Article ID: | iaor20133819 |
Volume: | 77 |
Issue: | 2 |
Start Page Number: | 147 |
End Page Number: | 176 |
Publication Date: | Apr 2013 |
Journal: | Mathematical Methods of Operations Research |
Authors: | Knessl Charles, Zhen Qiang |
Keywords: | differential equations |
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