Fast Engset computation
Numerical Analysis
2016-05-04 v4
Abstract
The blocking probability of a finite-source bufferless queue is a fixed point of the Engset formula, for which we prove existence and uniqueness. Numerically, the literature suggests a fixed point iteration. We show that such an iteration can fail to converge and is dominated by a simple Newton's method, for which we prove a global convergence result. The analysis yields a new Tur\'an-type inequality involving hypergeometric functions, which is of independent interest.
Keywords
Cite
@article{arxiv.1511.00291,
title = {Fast Engset computation},
author = {Parsiad Azimzadeh and Tommy Carpenter},
journal= {arXiv preprint arXiv:1511.00291},
year = {2016}
}
Comments
13 pages, 2 figures, 4 tables. Error in statement of Lemma 11 in [v2] fixed. Error in proof of Lemma 2 in [v3] fixed