The Maximum Overlap Time in the M/M/1 Queue
Probability
2023-11-15 v2
Abstract
In this paper, we analyze the steady state maximum overlap time in the M/M/1 queue. We derive the maximum overlap time tail distribution, its moments and the moment generating function. We also analyze the steady state minimum overlap time of the adjacent customers and compute its moments and moment generating function. Our results provide new insight on how customers become infected in the M/M/1 queue.
Keywords
Cite
@article{arxiv.2311.04387,
title = {The Maximum Overlap Time in the M/M/1 Queue},
author = {Sergio Palomo and Jamol Pender},
journal= {arXiv preprint arXiv:2311.04387},
year = {2023}
}