A proposed solution for the load balancing problem on heterogeneous clusters based on a delayed neural network

Abstract

PurposeThe purpose of this paper is to analyze the load balancing (LB) problem in clusters of heterogeneous processors using delayed artificial neural networks theory, optimal control theory, and linear matrix inequalities (LMIs).Design/methodology/approachStarting with a mathematical model that includes delays and processors with different processing velocities, this model is transformed into a special case of a neural network model known as delayed cellular neural network (DCNN) model. A new energy function is proposed to this delayed neural network special case, assuring convergence conditions through the use of LMIs. Some performance criteria subject to stability conditions to the non‐linear model version are analyzed, and a new LB controller systematic method of synthesis is proposed, using two coupled LMIs – one guaranteeing global convergence and the other guaranteeing performance in a linear region of operation. Simulations and experiments proves the efficiency of this approach, reducing LB time with a viable computational cost for clusters with high number of processors.FindingsA new approach for the LB problem was proposed based on an special case of a delayed neural network model. Performance criterium can also be imposed over it using a quadratic cost function, giving a possibility to extend the idea to other classes of delayed neural network.Originality/valueThe novelty associated with this paper is the introduction of an approach which the LB problem on an heterogeneous cluster of local processors can be modeled as a delayed neural network and the performance of the LB algorithm can be imposed, at least locally, by a quadratic cost function. Also, the delayed neural network can also be seen as a Persidskii system with delay.