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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2020

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

Monique Laurent
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Daniel Brosch
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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
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Dates et versions

hal-03141433 , version 1 (15-02-2021)

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  • HAL Id : hal-03141433 , version 1

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Monique Laurent, Andries Steenkamp, Daniel Brosch. Optimizing hypergraph-based polynomials modeling job-occupancy in queueing with redundancy scheduling. SIAM Journal on Control and Optimization, 2020. ⟨hal-03141433⟩
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