Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 cadlag 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.
['Henk M. Jansen', 'M.R.H. Mandjes', 'K. De Turck', 'Sabine Wittevrongel']
I am writing a research paper on a idea A large deviations principle for infinite-server queues in a random environment
[{"from": "human", "value": "I am writing a research paper on a idea A large deviations principle for infinite-server queues in a random environment"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 cadlag 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."}]