A Technique for Discussing the Passage Time Distribution for Stable Systems†

Abstract

For many processes arising in reliability and congestion studies, passage time distributions required are difficult to exhibit. An asymptotic discussion is often available centring about a limit theorem given previously, and asymptotic equality of the mean passage time and an associated mean sojourn time, the latter obtainable directly from the ergodic distribution for the process. Theorems are presented exhibiting this equality for a variety of Markov chains.