A Note on Many-server Fluid Models with Time-varying Arrivals
Probability
2019-05-01 v1
Abstract
We extend the measure-valued fluid model, which tracks residuals of patience and service times, to allow for time-varying arrivals. The fluid model can be characterized by a one-dimensional convolution equation involving both the patience and service time distributions. We also make an interesting connection to the measure-valued fluid model tracking the elapsed waiting and service times. Our analysis shows that the two fluid models are actually characterized by the same one-dimensional convolution equation.
Cite
@article{arxiv.1806.00773,
title = {A Note on Many-server Fluid Models with Time-varying Arrivals},
author = {Zhenghua Long and Jiheng Zhang},
journal= {arXiv preprint arXiv:1806.00773},
year = {2019}
}