Waiting-time approximations in multi-queue systems with cyclic service

Boxma, Onno; Meister, Bernd

doi:10.1016/0166-5316(87)90057-5

Cited by 25 publications

(12 citation statements)

References 7 publications

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“…We applied the approximation for the mean end-to-end delay per type to a model based on a Network on Chip using the Boxma-Meister approximation [6] to obtain the necessary single-station results. Although the Boxma-Meister approximation is less accurate for asymmetric systems, we could still accurately approximate the mean type i j end-to-end delay up to moderately high loads (around 0.7) in an asymmetric case study.…”

Section: Resultsmentioning

confidence: 99%

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End-to-end delays in polling tree networks

Beekhuizen

Denteneer

Resing

2008

Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools

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We consider a tree network of polling stations operating in discrete-time. Packets arrive from external sources to the network according to batch Bernoulli arrival processes. We assume that all nodes have a service discipline that is HoL-based. The class of HoL-based service disciplines contains for instance the Bernoulli and limited service disciplines, and hence also the classical exhaustive and 1-limited. We obtain an exact expression for the overall mean end-to-end delay, and an approximation for the mean end-to-end delay of packets per source. The study is motivated by Networks on Chips where multiple processors share a single memory.

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Section: Resultsmentioning

confidence: 99%

“…We give the approximation proposed by Boxma and Meister [6] for 1-limited polling systems. Although their analysis is aimed at continuous-time systems, it can easily be established that the key steps in their derivation are valid for discrete-time systems as well.…”

Section: -Limitedmentioning

confidence: 99%

End-to-end delays in polling tree networks

Beekhuizen

Denteneer

Resing

2008

Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools

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“…Of those, we found that the Boxma-Meister [9] and Levy-Groenendijk [16] approximations could be extended to the discrete-time domain without much additional effort. We will compare our approximation with these two approximations in Section 5.…”

Section: Relevant Literaturementioning

confidence: 99%

“…Other authors, such as Boxma and Meister [9], Fuhrmann and Wang [15], Levy and Groenendijk [16], and Srinivasan [26], only approximated mean waiting times in cyclic 1-limited polling systems (and by Little's law, mean queue lengths). Of those, we found that the Boxma-Meister [9] and Levy-Groenendijk [16] approximations could be extended to the discrete-time domain without much additional effort.…”

Section: Relevant Literaturementioning

confidence: 99%

Approximation of discrete-time polling systems via structured Markov chains

Beekhuizen

Resing

2009

Proceedings of the 4th International ICST Conference on Performance Evaluation Methodologies and Tools

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We devise an approximation of the marginal queue length distribution in discrete-time polling systems with batch arrivals and fixed packet sizes. The polling server uses the Bernoulli service discipline and Markovian routing. The 1-limited and exhaustive service disciplines are special cases of the Bernoulli service discipline, and traditional cyclic routing is a special case of Markovian routing. The key step of our approximation is the translation of the polling system to a structured Markov chain, while truncating all but one queue. Numerical experiments show that the approximation is very accurate in general. Our study is motivated by networks on chips with multiple masters (e.g., processors) sharing a single slave (e.g., memory).

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“…In deriving this approximation, we aim to fulfill the following criteria, which was proposed by Boxma and Meister in [35]: (i) It is exact in the completely symmetric case, by which we mean the arrival distributions for all classes are identical; the service distributions for all classes are also identical; all queues are served with the same probability when they are nonempty and polled by the server, i.e. ½ ¾ for the two-class case.…”

Section: Approachmentioning

confidence: 99%

Delay analysis of a probabilistic priority discipline

Jiang

Tham

2002

Trans Emerging Tel Tech

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Abstract. In computer networks, the Strict Priority (SP) discipline is perhaps the most common and simplest method to schedule packets from different classes of applications, each with diverse performance requirements. With this discipline, however, packets at higher priority levels can starve packets at lower priority levels. To resolve this starvation problem, we propose to assign a parameter to each priority queue in the SP discipline. The assigned parameter determines the probability or extent by which its corresponding queue is served when the queue is polled by the server. We thus form a new packet service discipline, referred to as the Probabilistic Priority (PP) discipline. By properly adjusting the assigned parameters, not only is the performance of higher priority classes satisfied, but also the performance of lower priority classes can be improved. This paper analyzes the delay performance of the PP discipline. A decomposition approach is proposed for calculating the average waiting times and their bounds are studied. Two approximation approaches are proposed to estimate the waiting times. Simulation results that validate the numerical analysis are presented and examined. A numerical example which demonstrates the use of the PP discipline to achieve service differentiation is presented. This example also shows how the assigned parameters can be determined from the results of analysis mentioned above.

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Waiting-time approximations in multi-queue systems with cyclic service

Cited by 25 publications

References 7 publications

End-to-end delays in polling tree networks

End-to-end delays in polling tree networks

Approximation of discrete-time polling systems via structured Markov chains

Delay analysis of a probabilistic priority discipline

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