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arXiv · 2009.04510

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

Daniel Brosch·Monique Laurent·Andries Steenkamp
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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.

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Daniel Brosch, Monique Laurent, Andries Steenkamp. 2020-09-09. Optimizing hypergraph-based polynomials modeling job-occupancy in queueing with redundancy scheduling. https://doi.org/10.1137/20m1369592

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