**SMS scnews item created by Eduardo Altmann at Wed 18 Jan 2017 1157**

Type: Seminar

Distribution: World

Expiry: 1 Mar 2017

**Calendar1: 22 Feb 2017 1400-1500**

**CalLoc1: AGR Carslaw 829**

CalTitle1: Heavy-traffic limits for layered queueing networks

Auth: ega@como.maths.usyd.edu.au

### Applied Maths Seminar

# Heavy-traffic limits for layered queueing networks

### Vlassiou

Dr. Maria Vlassiou (Eindhoven University of Technology, Netherlands)

** Title:** Heavy-traffic limits for layered queueing networks

** Abstract: ** Heavy-traffic limits for queueing networks are a topic of continuing interest. Presently, the class of networks for which these limits have been rigorously derived is restricted. An important ingredient in such work is the demonstration of state space collapse (SSC), which loosely speaking shows that in diffusion scale the queuing process for the stochastic model can be approximately recovered as a continuous lifting of the workload process. This often results in a reduction of the dimensions of the original system in the limit, leading to improved tractability. In this talk, we discuss diffusion approximations of layered queuing networks through two examples.

In the first example, we establish a heavy-traffic limit through SSC for a computer network model. For this model, SSC is related to an intriguing separation of time scales in heavy traffic. The main source of randomness occurs at the top layer; the interactions at the other layer are shown to converge to a fixed point at a faster time scale.

The second example focuses on a network of parallel single-server queues, where the speeds of the servers are varying over time and governed by a single continuous-time Markov chain. We obtain heavy-traffic limits for the distributions of the joint workload, waiting-time and queue length processes. We do so by using a functional central limit theorem approach, which requires the interchange of steady-state and heavy-traffic limits. For this model, we show that the SSC property does not hold.
Applied Maths Seminars are held at 2:00 pm on Wednesdays in the Access Grid Room