Hosts: prof. dr hab. Ryszard Szekli, prof. dr hab. Krzysztof Dębicki

Contact: dr Michał Krawiec (secretary), michal.krawiec at math.uni.wroc.pl

Current activity:

The seminar takes place once a week, on Thursdays from 12:15 - 14:00 in the form of a stationary meeting in room 603 (Mathematical Institute, UWr) or an online meeting on the Zoom platform. All current and more detailed information can be obtained from the seminar secretary.

Next seminar: 2025-10-23, 12:15 - 14:00

dr Nikolai Kriukov (University of Amsterdam)

Limit theorems for Gaussian-fed queueing networks in light and heavy traffic

Abstract:
In this talk we consider a queueing network operating under a strictly upper-triangular routing matrix with per column at most one positive entry. The root node is fed by a Gaussian process with stationary increments. Our aim is to characterize the distribution of the multivariate stationary workload process under a specific scaling of the queue's service rates. In the main results we identify, under mild conditions on the standard deviation function of the driving Gaussian process, in both light and heavy traffic, the limiting law of an appropriately scaled version (in both time and space) of the joint stationary workload process. In particular, we develop conditions under which specific queues of the network effectively decouple, i.e., become independent in the limiting regime.