2015/02/03 by H. M. Jansen, Jansen, H. M., Michel Mandjes +5
Business, Management and Accounting · Decision Sciences · Mathematics · #60F10 (Secondary) #60K25 (Primary) #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1502.00885
openalex publication_date 2015/02/03 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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.