The aggregate capacity of virtual resources – linear models

Abstract

This article addresses resource modelling with a specific interest on capacity aggregation. The capacity of a resource with regard to d types of tasks is modelled by a simplex and by a cube in the d-dimensional space. The aggregate capacity model of a virtual resource, that is, of a pool of r resources, is the d-polytope provided by the Minkowski sum of the simplices and cubes modelling the resources. The parametric identification of the d-planes supporting the facets of the polytope is established for r = 2 and linear simplifications are provided in the (r, d) general case. Formulated as linear inequalities, the aggregate capacity models fit in with linear programming and quadratic programming optimization techniques.

Keywords:

• virtual resource
• aggregate capacity
• piecewise linear constraints
• Minkowski sum

AMS Subject Classifications::

• 51B20
• 52B70
• 91B32