The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

Skip to content

SCS

Seminar

Timescaling results for Markov modulated infinite-server systems and OU processes

Mandjes, M (Universiteit van Amsterdam)
Friday 16 August 2013, 10:00-10:45

Seminar Room 1, Newton Institute

Abstract

Co-authors: J. Blom (CWI), K. de Turck (Ghent), O. Kella (Jerusalem), D. Anderson (Wisconsin), H. Thorsdottir (CWI), G. Huang (Amsterdam), P. Spreij (Amsterdam)

In this talk I'll consider an infinite-server queue whose input is modulated by a Markovian background process, with a focus on the analysis of the number of customers in the system, both in the central-limit and the large deviations regime. In the scaling that we study, the background process is sped up by a factor N^f, while the arrival rate are scaled by N. Interestingly, in the CLT regime crucially different results come out for f > 1 and for f < 1; in the former case the input process essentially behaves as a (normal) Poisson process, while in the latter case the CLT involves deviation matrices. A similar distinction applies in the LD context. In the second part of the talk I'll address similar issues for the Markov modulated Ornstein-Uhlenbeck process. The last part of the presentation is about multiple infinite-servers systems (or multiple OU systems), modulated by a single background process, thus creating correlation between the individual components. A PDE that characterizes the joint distribution of all coordinates is derived, leading to recursive expressions for all moments. Also a multidimensional CLT is established.

Presentation

[pdf ]

Video

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.

Back to top ∧