Levy driven queues and fluctuation theory
Summary
The main object of interest is a continuous time queueing system or otherwise, a Levy-driven queue. The goal of my master thesis was twofold. At first I wanted to study some structural properties of the workload process and to generalize some results already known for the case of a spectrally one sided input process. Secondly, I studied the transient behaviour of the workload process. My goal was to find a way to approximate the transform of the workload process at a deterministic time t. This was done separately for the case of a spectrally positive and spectrally negative input process.