Error bounds for asymptotic approximations of the partition function

Error bounds for asymptotic approximations of the partition function

0.00 Avg rating0 Votes
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: ,
Keywords: queueing networks
Abstract:

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.

Reviews

Required fields are marked *. Your email address will not be published.