Analysis of the Task Assignment based on Guessing Size policy

Bachmat, Eitan; Doncel, Josu; Sarfati, Hagit

doi:10.1016/j.peva.2020.102122

Cited by 7 publications

(2 citation statements)

References 22 publications

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“…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%

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: Related Workmentioning

confidence: 99%

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

Bachmat

Doncel

2021

Sensors

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“…Taking into account the difficulty of the analytical study of the optimal SITA policy, some size-interval variants have been presented in the literature, see for example [11,4] for the task assignment by guessing size and [7] for the application to web servers. Other authors have studied SITA-E instead of the optimal SITA policy, see for instance [8,9].…”

Section: Related Workmentioning

confidence: 99%

Performance balancing size-interval routing policies

Doncel

2020

INFOR: Information Systems and Operational Research

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We study a parallel-queue system with Poisson arrivals, in which a dispatcher sends the incoming traffic to K queues using Size Interval Task Assignment (SITA) policy that aims to equalize the performance of all queues. We study existence and uniqueness of the allocation thresholds for a large set of performance functions of the queues. We also provide a family of performance functions of the queues such that the performance of the system is characterized. For a particular case of the latter family of functions, we show that the performance of the SITA policy we study coincides with the performance of the SITA policy in which the load are balanced. We investigate the optimality of the SITA policy under study and, according to our numerical experiments, for FCFS queues and Bounded Pareto distributed job sizes, the SITA policy we study is almost optimal, when we consider the mean queue length and α < 1 as well as when we consider the mean slowdown.

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Optimal performance of parallel-server systems with job size prediction errors

Doncel

Mancuso

2021

Operations Research Letters

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Analysis of the Task Assignment based on Guessing Size policy

Cited by 7 publications

References 22 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

Performance balancing size-interval routing policies

Optimal performance of parallel-server systems with job size prediction errors

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