论文标题
优化基于超法的多项式建模在排队中进行冗余调度
Optimizing hypergraph-based polynomials modeling job-occupancy in queueing with redundancy scheduling
论文作者
论文摘要
我们研究了两类的多元多项式，其变量由均匀的超图和系数的边缘索引，具体取决于边缘联合的某些模式。这些多项式自然而然地是为了在一些排队问题的问题中建模工作，并具有冗余调度策略。由Cardineels，Borst和Van Leeuwaarden提出的问题（Arxiv：2005.14566，2020）是为了决定是否在统一的概率分布下实现了其全球最小值。通过利用这些多项式的对称特性，我们可以为第二类和部分结果给出积极的答案，实际上，我们实际上显示了这些多项式在单纯形上具有更强的凸性属性。
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.
