Temporal Analysis of Load Imbalance in Distributed Computing Systems

Distributed computing systems consist of computers interconnected by communications links. In such systems, statistical fluctuations in job arrival and service patterns cause episodes of load imbalance during which some computers are lightly loaded while others are simultaneously overloaded. Load sharing is the process of transferring jobs from overloaded to underloaded computers to improve overall system performance. Load sharing is implemented by means of load sharing algorithms . However, since little has been known about the temporal characteristics of load imbalance, various pitfalls arise in the operation of load sharing algorithms which prevent full realization of the potential benefits of load sharing. In this paper, we present a stochastic analysis of time durations of load imbalance. The notions of Transfer Pair , and Load Sharing Window are introduced. Using first passage times, a general expression for the probability distribution function of the Load Sharing Window is derived. A class of rules, called quantile rules, is introduced. Their role in avoiding unproductive job redistribution as well as to make bulk job transfers, is explained. The general technique is applied to the specific case of a distributed computing system consisting of M/M/1 queues. For this case, an expression for the mean of the Load Sharing Window is derived. Numerical computations, in the form of graphs, are presented, and their significance discussed.