Numerical Solution of Cloud Servicing Models

This paper presents a method for numerical solution of Markov-chain based models of dynamic load balancing schemes for cloud clusters. These schemes were presented in detail in earlier publications. Here we are describing the fast converging iterative solution of a class of such models. The numerical solution of the dynamic load-balancing models by computer solvers proved to be problematic if not applicable due to its computational instability. Other numerical methods available for solving Markov chains relay on constant transition rates or at least on rates that are not depending on the state probabilities. The proposed method combines analytical approach with the simple computations based on electronic tables and gives a solution in just a few iteration steps. It is designed especially for Markov chains in which transition rates are functions of the steady-state probabilities -- and that is the case of most dynamic load balancing schemes. The simplicity of this numerical method allows to compute the parameters for vast modeling space thus providing a broad picture of cloud servers' performance.