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arXiv 2005.13847cs.ITmath.IT
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随机共享Cache网络的基本极限

Fundamental Limits of Stochastic Shared Caches Networks

Adeel Malik, Berksan Serbetci, Emanuele Parrinello, Petros Elia

摘要:

这项工作建立了确切的性能限制随机编码缓存时,用户共享有限数量的缓存状态,当用户和缓存之间的关联,是随机的。在更平衡的用户到缓存的关联比不平衡的关联表现得更好的前提下,我们的工作提供了一个这样的网络的平均性能的统计分析,确定在封闭的形式,确切的最佳平均交付时间。为了深刻地捕捉这种延迟,我们推导出易于计算的封闭形式的分析界限,证明严格的限制大量的$Λ$的缓存状态。在交付涉及$K$用户的情况下,我们得出结论,由于随机性导致的乘法性能恶化-与众所周知的确定性均匀情况相比-可以是无界的,并且可以在$K=Θ\left(Λ\right)$上扩展为$Θ\left( \frac{\log Λ}{\log \log Λ} \right)$,并且当$K=Ω\left(Λ\log Λ\right)$时,这种扩展消失。为了减轻这种不利影响的缓存负载不平衡,我们考虑各种负载均衡方法,并表明,采用接近有界的负载均衡的能力,选择从$h$相邻的缓存,上述缩放减少到$Θ\left(\frac{\log(Λ/ h)}{ \log \log(Λ/ h)} \right)$,而当邻近约束被删除,缩放是一个慢得多的顺序$Θ\left( \log \log Λ\right)$。上述分析得到了广泛的数值验证。

英文摘要:

The work establishes the exact performance limits of stochastic coded caching when users share a bounded number of cache states, and when the association between users and caches, is random. Under the premise that more balanced user-to-cache associations perform better than unbalanced ones, our work provides a statistical analysis of the average performance of such networks, identifying in closed form, the exact optimal average delivery time. To insightfully capture this delay, we derive easy to compute closed-form analytical bounds that prove tight in the limit of a large number $Λ$ of cache states. In the scenario where delivery involves $K$ users, we conclude that the multiplicative performance deterioration due to randomness -- as compared to the well-known deterministic uniform case -- can be unbounded and can scale as $Θ\left( \frac{\log Λ}{\log \log Λ} \right)$ at $K=Θ\left(Λ\right)$, and that this scaling vanishes when $K=Ω\left(Λ\log Λ\right)$. To alleviate this adverse effect of cache-load imbalance, we consider various load balancing methods, and show that employing proximity-bounded load balancing with an ability to choose from $h$ neighboring caches, the aforementioned scaling reduces to $Θ\left(\frac{\log(Λ/ h)}{ \log \log(Λ/ h)} \right)$, while when the proximity constraint is removed, the scaling is of a much slower order $Θ\left( \log \log Λ\right)$. The above analysis is extensively validated numerically.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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