Global Attraction of ODE-based Mean Field Models with Hyperexponential Job Sizes

Houdt, Benny Van

doi:10.1145/3341617.3326137

Cited by 8 publications

(2 citation statements)

References 43 publications

(65 reference statements)

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“…The key challenge is to prove the uniqueness and existence of the stationary point and the fact that all possible trajectories of the mean-field limit converges to this unique stationary point (global attraction) [6,33].…”

Section: Clientsmentioning

confidence: 99%

On the Throughput Optimization in Large-Scale Batch-Processing Systems

Kar

Rehrmann

Mukhopadhyay

et al. 2021

SIGMETRICS Perform. Eval. Rev.

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We analyze a data-processing system with n clients producing jobs which are processed in batches by m parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup function that arises due to overhead amortization. In practice, throughput optimization relies on numerical searches for the optimal batch size which is computationally cumbersome. In this paper, we model this system in terms of a closed queueing network assuming certain forms of service speedup; a standard Markovian analysis yields the optimal throughput in w n4 time. Our main contribution is a mean-field model that has a unique, globally attractive stationary point, derivable in closed form. This point characterizes the asymptotic throughput as a function of the batch size that can be calculated in O(1) time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes.

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Section: Clientsmentioning

confidence: 99%

On the Throughput Optimization in Large-Scale Batch-Processing Systems

Kar

Rehrmann

Mukhopadhyay

et al. 2021

SIGMETRICS Perform. Eval. Rev.

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“…To show that the convergence can be extended to the stationary regime one also needs to establish global attraction of the fixed point. Global attraction is often proven using monotonicity arguments [5,21,24], but our multithreading models are not monotone (as the service time of a complete job does not necessarily have a decreasing hazard rate). We consider different scenarios for varying probe rates and the two stealing strategies, for N = 500 with µ 1 = 1, µ 2 = 2 and child job distribution p = [5, 4, 3, 2, 1]/15 ≈ [0.33, 0.27, 0.20, 0.13, 0.07].…”

Section: Model Validationmentioning

confidence: 99%

Performance Analysis of Work Stealing in Large-scale Multithreaded Computing

Sonenberg

Kielanski

Houdt

2021

ACM Trans. Model. Perform. Eval. Comput. Syst.

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Randomized work stealing is used in distributed systems to increase performance and improve resource utilization. In this article, we consider randomized work stealing in a large system of homogeneous processors where parent jobs spawn child jobs that can feasibly be executed in parallel with the parent job. We analyse the performance of two work stealing strategies: one where only child jobs can be transferred across servers and the other where parent jobs are transferred. We define a mean-field model to derive the response time distribution in a large-scale system with Poisson arrivals and exponential parent and child job durations. We prove that the model has a unique fixed point that corresponds to the steady state of a structured Markov chain, allowing us to use matrix analytic methods to compute the unique fixed point. The accuracy of the mean-field model is validated using simulation. Using numerical examples, we illustrate the effect of different probe rates, load, and different child job size distributions on performance with respect to the two stealing strategies, individually, and compared to each other.

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