A decomposition algorithm for optimal static load balancing in tree hierarchy network configurations

We study the static load balancing problem in a distributed computer system with the tree hierarchy configuration. It is formulated as a nonlinear optimization problem. After studying the conditions that the solution to the optimization problem of the tree hierarchy network satisfies, we demonstrate that the special structure of the optimization problem leads to an interesting decomposition technique. A new effective decomposition algorithm to solve the optimization problem is presented. The proposed algorithm Is compared with two other well known algorithms: the Flow Deviation (FD) algorithm and the Dafermos-Sparrow (D-S) algorithm. It is shown that the amounts of the storage required for the proposed algorithm and the FD algorithm are O(n) for load balancing of an n-node system. However, the amount of the storage required for the D-S algorithm is O(n log(n)). By using numerical experiments, we show that both the proposed algorithm and the D-S algorithm have much faster convergence in terms of central processing unit (CPU) time than the FD algorithm