Fair sharing of resources in a supply network with constraints
Fair sharing of resources in a supply network with constraints
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DOI：
10.1103/physreve.85.046101
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发表时间：
2012-04-02
影响因子：
2.4
通讯作者：
Arrowsmith, David K.
中科院分区：
文献类型：
--
作者：
Carvalho, Rui;Buzna, Lubos;Arrowsmith, David K.
本文研究了网络拓扑对一组代理之间网络资源公平分配的影响，这是我们周围交通网络效率的一个非常重要的问题。我们分析了一种在现有流量需求之间公平分配网络容量的通用机制。当传输发生在最短路径上时，可以通过具有一对源和汇的最近邻图上的半解析方法来解决该问题。对于此设置，我们揭示了作为源和汇之间距离的函数的相交最短路径的广泛模式。当交叉点数量最多且源点和汇点之间的距离较大时，我们发现公平分配意味着最大吞吐量至少下降 50%。我们还发现分配给代理的流量分配的直方图按照指数为 -1 的幂律衰减。我们的半分析框架对众所周知的公平分配吞吐量下降提出了可能的解释。它还表明，网络拓扑和路由规则的组合可能会导致资源分配高度不均匀（但公平），这是网络设计者需要注意的一个事项。
This paper investigates the effect of network topology on the fair allocation of network resources among a set of agents, an all-important issue for the efficiency of transportation networks all around us. We analyze a generic mechanism that distributes network capacity fairly among existing flow demands. The problem can be solved by semianalytical methods on a nearest-neighbor graph with one source and sink pair, when transport occurs over shortest paths. For this setup, we uncover a broad range of patterns of intersecting shortest paths as a function of the distance between the source and the sink. When the number of intersections is the maximum and the distance between the source and the sink is large, we find that a fair allocation implies a decrease of at least 50% from the maximum throughput. We also find that the histogram of the flow allocations assigned to the agents decays as a power law with exponent -1. Our semianalytical framework suggests possible explanations for the well-known reduction of the throughput in fair allocations. It also suggests that the combination of network topology and routing rules can lead to highly uneven (but fair) distributions of resources, a remark of caution to network designers.