The exponential-dual matrix method: Applications to Markov chain analysis

Classic performance evaluation using queueing theory is usually done assuming a stable model in equilibrium. However, there are situations where we interested the transient phase. In this case, main metrics built around model’s state distribution at an arbitrary point time. dependability, significant part of analysis previous work, developed approach to derive distributions some continuous time Markovian models, uniformization (also called Jensen’s method), transforming problem into discrete one, and concept stochastic duality. This combination tools provides simplifications many cases. duality does not always exist. Recently, discovered that idea algebraic duality, formally similar can be defined applied any linear differential system (or equivalently, matrix). no limitation, transformation possible. We call it exponential-dual matrix method. article, describe limitations how method operates for system, or not. These concepts illustrated throughout our article with specific examples, including case infinite matrices.