We study networks of M/M/1 queues in which nodes act as caches that store objects. Exogenous requests for objects are routed towards nodes that store them; as a result, object traffic in the network is determined not only by demand but, crucially, by where objects are cached. We determine how to place objects in caches to attain a certain design objective, such as, e.g., minimizing network congestion or retrieval delays. We show that for a broad class of objectives, including minimizing both the expected network delay and the sum of network queue lengths, this optimization problem can be cast as an NP-hard submodular maximization problem. We show that so-called continuous greedy algorithm attains a ratio arbitrarily close to $1-1/e\approx 0.63$ using a deterministic estimation via a power series; this drastically reduces execution time over prior art, which resorts to sampling. Finally, we show that our results generalize, beyond M/M/1 queues, to networks of M/M/ $k$ and symmetric M/D/1 queues.

中文翻译：

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凯利缓存网络

我们研究M / M / 1队列的网络，其中节点充当存储对象的缓存。对对象的外来请求被路由到存储对象的节点；结果，网络中的对象流量不仅取决于需求，而且还取决于对象的缓存位置。我们确定如何将对象放置在缓存中以实现某个设计目标，例如最大程度地减少网络拥塞或检索延迟。我们表明，对于广泛的目标类别（包括最小化预期的网络延迟和网络队列长度的总和），可以将此优化问题转换为NP硬子模最大化问题。我们证明了所谓的持续的贪婪 算法达到任意接近的比率 $ 1-1 / e \约0.63 $ 通过幂级数使用确定性估计；与采用采样的现有技术相比，这大大减少了执行时间。最后，我们表明，我们的结果将M / M / 1队列以外的内容推广到M / M / $ k $ 和对称的M / D / 1队列。