Erlang Redux: An Ansatz Method for Solving the M/M/m Queue
Performance
2020-08-18 v1 Distributed, Parallel, and Cluster Computing
Networking and Internet Architecture
Abstract
This exposition presents a novel approach to solving an M/M/m queue for the waiting time and the residence time. The motivation comes from an algebraic solution for the residence time of the M/M/1 queue. The key idea is the introduction of an ansatz transformation, defined in terms of the Erlang B function, that avoids the more opaque derivation based on applied probability theory. The only prerequisite is an elementary knowledge of the Poisson distribution, which is already necessary for understanding the M/M/1 queue. The approach described here supersedes our earlier approximate morphing transformation.
Cite
@article{arxiv.2008.06823,
title = {Erlang Redux: An Ansatz Method for Solving the M/M/m Queue},
author = {Neil J. Gunther},
journal= {arXiv preprint arXiv:2008.06823},
year = {2020}
}
Comments
13 pages, 7 figures, 2 Tables