Computational techniques in queueing and fluctuation theory

The main objective of this thesis is to develop numerical techniques to calculate the probability distribution of the running maximum of Lévy processes, and consider a number of specific financial applications. The other objective is to propose a numerical method to optimize the energy consumption of servers handling traffic in a communication network. The traffic itself is modeled by a random process, usually an on-off process with random on- and off-times.
In this thesis, a numerical technique based on the Wiener-Hopf factorization is developed to evaluate the probability distribution of the running maximum (or minimum) of a general Lévy process. This method can be employed for pricing many options which depend on the maximum and/or minimum attained by the underlying Lévy process, for instance lookback option.
The second technique which is presented in this book is importance sampling. This technique is essentially used to reduce the variance of the simulation-based estimator. Straightforward simulation for estimating rare event probabilities being inefficient and inaccurate, the idea of importance sampling is to generate simulation paths under an alternative measure such that the event is not rare anymore.
Energy-aware processors are intended to operate efficiently by adapting the speed of the server CPU to the processing load and the service level requirement. In this thesis, we consider a performance objective which is a linear combination of energy usage, queuing cost (reflected by delay) and speed switching cost for a multi-core processor. We discuss several schemes that lead to energy consumption reduction.