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

TL;DR

This paper establishes a large deviations principle for infinite-server queues influenced by a stochastic background process, generalizing existing results and introducing the concept of attainable parameters for various scalings.

Contribution

It introduces the concept of attainable parameters and derives a large deviations principle for queues modulated by a general cdle0g background process, extending prior work.

Findings

Large deviations principle for queue length distribution established.

Generalization of known Markov-modulated queue results.

New results for different background processes and scalings.

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.