Higher order approximations for the single server queue with splitting, merging and feedback

The performance evaluation of many modern communication and manufacturing systems has been made possible by modeling them as queuing networks. Due to the limitations of exact algorithms to analyze general queuing networks, researchers have been focusing on developing approximations. Most of the approximations are lower order approximations in the sense that only a few parameters of the interarrival and service time distributions are used. This could lead to large errors in many conditions. In this paper, higher order approximations are developed for the single server queue with splitting, merging and feedback phenomena, which can then be integrated along with parametric decomposition to develop higher order approximations for queueing networks. Not only are the higher order approximations more accurate, but they can also be used to estimate the higher moments of the performance measures.