Modelling and predicting resource allocation using eigenvalues and eigenvectors

摘要

A state of resource allocation is represented as a matrix. Each intersection of a row and column of the matrix indicates a number of units of a resource being provided by a respective node and consumed by a respective client. The allocation is modeled using a characteristic equation of the matrix. The characteristic equation is applied to the matrix to find an eigenvalue indicating a degree of scale the allocation can tolerate. An eigenvector is found for the eigenvalue to determine a direction of scale. A prediction is made as to whether the current state can scale at least one of upwards or downwards by the eigenvector.