Article ID: | iaor19993199 |
Country: | United States |
Volume: | 23 |
Issue: | 1/4 |
Start Page Number: | 217 |
End Page Number: | 234 |
Publication Date: | Jan 1996 |
Journal: | Queueing Systems |
Authors: | Kogan Yaakov, Birman Alexander |
Keywords: | queueing networks |
We consider Markovian queueing models with a finite number of states and a product form solution for its steady state probability distribution. Starting from the integral representation for the partition function in complex space we construct error bounds for its asymptotic expansion obtained by the saddle point method. The derivation of error bounds is based on an idea by Olver applicable to integral transforms with an exponentially decaying kernel. The bounds are expressed in terms of the supremum of a certain function and are asymptotic to the absolute value of the first neglected term in the expansion as the large parameter approaches infinity. The application of these error bounds is illustrated for two classes of queueing models: loss systems and single chain closed queueing networks.