Reversal Argument for Storage Models Defined on Semi-Markov Processes

摘要

For many storage models defined on some semi-Markov process X(t), the asymptotic distribution of the imbedded discrete time process can often be determined by exploiting the properties of the dual of the underlying Markov chain X sub n, which effectively reverses the process. If this is the case, a technique is given which under certain regularity conditions shows the asymptotic distribution of the entire continuous time process can be obtained, and is equal to an altered version of the reversed discrete time process. It is shown this method not only can be applied to models where the asymptotic distribution was previously unknown, but can also improve upon characterizing many of the results for models in which the asymptotic behavior is obtained by a renewal argument. (Author)