Optimal resource capacity management for stochastic loss network systems with applications in clouds and data centers

In this paper, we develop a framework for considering the problem of optimal resource capacity management in general stochastic loss network systems. The stochastic optimization problem consists of determining the capacities of different types of resources that minimize the total weighted loss probabilities over the entire time horizon. Since computing the exact (multi-dimensional) Erlang formula is #P-complete in the size of the network, we first consider the canonical Erlang fixed-point approximation for the blocking probability. We further propose a QED fixed-point approximation for blocking probability which is shown to be asymptotically exact and always outperform Erlang fixed-point approximation. We then improve the stochastic optimization problem by the QED fixed-point approximation. We also design an iterative algorithm to solve the optimization problem and show that it has a unique solution. We numerically demonstrate that it yields an improved solution compared to the optimization problem based on the Erlang fixed-point approximation. Numerical experiments have be obtained to confirm and support our theoretical results.