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

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`adì ag 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. Keywords. infinite-server queue random environment modulation large deviations principle
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H.M. Jansen, Michel Mandjes, Koen de Turck, S Wittevrongel. A large deviations principle for infinite-server queues in a random environment. Queueing Systems, Springer Verlag, 2016, 82 (1-2), pp.199-235. ⟨10.1007/s11134-015-9470-x⟩. ⟨hal-01256755⟩

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