The minimal quasi-stationary distribution of the absorbed M/M/$\infty$ queue
Probability
2023-07-19 v1
Abstract
We give in this paper two characterizations of the minimal exponential rate of survival * of the M/M/ queue. The first one is a derivation of a known result on the duration of excursions of this process. The second one was conjectured by Mart{\'i}nez and Ycart [8] and is proved using complex analysis by establishing a connection with the first characterization in terms of the incomplete gamma function.
Keywords
Cite
@article{arxiv.2307.09034,
title = {The minimal quasi-stationary distribution of the absorbed M/M/$\infty$ queue},
author = {Elie Cerf},
journal= {arXiv preprint arXiv:2307.09034},
year = {2023}
}