SMOR Seminar, Michel Mandjes, Infinite-server queues and Ornstein-Uhlenbeck processes: reflection and Markov modulation
In this talk we consider infinite-server queues and their Gaussian counterpart: Ornstein-Uhlenbeck processes.
In the first part of the talk we consider Ornstein-Uhlenbeck processes with single and double reflection, with
a focus on large deviations, as well as a CLT for the loss process.
In the second part of the talk, we consider infinite-server queues with Markov modulated input. With specific
scalings of the modulating background process and the arrival rates, we show that various limiting regimes come
out. In the corresponding CLTs an intriguing role is played by the so-called deviation matrix. We also derive
the corresponding large deviations results.
A similar setup can be followed for the Markov modulated Ornstein-Uhlenbeck process. We derive the mean
and variance of the transient distribution, and then derive CLTs and LD results under specific scalings (similar
to the Markov modulated infinite server setting).
Joint work with: D. Anderson, J. Blom, K. de Turck, G. Huang, O. Kella, P. Spreij, H. Thorsdottir.