Supplementary variable technique in stochastic models

In this article, we formalize the framework for the supplementary variable technique in stochastic models. Specifically, we show that the use of remaining or elapsed times (or any metric) as supplementary variables leads to the notion of forward or backward Chapman–Kolmogorov equations, respectively. We further show that for a class of queueing systems, using remaining time as the supplementary variable makes analysis simpler.