System theory modeling and performance analysis of a distributed load balancing algorithm

Useful connections between distributed load balancing and classical linear system theory are established. It is observed that important aspects of the behavior and performance of two versions of a novel load-balancing algorithm using graph coloring can be modeled and studied using linear system theory tools. It is shown that the load-balancing algorithm, after running for a log L steps, results in each processor having a load deviating by at most b log L from the average load. Here L is the sum of all loads and a and b depend only on the graph used to model the interconnection network of the system. It is also shown that the n-cube, with 2ⁿ nodes, within n steps each processor has a load at most n/2 away from the average. More generally, the work opens up the possibility of applying system theory ideas to significant problems in distributed systems