处理器共享系统中的多对称性
Poly-Symmetry in Processor-Sharing Systems
摘要：
我们考虑一个系统的处理器共享队列与状态相关的服务率。这些是根据一个polymatroid容量集内的平衡公平分配的。平衡的公平性在这样的系统中既不敏感又是帕累托有效的，这确保了性能指标在可计算时将提供对所考虑的系统的真实性能的鲁棒洞察。我们首先表明，这些性能指标可以评估的复杂性是多项式的系统大小，如果系统被划分成有限数量的部分，使队列是可交换的每个部分和不同的部分之间的不对称。这反过来又使我们能够推导出一个更大的一类系统，满足较少限制的对称性假设的随机界。这些结果被应用到树型数据网的实际例子，如互联网服务提供商的回程网络和计算机集群。
英文摘要：
We consider a system of processor-sharing queues with state-dependent service rates. These are allocated according to balanced fairness within a polymatroid capacity set. Balanced fairness is known to be both insensitive and Pareto-efficient in such systems, which ensures that the performance metrics, when computable, will provide robust insights into the real performance of the system considered. We first show that these performance metrics can be evaluated with a complexity that is polynomial in the system size if the system is partitioned into a finite number of parts, so that queues are exchangeable within each part and asymmetric across different parts. This in turn allows us to derive stochastic bounds for a larger class of systems which satisfy less restrictive symmetry assumptions. These results are applied to practical examples of tree data networks, such as backhaul networks of Internet service providers, and computer clusters.
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