Approximate analysis of fork/join synchronization in parallel queues

Nelson, Randolph; Tantawi, Asser N.

doi:10.1109/12.2213

Cited by 304 publications

(210 citation statements)

References 5 publications

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“…As proven by Nelson and Tantawi (1988), in case of two homogeneous servers with exponentially distributed service times, the mean sojourn time obeys the strikingly simple formula…”

Section: The Homogeneous M/m/1 Fork-join Systemmentioning

confidence: 99%

“…The asymptotics of this distribution are analyzed in Flatto (1985); these provide insight into the dependence between the two queues. For this M/M/1 fork-join system, under the additional assumption that the service times at both queues stem from the same exponential distribution, the mean sojourn time can be derived explicitly from the system's balance equations, see Nelson and Tantawi (1988), and obeys a simple closed-form expression. It is noted, however, that the underlying argument breaks down as soon as we depart from the exponentiality and homogeneity assumptions.…”

Section: Introductionmentioning

confidence: 99%

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Mean sojourn times in two-queue fork-join systems: bounds and approximations

Kemper

Mandjes

2011

OR Spectrum

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This paper considers a fork-join system (or: parallel queue), which is a two-queue network in which any arrival generates jobs at both queues and the jobs synchronize before they leave the system. The focus is on methods to quantify the mean value of the 'system's sojourn time' S: with S i denoting a job's sojourn time in queue i, S is defined as max{S 1 , S 2 }. Earlier work has revealed that this class of models is notoriously hard to analyze. In this paper, we focus on the homogeneous case, in which the jobs generated at both queues stem from the same distribution. We first evaluate various bounds developed in the literature, and observe that under fairly broad circumstances these can be rather inaccurate. We then present a number

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“…As proven by Nelson and Tantawi (1988), in case of two homogeneous servers with exponentially distributed service times, the mean sojourn time obeys the strikingly simple formula…”

Section: The Homogeneous M/m/1 Fork-join Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mean sojourn times in two-queue fork-join systems: bounds and approximations

Kemper

Mandjes

2011

OR Spectrum

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“…For this reason, a number of approximation methods have been proposed. In particular, [29] proposed a good approximation technique that, however, is based on service time exponential distribution, which is not the case for Hadoop deployments. Our initial experiments showed that mapper and reducer times follow general distributions, which can be approximated by phase type or in some cases Erlang.…”

Section: Modeling Hadoop 2x Applications Performancementioning

confidence: 99%

Modeling Performance of Hadoop Applications: A Journey from Queueing Networks to Stochastic Well Formed Nets

Ardagna

Bernardi

Gianniti

et al. 2016

Algorithms and Architectures for Parallel Processing

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Nowadays, many enterprises commit to the extraction of actionable knowledge from huge datasets as part of their core business activities. Applications belong to very different domains such as fraud detection or one-to-one marketing, and encompass business analytics and support to decision making in both private and public sectors. In these scenarios, a central place is held by the MapReduce framework and in particular its open source implementation, Apache Hadoop. In such environments, new challenges arise in the area of jobs performance prediction, with the needs to provide Service Level Agreement guarantees to the end-user and to avoid waste of computational resources. In this paper we provide performance analysis models to estimate MapReduce job execution times in * Acknowledgments: This work has received funding from the European Union Horizon 2020 research and innovation program under grant agreement No. 644869 (DICE). Experimental data are available as open data at https://zenodo.org/record/58847#.V5i0wmXA45Q. 1Hadoop clusters governed by the YARN Capacity Scheduler. We propose models of increasing complexity and accuracy, ranging from queueing networks to stochastic well formed nets, able to estimate job performance under a number of scenarios of interest, including also unreliable resources. The accuracy of our models is evaluated by considering the TPC-DS industry benchmark running experiments on Amazon EC2 and the CINECA Italian supercomputing center. The results have shown that the average accuracy we can achieve is in the range 9-14%.

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“…For example, Harrison and Zertal present an approximation for moments of the maximum of service times in a split-merge queueing system with general heterogeneous service times [8]; this gives an exact result in the case of exponential queues. For fork-join systems with homogeneous Markovian service time distributions, Nelson and Tantawi describe a technique which yields approximate upper and lower bounds on the mean response time as a function of the number of servers [13]. For the same system, Varki et al [17] present approximate bounds on mean response time.…”

Section: Introductionmentioning

confidence: 99%

Controlling Variability in Split-Merge Systems

Tsimashenka

Knottenbelt

Harrison

2012

Analytical and Stochastic Modeling Techniques and Applications

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Abstract. We consider split-merge systems with heterogeneous subtask service times and limited output buffer space in which to hold completed but as yet unmerged subtasks. An important practical problem in such systems is to limit utilisation of the output buffer. This can be achieved by judiciously delaying the processing of subtasks in order to cluster subtask completion times. In this paper we present a methodology to find those deterministic subtask processing delays which minimise any given percentile of the difference in times of appearance of the first and the last subtasks in the output buffer. Technically this is achieved in three main steps: firstly, we define an expression for the distribution of the range of samples drawn from n independent heterogeneous service time distributions. This is a generalisation of the well-known order statistic result for the distribution of the range of n samples taken from the same distribution. Secondly, we extend our model to incorporate deterministic delays applied to the processing of subtasks. Finally, we present an optimisation scheme to find that vector of delays which minimises a given percentile of the range of arrival times of subtasks in the output buffer. A case study illustrates the applicability of our proposed approach.

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Approximate analysis of fork/join synchronization in parallel queues

Cited by 304 publications

References 5 publications

Mean sojourn times in two-queue fork-join systems: bounds and approximations

Mean sojourn times in two-queue fork-join systems: bounds and approximations

Modeling Performance of Hadoop Applications: A Journey from Queueing Networks to Stochastic Well Formed Nets

Controlling Variability in Split-Merge Systems

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