Economies of Scale in Parallel-Server Systems

Josu Doncel; Samuli Aalto; Urtzi Ayesta

doi:10.1109/INFOCOM.2017.8057093

Economies of Scale in Parallel-Server Systems

Josu Doncel, Samuli Aalto, Urtzi Ayesta

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

2 Citations (Scopus)

151 Downloads (Pure)

Abstract

We consider a parallel-server system with K homogeneous servers where incoming tasks, arriving at rate λ, are dispatched by n dispatchers. Servers are FCFS queues and dispatchers implement a size-based policy such that the servers are equally loaded. We compare the performance of a system with n> 1 dispatchers and of a system with a single dispatcher. Every dispatcher handles a fraction 1/n of the incoming traffic and balances the load to K/n servers. We show that the performance of a system with n dispatchers, K servers and arrival rate λ coincides with that of a system with one dispatcher, K/n servers and arrival rate λ/n. Therefore, the performance comparison can be interpreted as the economies of scale in a system with one dispatcher when we scale up the number of servers and the arrival rate proportionately. We consider two continuous service time distributions: uniform and Bounded Pareto that have increasing and decreasing failure rates, respectively; and a discrete distribution with two values, which is the distribution that maximizes the variance for a given mean. We show that the performance degradation is small for uniformly distributed job sizes, but that for Bounded Pareto and two points distributions it can be unbounded.

Original language	English
Title of host publication	IEEE Conference on Computer Communications
Subtitle of host publication	Proceedings : IEEE INFOCOM
Publisher	IEEE
Pages	1350-1358
Number of pages	9
ISBN (Electronic)	978-1-5090-5336-0
DOIs	https://doi.org/10.1109/INFOCOM.2017.8057093
Publication status	Published - 2017
MoE publication type	A4 Article in a conference publication
Event	IEEE Conference on Computer Communications - Atlanta, United States Duration: 1 May 2017 → 4 May 2017 http://infocom2017.ieee-infocom.org/

Publication series

Name	IEEE Conference on Computer Communications
ISSN (Print)	0743-166X

Conference

Conference	IEEE Conference on Computer Communications
Abbreviated title	INFOCOM
Country	United States
City	Atlanta
Period	01/05/2017 → 04/05/2017
Internet address	http://infocom2017.ieee-infocom.org/

Access to Document

10.1109/INFOCOM.2017.8057093

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Doncel, J., Aalto, S., & Ayesta, U. (2017). Economies of Scale in Parallel-Server Systems. In IEEE Conference on Computer Communications: Proceedings : IEEE INFOCOM (pp. 1350-1358). (IEEE Conference on Computer Communications). IEEE. https://doi.org/10.1109/INFOCOM.2017.8057093

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abstract = "We consider a parallel-server system with K homogeneous servers where incoming tasks, arriving at rate λ, are dispatched by n dispatchers. Servers are FCFS queues and dispatchers implement a size-based policy such that the servers are equally loaded. We compare the performance of a system with n> 1 dispatchers and of a system with a single dispatcher. Every dispatcher handles a fraction 1/n of the incoming traffic and balances the load to K/n servers. We show that the performance of a system with n dispatchers, K servers and arrival rate λ coincides with that of a system with one dispatcher, K/n servers and arrival rate λ/n. Therefore, the performance comparison can be interpreted as the economies of scale in a system with one dispatcher when we scale up the number of servers and the arrival rate proportionately. We consider two continuous service time distributions: uniform and Bounded Pareto that have increasing and decreasing failure rates, respectively; and a discrete distribution with two values, which is the distribution that maximizes the variance for a given mean. We show that the performance degradation is small for uniformly distributed job sizes, but that for Bounded Pareto and two points distributions it can be unbounded.",

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AB - We consider a parallel-server system with K homogeneous servers where incoming tasks, arriving at rate λ, are dispatched by n dispatchers. Servers are FCFS queues and dispatchers implement a size-based policy such that the servers are equally loaded. We compare the performance of a system with n> 1 dispatchers and of a system with a single dispatcher. Every dispatcher handles a fraction 1/n of the incoming traffic and balances the load to K/n servers. We show that the performance of a system with n dispatchers, K servers and arrival rate λ coincides with that of a system with one dispatcher, K/n servers and arrival rate λ/n. Therefore, the performance comparison can be interpreted as the economies of scale in a system with one dispatcher when we scale up the number of servers and the arrival rate proportionately. We consider two continuous service time distributions: uniform and Bounded Pareto that have increasing and decreasing failure rates, respectively; and a discrete distribution with two values, which is the distribution that maximizes the variance for a given mean. We show that the performance degradation is small for uniformly distributed job sizes, but that for Bounded Pareto and two points distributions it can be unbounded.

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