Uniformization: Basics, extensions and applications

Uniformization, also referred to as randomization, is a well-known performance evaluation technique to model and analyse continuous-time Markov chains via an easier to performance measures via iteration of the one-step transition matrix of the discrete-time Markov chain. The number of iterations has a Poisson distribution with rate dominating the maximum exit rate from the states of the continuous-time Markov chain. This paper contains an expository presentation of uniformization techniques to increase awareness and to provide a formal and intuitive justification of several exact and approximate extensions, including: exact uniformization for reward models, exact uniformization for time-inhomogeneous rates, a numerical comparison with simple time-discretization, approximate uniformization for unbounded transition rates, and exact uniformization for continuous state variables for non-exponential networks. Furthermore, several of these results are numerically illustrated for a processor sharing web server tandem model of practical interest. (C) 2017 Elsevier B.V. All rights reserved.