On spectral properties of finite population processor shared queues
Document Type
Article
Publication Date
4-1-2013
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 ≫. 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. © 2012 Springer-Verlag Berlin Heidelberg.
Publication Title
Mathematical Methods of Operations Research
Volume
77
Issue
2
First Page
147
Last Page
176
Digital Object Identifier (DOI)
10.1007/s00186-012-0421-6
ISSN
14322994
E-ISSN
14325217
Citation Information
Zhen, & Knessl, C. (2012). On spectral properties of finite population processor shared queues. Mathematical Methods of Operations Research (Heidelberg, Germany), 77(2), 147–176. https://doi.org/10.1007/s00186-012-0421-6