Kelly Cache Networks
Abstract
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 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.
Cite
@article{arxiv.1901.04092,
title = {Kelly Cache Networks},
author = {Milad Mahdian and Armin Moharrer and Stratis Ioannidis and Edmund Yeh},
journal= {arXiv preprint arXiv:1901.04092},
year = {2019}
}
Comments
This is the extended version of the Infocom 2019 paper with the same title. The authors gratefully acknowledge support from National Science Foundation grant NeTS-1718355, as well as from research grants by Intel Corp. and Cisco Systems