The Theory Of Large Deviations In The Queuing System

This thesis is an overview of the application of Large Deviation(LD) theory in queueing systems. As is known to all, LD theory provides a method for computing probabilities of rare events which, despite of its small occurring probability, could lead to very crucial subsequence. Therefore the research of rare events is definitely necessary. LD analysis provides an expression for the probabilities in terms of a solution to a related variational problem. The strengths of LD theory are these: it is general enough that one can answer many questions which are hard to answer otherwise, and it is powerful enough that one can draw conclusions without relying on special calculations. We will have such a feeling that sometimes abstraction can serve to simplify problems rather than to obscure them. This thesis briefly introduces some basic definitions and propositions in LDP area and also summarizes the main results and latest developments in different queueing networks, including single-server queue, Jackson network, feedforward network, feedback network and monotone-separable network. Although quite a few LD results appeared in recent years, there is still room for improvements. Hopefully it can be useful for those who are currently doing research in this area.