Presented by: 
Wendy Ellens - University of Amsterdam
Tue 3 Jun, 11:00 am - 12:00 pm

Abstract: Birth-death processes are a popular way to model the number of active clients (or packets, or web requests) in communication networks. Generally, the throughput (delivery rate) of a communication system depends on the number of active clients. Therefore the number of active clients is measured on a regular basis, for example every second or minute. However, such measurements do not give the network operator information about the situation between measurements. Questions like: "How probable is it that the number of clients exceeds a certain critical level? How long does such an undesirable situation persist, and how many clients suffer from it?" remain unanswered.

The goal of this talk is to set up the mathematical theory to answer the above questions. The distribution of the maximum of a birth-death process on an interval of given length and width given endpoints is derived. Also other metrics - like the time and the area of the process above a predefined level - are treated. In addition, some symmetry properties of these metrics are proven using the reversibility property of (transient) birth-death processes.