Infinite server queues in a random fast oscillatory environment
Probability
2020-04-13 v1
Abstract
In this paper, we consider a infinite server queueing model in a random environment. More specifically, the arrival rate in our server is modeled as a highly fluctuating stochastic process, which arguably takes into account some small time scale variations often observed in practice. We show a homogenization property for this system, which yields an approximation by a queue with modified parameters. Our limiting results include the description of the number of active servers, the total accumulated input and the solution of the storage equation. Hence in the fast oscillatory context under consideration, we show how the queuing system in a random environment can be approximated by a more classical Markovian system.
Keywords
Cite
@article{arxiv.2004.05034,
title = {Infinite server queues in a random fast oscillatory environment},
author = {Harsha Honnappa and Yiran Liu and Samy Tindel and Aaron Yip},
journal= {arXiv preprint arXiv:2004.05034},
year = {2020}
}