Optimizing hypergraph-based polynomials modeling job-occupancy in queueing with redundancy scheduling

Abstract

We investigate two classes of multivariate polynomials with variables indexed by the edges of a uniform hypergraph and coefficients depending on certain patterns of union of edges. These polynomials arise naturally to model job-occupancy in some queuing problems with redundancy scheduling policy. The question, posed by Cardinaels, Borst and van Leeuwaarden (arXiv:2005.14566, 2020), is to decide whether their global minimum over the standard simplex is attained at the uniform probability distribution. By exploiting symmetry properties of these polynomials we can give a positive answer for the first class and partial results for the second one, where we in fact show a stronger convexity property of these polynomials over the simplex.

39 pages, including 2 figures and 10 tables

References in corpus (2)

• Symmetry groups, semidefinite programs, and sums of squares
• Semidefinite bounds for nonbinary codes based on quadruples

Cited by in corpus (1)

• Symmetry reduction to optimize a graph-based polynomial from queueing theory