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

Multi-class Fork-Join queues are extension of single-class Fork-Join queues. In a multi-class Fork-Join queuing system, different types of jobs arrive, and then split into several sub-jobs. Those sub-jobs go to parallel processing queues. Then, the synchronization is required before the departure of a job. We found very few scientific efforts in analyzing the multi-class Fork-Join queues. In this thesis, we analyzed the expected sojourn time and the expected synchronization time. Since it is difficult to derive analytical expressions for them, we used approximation methods to approximate them. Through extensive numerical results, we showed that the approximations provide a close approximation for the expected sojourn time and an accurate approximation of the optimal synchronization buffer.