Sojourn times in G/M/1 fork‐join networks

Ko, Sung-Seok; Serfozo, Richard F.

doi:10.1002/nav.20294

Cited by 29 publications

(19 citation statements)

References 9 publications

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“…The performance of FJ queueing systems has been subject of multiple studies such as [5, 31,40,25,28,6,8]. In particular, [5] notes that an exact performance evaluation of general FJ systems is remarkably hard due to the synchronization constraints on the input and output streams.…”

Section: Related Workmentioning

confidence: 99%

“…The authors of [15] provide the stationary joint workload distribution for a two-server FJ system under Poisson arrivals and independent exponential service times. For the general case of more than two parallel servers there exists a number of works that provide approximations [31,40,28,29] and bounds [5,6] for certain performance metrics of the FJ system. Given renewal arrivals, [6] significantly improves the lower bounds from [5] in the case of heterogeneous phase-type servers using a matrix-geometric algorithmic method.…”

Section: Related Workmentioning

confidence: 99%

“…Given renewal arrivals, [6] significantly improves the lower bounds from [5] in the case of heterogeneous phase-type servers using a matrix-geometric algorithmic method. The authors of [28] provide an approximation of the sojourn time distribution in a renewal driven FJ system consisting of multiple G/M/1 nodes. They show that the approximation error diminishes at extremal utilizations.…”

Section: Related Workmentioning

confidence: 99%

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

2016

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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 under full (bijective) and partial (injective) mapping of tasks to servers. 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(log N ), 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.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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

2016

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“…The performance of FJ queueing systems has been subject of multiple studies such as [4,26,35,21,24,5,7]. In particular, [4] notes that an exact performance evaluation of general FJ systems is remarkably hard due to the synchronization constraints on the input and output streams.…”

Section: Related Workmentioning

confidence: 99%

Computable Bounds in Fork-Join Queueing Systems

Rizk

Poloczek

Ciucu

2015

Proceedings of the 2015 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems

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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 multiservice 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(log N ), 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.

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“…In their work, special attention is paid to the impact of the number of servers operating in parallel (which we assume to be 2 throughout this paper). We finally note that results on the corresponding G/M/1 queue are given in Ko and Serfozo (2008).…”

Section: Introductionmentioning

confidence: 96%

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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Sojourn times in G/M/1 fork‐join networks

Cited by 29 publications

References 9 publications

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

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

Computable Bounds in Fork-Join Queueing Systems

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

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