Heavy-tailed limits for medium size jobs and comparison scheduling

Predrag Jelenković (), Xiaozhu Kang () and Jian Tan ()

Annals of Operations Research, 2009, vol. 170, issue 1, 133-159

Abstract: We study the conditional sojourn time distributions of processor sharing (PS), foreground background processor sharing (FBPS) and shortest remaining processing time first (SRPT) scheduling disciplines on an event where the job size of a customer arriving in stationarity is smaller than exactly k≥0 out of the preceding m≥k arrivals. Then, conditioning on the preceding event, the sojourn time distribution of this newly arriving customer behaves asymptotically the same as if the customer were served in isolation with a server of rate (1−ρ)/(k+1) for PS/FBPS, and (1−ρ) for SRPT, respectively, where ρ is the traffic intensity. Hence, the introduced notion of conditional limits allows us to distinguish the asymptotic performance of the studied schedulers by showing that SRPT exhibits considerably better asymptotic behavior for relatively smaller jobs than PS/FBPS. Inspired by the preceding results, we propose an approximation to the SRPT discipline based on a novel adaptive job grouping mechanism that uses relative size comparison of a newly arriving job to the preceding m arrivals. Specifically, if the newly arriving job is smaller than k and larger than m−k of the previous m jobs, it is routed into class k. Then, the classes of smaller jobs are served with higher priorities using the static priority scheduling. The good performance of this mechanism, even for a small number of classes m+1, is demonstrated using the asymptotic queueing analysis under the heavy-tailed job requirements. We also discuss refinements of the comparison grouping mechanism that improve the accuracy of job classification at the expense of a small additional complexity. Copyright Springer Science+Business Media, LLC 2009

Keywords: Comparison scheduling; Scalability; Fairness; Adaptive thresholds; M/G/1 queue; Processor sharing; Shortest remaining processing time first; Foreground background processor sharing; Asymptotic analysis; Heavy tails; Medium size jobs (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s10479-008-0432-0 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:170:y:2009:i:1:p:133-159:10.1007/s10479-008-0432-0

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-008-0432-0

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().