Loss Rates and Structural Properties of Reflected Stochastic Processes
The thesis Loss Rates and Structural Properties of Reflected Stochastic Processes provides results on reflected stochastic processes. By relying on new explicit representations for the reflected process, it provides proof of monotonicity and concavity of the mean value function of the reflected process, when the original process has stationary increments. Furthermore, the thesis expands upon previous work on the stationary loss rate for reflected Levy processes, as new asymptotic expressions for this object are derived. The loss rate is used as a model for data loss in a finite buffer system. Finally, a paper, which is separate in content from the rest of the thesis, treats an extreme value problem, which arises in parallel computing.
Thesis advisor: Søren Asmussen