Performance and Stability Analysis of the Task Assignment Based on Guessing Size Routing Policy

Bachmat, Eitan; Doncel, Josu; Sarfati, Hagit

doi:10.1109/mascots.2019.00012

Cited by 7 publications

(14 citation statements)

References 25 publications

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“…The analysis of this ratio can be seen as the penalty for not knowing the size of incoming tasks. The authors of [2] showed that, when r is large, this ratio is upper-bounded by 2. Therefore, they conclude that the penalty for not knowing the size of incoming jobs is, at most, 2 in the regime they consider.…”

Section: Application Of This Theory To the Resultsmentioning

confidence: 99%

“…The TAGS policy was introduced in [20] as a size-based routing policy in the setting where the sizes of incoming jobs does not need to be known. The authors of [2,21] prove that for Bounded Pareto distributions, when the ratio between the largest job size and the shortest job size tends to infinity and the system load is fixed and less than one, the ratio between the average waiting times of TAGS and SITA systems with optimal intervals is at most two. This result means that, in that regime, the penalty for not knowing the job size of incoming tasks is, at most, 2.…”

Section: Related Workmentioning

confidence: 99%

“…As SITA assumes that the size of tasks is known and routes directly to the end server, while TAGS incurs overheads, it is clear that SITA outperforms TAGS. An important result comparing the performance of these two policies [2] states that in the asymptotic regime, where the ratio of the largest to shortest job tends to infinity and the system load is fixed and low, the average waiting time of SITA with optimal intervals is, at most, two times that of TAGS with optimal intervals.…”

Section: Introductionmentioning

confidence: 99%

“…The stability condition for TAGS systems [2] says that the arrival rate times and the mean job size must be less than a critical load that depends on the job size distribution. Let us note that this stability condition does not depend on the number of servers present in the system.…”

Section: Introductionmentioning

confidence: 99%

“…The goal is to elucidate the maximum number of groups that can operate under TAGS so as to satisfy a quality of service constraint that states that the average waiting time of the system does not exceed a given threshold. As the performance of TAGS and SITA is very difficult to analyze in a precise manner, we focus on a suboptimal, yet reasonable solution which uses the results of [2].…”

Section: Introductionmentioning

confidence: 99%

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Size-Based Routing Policies: Non-Asymptotic Analysis and Design of Decentralized Systems

Bachmat

Doncel

2021

Sensors

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Size-based routing policies are known to perform well when the variance of the distribution of the job size is very high. We consider two size-based policies in this paper: Task Assignment with Guessing Size (TAGS) and Size Interval Task Assignment (SITA). The latter assumes that the size of jobs is known, whereas the former does not. Recently, it has been shown by our previous work that when the ratio of the largest to shortest job tends to infinity and the system load is fixed and low, the average waiting time of SITA is, at most, two times less than that of TAGS. In this article, we first analyze the ratio between the mean waiting time of TAGS and the mean waiting time of SITA in a non-asymptotic regime, and we show that for two servers, and when the job size distribution is Bounded Pareto with parameter α=1, this ratio is unbounded from above. We then consider a system with an arbitrary number of servers and we compare the mean waiting time of TAGS with that of Size Interval Task Assignment with Equal load (SITA-E), which is a SITA policy where the load of all the servers are equal. We show that in the light traffic regime, the performance ratio under consideration is unbounded from above when (i) the job size distribution is Bounded Pareto with parameter α=1 and an arbitrary number of servers as well as (ii) for Bounded Pareto distributed job sizes with α∈(0,2)\{1} and the number of servers tends to infinity. Finally, we use the result of our previous work to show how to design decentralized systems with quality of service constraints.

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Section: Application Of This Theory To the Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Size-Based Routing Policies: Non-Asymptotic Analysis and Design of Decentralized Systems

Bachmat

Doncel

2021

Sensors

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Analysis of the Task Assignment based on Guessing Size policy

Bachmat

Doncel

Sarfati

2020

Performance Evaluation

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Frequency scaling in multilevel queues

Elahi

Marin

Rossi

et al. 2020

Performance Evaluation

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In this paper, we study a variant of PS+PS multilevel scheduling, which we call the PS+IS queue. Specifically, we use Processor Sharing (PS) at both queues, but with linear frequency scaling on the second queue, so that the latter behaves like an Infinite Server (IS) queue. The goals of the system are low response times for small jobs in the first queue, and reduced power consumption for large jobs in the second queue. The novelty of our model includes the frequency scaling at the second queue, and the batch arrival process at the second queue induced by the busy period structure of the first queue which has strictly higher priority. We derive a numerical solution for the PS+IS queueing system in steady-state, and then study its properties under workloads obtained from fitting of TCP flow traces. The simulation results confirm the e cacy of the PS+IS model. This article is an introduction to our longer paper in [5].

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Performance and Stability Analysis of the Task Assignment Based on Guessing Size Routing Policy

Cited by 7 publications

References 25 publications

Size-Based Routing Policies: Non-Asymptotic Analysis and Design of Decentralized Systems

Size-Based Routing Policies: Non-Asymptotic Analysis and Design of Decentralized Systems

Analysis of the Task Assignment based on Guessing Size policy

Frequency scaling in multilevel queues

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