Multi - class Fork - Join queues & The stochastic knapsack problem

Preface This thesis is a result of my internship at the Centrum Wiskunde en Informatica (CWI). It is also an important part of my master study in Leiden University (UL). First of all, I want to give my special thanks to Chrétien Verhoef for all the daily advices and help from the beginning to the very end. I came to CWI with very little pre-knowledge about queueing theory and programming. His patience and clear explanation have helped me a lot. Also, I want to thank Floske Spieksma, my supervisor in Leiden, who spent a lot of time to correct my thesis and provided me with her solid theoretic knowledge. I also want to thank Rob van der Mei, who gave me the opportunity to do my internship in CWI. Rob, Floske and Sandjai Bhulai always inspired me with their professional and insightful thinking. They are all very dedicated researchers. I learned not only from their knowledge, but also from their active working attitudes. I want to thank all the colleagues in PNA2, and Bram de Vries who shared the office with me, all of you made this period of my life colorful and special. All those ping-pong playing times and interesting lunch talks are unforgettable for me. Through my experience in CWI, I redefine the term " research " , because it brought so much joy and happiness everyday. Last but not least, I want to thank my parents, who are loving me and supporting me all along. I also give my thanks to Stella, who always has faith in me and our future. ii Summary This thesis consists of two topics: 1. Performance analysis of multi-class Fork-Join queueing systems 2. Call admission control policy of stochastic knapsack problem The multi-class Fork-Join queueing system is an extension of the single-class Fork-Join queueing system. In such a system, different types of jobs arrive, and then split into several sub-jobs. Those sub-jobs go to parallel processing queues. Sub-jobs from different types may go to the same queue, and we call this overlapping. There is a server in front of each queue. After all sub-jobs of one job are completed, they synchronize in the synchronization buffer and then leave the system. Many communication and networking systems can be modeled as such systems. In the literature, hardly any exact results are known for the expected sojourn time of the multi-class Fork-Join queueing systems, and …