A partially asynchronous and iterative algorithm for distributed load balancing

Defining tasks as independent entities with identical execution time and workload as the number of tasks, the author proposes a partially asynchronous and iterative algorithm for distributed load balancing, shows its properties, and reports its simulation results. The algorithm converges geometrically according to a theorem proved elsewhere. He proves that the algorithm can achieve the maximum load imbalance of not more than [^d/₂] tasks, where d is the diameter of a network. His simulation of a synchronous version of the algorithm not only validated the properties but also showed that the algorithm could produce much smaller load imbalances for hypercubes. The obtained imbalances for hypercubes of order up to ten were no more than two tasks and 56% of the sample runs produced only one task difference, as opposed to the theoretical maximum of six tasks