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Computable Bounds in Fork-Join Queueing Systems

Content Provider	ACM Digital Library
Author	Ciucu, Florin Rizk, Amr Poloczek, Felix
Abstract	In a Fork-Join (FJ) queueing system an upstream fork station splits incoming jobs into N tasks to be further processed by N parallel servers, each with its own queue; the response time of one job is determined, at a downstream join station, by the maximum of the corresponding tasks' response times. This queueing system is useful to the modelling of multi-service systems subject to synchronization constraints, such as MapReduce clusters or multipath routing. Despite their apparent simplicity, FJ systems are hard to analyze. This paper provides the first computable stochastic bounds on the waiting and response time distributions in FJ systems. We consider four practical scenarios by combining 1a) renewal and 1b) non-renewal arrivals, and 2a) non-blocking and 2b) blocking servers. In the case of non blocking servers we prove that delays scale as O(logN), a law which is known for first moments under renewal input only. In the case of blocking servers, we prove that the same factor of log N dictates the stability region of the system. Simulation results indicate that our bounds are tight, especially at high utilizations, in all four scenarios. A remarkable insight gained from our results is that, at moderate to high utilizations, multipath routing 'makes sense' from a queueing perspective for two paths only, i.e., response times drop the most when N = 2; the technical explanation is that the resequencing (delay) price starts to quickly dominate the tempting gain due to multipath transmissions.
Starting Page	335
Ending Page	346
Page Count	12
File Format	PDF
ISBN	9781450334860
DOI	10.1145/2745844.2745859
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2015-06-15
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Multipath Performance evaluation Parallel systems Mapreduce Fork-join queue
Content Type	Text
Resource Type	Article

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Computable Bounds in Fork-Join Queueing Systems

Computable Bounds in Fork-Join Queueing Systems

Stochastic bounds in Fork–Join queueing systems under full and partial mapping

The fork-join queue and related systems with synchronization constraints: stochastic ordering, approximations and computable bounds (1987)

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

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Analysis of balanced fork-join queueing networks (1996).

Computing performance bounds for fork-join queueing models (1994).

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Computable Bounds in Fork-Join Queueing Systems

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