Markov Skeleton Processes And Its Applications To Frac/G/1 Queueing Systems

Markov skeleton process is a new type of stochastic process and containing many classical processes as special cases. In 1997, Prof Hou Zhenting and and his colleagues raised this kind of processes and used it to solve queueing theory problem.Queueing theory is a greatly important kind of application stochastic processes. The Frac/G/1 queueing systems are new type of queueing modes among all the queueing systems. In this dissertation, we drew the following conclusions:Firstly, we get a sufficient condition of normality for Markov skeleton process.Secondly, we give a concise proof of the backward equation for Markov skeleton process .Thirdly, we present the equation which satisfies the transient distribution ofthe length of (L(t),(t)2(t)) for Frac/G/1 queueing systems, and proves that the length (L(t),x(t)1(t)2(t) for GI/G/1 queueing systems satisfy two types of equation, as well as the equation that satisfies the waiting time of (W(t),x(t),(t)).Lastly, we derived two classes of differential-integral equations for Frac/G/1 queueing systems and gave its probabilistic solution by minimal nonnegative solution method.