we have to invert probability generating functions, since most important distributions in discrete-time queueing systems can be determined in the form of probability generating functions. In this paper, we calculate the tail probabilities of two particular random variables in discrete-time priority queueing systems, by means of the dominant singularity approximation. We show that obtaining these tail probabilities can be a complex task, and that the obtained tail probabilities are not necessarily exponential (as in most 'traditional' queueing systems). Further, we show the impact and significance of the various system parameters on the type of tail behavior. Finally, we compare our approximation results with simulations.keywords priority queueing systems, tail probabilities, dominant pole, non-exponential behavior

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“…For example, in [46] a Probabilistic Priority scheme is discussed that assigns a small probability p i to each class by which the server may skip service to class i+1, even though class-i packets are available. In case of two priority classes, [35,36] analyse different ways of implementing priority jumps (PJ), as proposed in [32]. The idea is to allow class-2 packets (with lower priority) to promote to class 1 on some occasions and 'jump' to the tail of the high-priority queue.…”

Section: Class-based Scheduling Mechanismsmentioning

confidence: 99%

“…For the variants of mechanisms with priority jumps (PJ) [35,36] mentioned in the introduction however, the required state space is usually υ 1,k , υ 2,k , leading to different variants of (9). For the Multiple Reservation mechanism (MR), recall that the jth packet in an arriving batch of 1-packets seizes the jth reserved space if j N .…”

Section: Equilibrium State Of Multi-class Queuesmentioning

confidence: 99%

See 1 more Smart Citation

Transform-Domain Analysis of Packet Delay in Network Nodes with QoS-Aware Scheduling

Vuyst

Wittevrongel

Bruneel

2011

Network Performance Engineering

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Abstract. In order to differentiate the perceived QoS between traffic classes in heterogeneous packet networks, equipment discriminates incoming packets based on their class, particularly in the way queued packets are scheduled for further transmission. We review a common stochastic modelling framework in which scheduling mechanisms can be evaluated, especially with regard to the resulting per-class delay distribution. For this, a discrete-time single-server queue is considered with two classes of packet arrivals, either delay-sensitive (1) or delay-tolerant (2). The steady-state analysis relies on the use of well-chosen supplementary variables and is mainly done in the transform domain. Secondly, we propose and analyse a new type of scheduling mechanism that allows precise control over the amount of delay differentiation between the classes. The idea is to introduce N reserved places in the queue, intended for future arrivals of class 1.

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On priority queues with priority jumps

Cited by 31 publications

References 12 publications

Stochastic queueing-theory approach to human dynamics

Stochastic queueing-theory approach to human dynamics

Priority queueing systems: from probability generating functions to tail probabilities

Transform-Domain Analysis of Packet Delay in Network Nodes with QoS-Aware Scheduling

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