Kelly Cache Networks

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 pla...

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Bibliographic Details
Published in:IEEE/ACM transactions on networking Vol. 28; no. 3; pp. 1130 - 1143
Main Authors: Mahdian, Milad, Moharrer, Armin, Ioannidis, Stratis, Yeh, Edmund
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Approximation algorithms
cache networks
Continuous casting
Delays
Greedy algorithms
ICN
IEEE transactions
Kelly networks
Networks
Nodes
Optimization
Peer-to-peer computing
Power series
Queues
Queuing theory
Servers
Steady-state
ISSN:1063-6692, 1558-2566
Online Access:Get full text
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Summary: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 <inline-formula> <tex-math notation="LaTeX">1-1/e\approx 0.63 </tex-math></inline-formula> 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/<inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> and symmetric M/D/1 queues.
Bibliography:ObjectType-Article-1
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ISSN:1063-6692
1558-2566
DOI:10.1109/TNET.2020.2982863