Analysis of Fork/Join and Related Queueing Systems

Thomasian, Alexander

doi:10.1145/2628913

Cited by 64 publications

(26 citation statements)

References 138 publications

(285 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, we are not only interested into mean performance estimates but also want to consider the more expressive probabilistic measures. The difficulty of using analytical methods to obtain mean estimates from fork-join models that consider variable threading levels is discussed in [14], [16], [17]. However, obtaining probabilistic estimates for such models adds additional layers of complexity.…”

Section: B Predictive Functionalitymentioning

confidence: 99%

Experiments or simulation? A characterization of evaluation methods for in-memory databases

Molka

Casale

2015

2015 11th International Conference on Network and Service Management (CNSM)

View full text Add to dashboard Cite

Abstract-The recent growth of interest for in-memory databases poses the question on whether established prediction methods such as response surfaces and simulation are effective to describe the performance of these systems. In particular, the limited dependence of in-memory technologies on the disk makes methods such as simulation more appealing than in the past, since disks are difficult to simulate. To answer this question, we study an in-memory commercial solution, SAP HANA, deployed on a high-end server with 120 physical cores. First, we apply experimental design methods to generate response surfaces that describe database performance as a function of workload and hardware parameters. Next, we develop a class-switching queueing network model to predict in-memory database performance under similar scenarios. By comparing the applicability of the two approaches to modeling multi-tenancy, we find that both queueing and response surface models yield mean prediction errors in the range 5%-22% with respect to mean memory occupancy and response times, but the accuracy for the latter deteriorates in response surfaces as the number of experiments are reduced, whereas simulation is effective in all cases. This suggests that simulation can be very effective in performance prediction for in-memory database management.

show abstract

Section: B Predictive Functionalitymentioning

confidence: 99%

Experiments or simulation? A characterization of evaluation methods for in-memory databases

Molka

Casale

2015

2015 11th International Conference on Network and Service Management (CNSM)

View full text Add to dashboard Cite

show abstract

“…By the choice of ϵ, |a 1 + a 2 | ≤ (11Λ + 8µ)ϵ = 1 2 pλ(1 − ρ) 2 . Therefore, R(π (n,2) ) < 0 by (34), which contradicts with the balance equation (33). This completes the proof of Theorem A.1.…”

mentioning

confidence: 65%

“…Classic fork-join model. The classic fork-join model, where the number of tasks in a job is equal to the number of servers, n, has n number of servers superscript (n) quantities in the n-server system k (n) number of tasks in a job Λ (n) job arrival rate [34] for a detailed survey. Here we just sample several most relevant papers.…”

Section: Related Workmentioning

confidence: 99%

Delay Asymptotics and Bounds for Multi-Task Parallel Jobs

Wang

Jiang

Scheller‐Wolf

et al. 2019

SIGMETRICS Perform. Eval. Rev.

View full text Add to dashboard Cite

We study delay of jobs that consist of multiple parallel tasks, which is a critical performance metric in a wide range of applications such as data file retrieval in coded storage systems and parallel computing. In this problem, each job is completed only when all of its tasks are completed, so the delay of a job is the maximum of the delays of its tasks. Despite the wide attention this problem has received, tight analysis is still largely unknown since analyzing job delay requires characterizing the complicated correlation among task delays, which is hard to do.We first consider an asymptotic regime where the number of servers, n, goes to infinity, and the number of tasks in a job, k (n) , is allowed to increase with n. We establish the asymptotic independence of any k (n) queues under the condition k (n) = o(n 1/4 ). This greatly generalizes the asymptotic-independence type of results in the literature where asymptotic independence is shown only for a fixed constant number of queues. As a consequence of our independence result, the job delay converges to the maximum of independent task delays.We next consider the non-asymptotic regime. Here we prove that independence yields a stochastic upper bound on job delay for any n and any k (n) with k (n) ≤ n. The key component of our proof is a new technique we develop, called "Poisson oversampling". Our approach converts the job delay problem into a corresponding balls-and-bins problem. However, in contrast with typical balls-andbins problems where there is a negative correlation among bins, we prove that our variant exhibits positive correlation.

show abstract

“…Anyway, this linear transformation technique is capable of estimating/bounding the performance of most of practical non-purging/purging (n, k) fork-join queueing systems, where (1, 1), (2, 2), ..., (20,20) Fork-Join Queues (µ=1) TABLE I APPROXIMATED NT n,k BASED ON SIMULATED T i (µ = 1) (n, k) ρ: 0.05 ρ :0.4 ρ: 0.8 (20,17) 25.17029838 -37.93974618 70.76161205 (20,18) 0.412468275 6.238904164 3.024177347 (20,19) 2.772567927 3.796009747 11.47066833 the replication factor (n) rarely exceeds 10, a result of costeffective tradeoff. For example, the replication factor of either Dynamo or Cassandra is commonly 3.…”

Section: Discussionmentioning

confidence: 99%

“…We refer readers to [20] for a more comprehensive survey on fork-join queuing systems. To conclude, our work is orthogonal to existing approximation methods for basic forkjoin queues.…”

Section: Discussionmentioning

confidence: 99%

Approximations and Bounds for (n, k) Fork-Join Queues: A Linear Transformation Approach

Wang

Shen

et al. 2018

2018 18th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGRID)

View full text Add to dashboard Cite

Compared to basic fork-join queues, a job in (n, k) fork-join queues only needs its k out of all n sub-tasks to be finished. Since (n, k) fork-join queues are prevalent in popular distributed systems, erasure coding based cloud storages, and modern network protocols like multipath routing, estimating the sojourn time of such queues is thus critical for the performance measurement and resource plan of computer clusters. However, the estimating keeps to be a well-known open challenge for years, and only rough bounds for a limited range of load factors have been given. In this paper, we developed a closed-form linear transformation technique for jointly-identical random variables: An order statistic can be represented by a linear combination of maxima. This brand-new technique is then used to transform the sojourn time of non-purging (n, k) forkjoin queues into a linear combination of the sojourn times of basic (k, k), (k + 1, k + 1), ..., (n, n) fork-join queues. Consequently, existing approximations for basic fork-join queues can be bridged to the approximations for non-purging (n, k) fork-join queues. The uncovered approximations are then used to improve the upper bounds for purging (n, k) fork-join queues. Simulation experiments show that this linear transformation approach is practiced well for moderate n and relatively large k.

show abstract

Analysis of Fork/Join and Related Queueing Systems

Cited by 64 publications

References 138 publications

Experiments or simulation? A characterization of evaluation methods for in-memory databases

Experiments or simulation? A characterization of evaluation methods for in-memory databases

Delay Asymptotics and Bounds for Multi-Task Parallel Jobs

Approximations and Bounds for (n, k) Fork-Join Queues: A Linear Transformation Approach

Contact Info

Product

Resources

About