Optimizing Hypergraph-Based Polynomials Modeling Job-Occupancy in Queuing with Redundancy Scheduling

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