Efficiency Improvements to Uniformization for Markovian Birth-and-Death Models

Abstract

Finding transient solutions in queuing systems is crucial in many applications, including of service system modeling. As many of such systems are Markovian, their natural description is that of a continuous-time Markov chain (CTMC), and uniformization is widely considered an efficient method for transient analysis of CTMCs. In this paper we present significant efficiency improvements to the standard uniformization algorithm when used for transient analysis of time-inhomogenous Markovian birth-and-death queuing models. We exploit some of the distinct properties of birth-and-death models in particular the structure of the generator matrix and the convergence properties of the model. Moreover, we utilize an example based on an realistic birth-and-death model of a call center in order to demonstrate that our proposal is especially advantageous for transient modeling of real service systems.