On spectral properties of finite population processor shared queues

Qiang Zhen () and Charles Knessl ()

Mathematical Methods of Operations Research, 2013, vol. 77, issue 2, 147-176

Abstract: We consider sojourn or response times in processor-shared queues that have a finite population of potential users. Computing the response time of a tagged customer involves solving a finite system of linear ODEs. Writing the system in matrix form, we study the eigenvectors and eigenvalues in the limit as the size of the matrix becomes large. This corresponds to finite population models where the total population is $$N\gg 1$$ . Using asymptotic methods we reduce the eigenvalue problem to that of a standard differential equation, such as the Hermite equation. The dominant eigenvalue leads to the tail of a customer’s sojourn time distribution. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Finite population; Processor sharing; Eigenvalue; Eigenvector; Asymptotics (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s00186-012-0421-6 (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:mathme:v:77:y:2013:i:2:p:147-176

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-012-0421-6

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().