Method of Supplementary Variables

Abstract

We have seen that if r.v.’s governing the dynamics of a queueing model are exponentially distributed, then we can describe the model by a continuous-time Markov chain. But if this is not the case, then we have to employ different tricks for studying such processes. Of course, we do not need necessarily a Markov character in order to derive some properties of the processes. For example, we exploited the concept of regeneration in Chapter 7 for proving the existence of limiting distributions and continuity analysis. But if we have to calculate limiting or pre-limiting distributions, then the Markov property is almost unique in enabling corresponding relations.