Analysis of a nonpreemptive priority queue with SPP arrivals of high class

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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“…[1,8,11,22], or via numerical methods in e.g. [23]. We finally note that the papers mentioned in this paragraph all assume infinite queue sizes.…”

Section: Introductionmentioning

confidence: 99%

Priority queueing systems: from probability generating functions to tail probabilities

2006

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“…Walraevens et al (2003) study the system content and packet delay, in the special case of an output queueing switch with Bernoulli arrivals. Furthermore, non-preemptive HOL priority queues have been considered by Rubin andTsai (1989), Stanford (1991), Takahashi and Hashida (1991), Takine et al (1994a), Sugahara et al (1995), Takine (1996, Walraevens et al (2000) and Walraevens et al (2002). Rubin and Tsai (1989) study the mean waiting time, for a discrete-time queue fed by an i.i.d.…”

Section: Introductionmentioning

confidence: 99%

“…Takahashi and Hashida (1991) study the packet delay of a priority queue with a general number of priority classes, using an analysis based on the calculation of the unfinished work and delay-cycles. Sugahara et al (1995) present a non-preemptive queue in continuous time, with a Switched Poisson arrival process for the high-priority packets. Takine et al (1994a) and Takine (1996) study discrete-time MAP/G/1 queues, using matrix-analytic techniques.…”

Section: Introductionmentioning

confidence: 99%

Delay Analysis of a HOL Priority Queue

et al. 2005

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Priority scheduling for packets is a hot topic, as interactive (voice,video) services are being integrated in existing data networks. In this paper, we consider a discrete-time queueing system with a non-preemptive (or Head-Of-the-Line) priority scheduling discipline and a general number of priority classes. Packets of variable length arrive in the queueing system. We derive expressions for the probability generating functions of the packet delays. From these functions, some performance measures (such as moments and approximate probabilities) are calculated. We illustrate the performance measures by means of some numerical examples and show how to apply the theoretical results to a queue that handles arriving multimedia traffic.

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“…In the related literature, there have been a number of contributions with respect to HOL priority scheduling (see e.g. [1][2][3][4][5][6][7]). …”

Section: Introductionmentioning

confidence: 99%

A Discrete-Time HOL Priority Queue with Multiple Traffic Classes

Walraevens

Steyaert

Moeneclaey

et al. 2005

Networking - ICN 2005

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Abstract. Priority scheduling for packets is a hot topic, as interactive (voice,video) services are being integrated in existing data networks. In this paper, we consider a discrete-time queueing system with nonpreemptive (or Head-Of-the-Line) priority scheduling and a general number of priority classes. Packets of variable length arrive in the queueing system. We derive expressions for the probability generating functions of the packet delays. From these functions, some performance measures (such as moments and approximate tail probabilities) are calculated. We apply the theoretical results to a queue that handles arriving multimedia traffic.

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Analysis of a nonpreemptive priority queue with SPP arrivals of high class

Cited by 25 publications

References 10 publications

Priority queueing systems: from probability generating functions to tail probabilities

Priority queueing systems: from probability generating functions to tail probabilities

Delay Analysis of a HOL Priority Queue

A Discrete-Time HOL Priority Queue with Multiple Traffic Classes

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