A large deviations principle for infinite-server queues in a random environment

H. M. Jansen; M. R. H. Mandjes; K. De Turck; S. Wittevrongel

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arXiv · 1502.00885

A large deviations principle for infinite-server queues in a random environment

H. M. Jansen·M. R. H. Mandjes·K. De Turck·S. Wittevrongel

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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 càdlàg 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.

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BibTeX RIS

H. M. Jansen, M. R. H. Mandjes, K. De Turck, S. Wittevrongel. 2015-02-03. A large deviations principle for infinite-server queues in a random environment. https://arxiv.org/abs/1502.00885

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