The Large Deviation Principle In Intree Network Applications

The sample path LDP has been effectively used in queueing theory. Using the contraction principle ,Chang[5] has derived a set of closure properties for sample path LDP. These properities include sum,composition and reflection mapping .Using these properities,they show that the exponential decay rates of the steady state queue length distributions in an Intree network with routing can be derived by a set of recursive equations. In paper[1],they consider arrival processes satisfying the LDP in a space of measures endowed with the weak~* topology,and the departure processes still satisfies the sample path LDP. The result is then applided to obtain the exponential decay rate of the queue length probability in an Intree network as was obtained by Chang[5].In this paper,we consider arrival processes satisfying the LDP in a space of continuous functions C_μ.We derive the closure properties for sample path LDP using contraction principle. Then through the properties we get the exponential decay rates of the steady state queue length distributions in an Intree network which has constant service rate and stationary departure process.