Large deviations of an infinite-server system with a linearly scaled background process
This paper studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. We focus on the probability that the number of jobs in the system attains an unusually high value. Scaling the arrival rates ?i ? i by a factor N N and the transition rates ?ij ? i j of the background process as well, a large-deviations based approach is used to examine such tail probabilities (where N N tends to ? ? ). The paper also presents qualitative properties of the systems behavior conditional on the rare event under consideration happening.
large deviations infinite-server systems queues markov modulation