Optimizing hypergraph-based polynomials modeling job-occupancy in queueing with redundancy scheduling
Résumé
We investigate two classes of multivariate polynomials with vari-ables indexed by the edges of a uniform hypergraph and coefficientsde-pending 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, Borstand van Leeuwaarden (arXiv:2005.14566, 2020), is to decide whethertheir global minimum over the standard simplex is attained at the uni-form probability distribution. By exploiting symmetry properties ofthese polynomials we can give a positive answer for the first class andpartial results for the second one, where we in fact show a stronger convexity property of these polynomials over the simplex
Domaines
Mathématiques [math]
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