Asymptotic analysis of spectral properties of finite capacity processor shared queues

Document Type

Article

Publication Date

8-1-2013

Abstract

We consider sojourn (or response) times in processor-shared queues that have a finite customer capacity. 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 capacity models where the system can only hold a large number K of customers. Using asymptotic methods we reduce the eigenvalue problem to that of a standard differential equation, such as the Airy equation. The dominant eigenvalue leads to the tail of a customer's sojourn time distribution. Some numerical results are given to assess the accuracy of the asymptotic results. © 2013 by the Massachusetts Institute of Technology.

Publication Title

Studies in Applied Mathematics

Volume

131

Issue

2

First Page

179

Last Page

210

Digital Object Identifier (DOI)

10.1111/sapm.12020

ISSN

00222526

E-ISSN

14679590

Link to Full Text

Share

COinS