A large deviations principle for infinite-server queues in a random environment
Probability
2015-02-04 v1
Abstract
This paper studies an infinite-server queue in a random environment, meaning that the arrival rate, the service requirements and the server work rate are modulated by a general c\`{a}dl\`{a}g stochastic background process. To prove a large deviations principle, the concept of attainable parameters is introduced. Scaling both the arrival rates and the background process, a large deviations principle for the number of jobs in the system is derived using attainable parameters. Finally, some known results about Markov-modulated infinite-server queues are generalized and new results for several background processes and scalings are established in examples.
Cite
@article{arxiv.1502.00885,
title = {A large deviations principle for infinite-server queues in a random environment},
author = {H. M. Jansen and M. R. H. Mandjes and K. De Turck and S. Wittevrongel},
journal= {arXiv preprint arXiv:1502.00885},
year = {2015}
}
Comments
28 pages, 2 figures