Asymptotic analysis of spectral properties of finite capacity processor shared queues
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.
Studies in Applied Mathematics
Digital Object Identifier (DOI)
Zhen, & Knessl, C. (2013). Asymptotic Analysis of Spectral Properties of Finite Capacity Processor Shared Queues. Studies in Applied Mathematics (Cambridge), 131(2), 179–210. https://doi.org/10.1111/sapm.12020