On Resource Pooling and Separation for LRU Caching

Tan, Jian; Quan, Guocong; Ji, Kaiyi; Shroff, Ness B.

doi:10.1145/3308809.3308824

Cited by 2 publications

(4 citation statements)

References 1 publication

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“…Lemma 1 is a direct consequence of Theorem 1 in [9]. Let the data item popularity distribution on a server be (q i , i ≥ 1).…”

Section: A Proof Of Theoremmentioning

confidence: 93%

“…However, the overall conditional asymptotic miss ratio of the cluster is always the same almost surely, depending on the probability distribution of the random hash function. Due to this equivalence, we comment that the engineering implications discussed in [9] for a single LRU cache can also be extended to a LRU cluster.…”

Section: Introductionmentioning

confidence: 89%

“…and using Lemma 1 in [9], we obtain, for ∀ 1 > 0, there exists a large x 2 such that for all x > x 2 ,…”

Section: A Proof Of Theoremmentioning

confidence: 94%

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Asymptotic Miss Ratio of LRU Caching with Consistent Hashing

Quan

Tan

2018

IEEE INFOCOM 2018 - IEEE Conference on Computer Communications

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To efficiently scale data caching infrastructure to support emerging big data applications, many caching systems rely on consistent hashing to group a large number of servers to form a cooperative cluster. These servers are organized together according to a random hash function. They jointly provide a unified but distributed hash table to serve swift and voluminous data item requests. Different from the single least-recentlyused (LRU) server that has already been extensively studied, theoretically characterizing a cluster that consists of multiple LRU servers remains yet to be explored. These servers are not simply added together; the random hashing complicates the behavior. To this end, we derive the asymptotic miss ratio of data item requests on a LRU cluster with consistent hashing. We show that these individual cache spaces on different servers can be effectively viewed as if they could be pooled together to form a single virtual LRU cache space parametrized by an appropriate cache size. This equivalence can be established rigorously under the condition that the cache sizes of the individual servers are large. For typical data caching systems this condition is common. Our theoretical framework provides a convenient abstraction that can directly apply the results from the simpler single LRU cache to the more complex LRU cluster with consistent hashing.

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“…Lemma 1 is a direct consequence of Theorem 1 in [9]. Let the data item popularity distribution on a server be (q i , i ≥ 1).…”

Section: A Proof Of Theoremmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 89%

See 1 more Smart Citation

Asymptotic Miss Ratio of LRU Caching with Consistent Hashing

Quan

Tan

2018

IEEE INFOCOM 2018 - IEEE Conference on Computer Communications

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“…To provide a neat version of thesis with closely correlated topics, this thesis does not include all of the author's works. We briefly talk about some representatives of the author's other research works [56,64,59,123,61,60,125,101,116,47,130,129,133] as follows.…”

Section: Other Phd Researchmentioning

confidence: 99%

Bilevel Optimization for Machine Learning: Algorithm Design and Convergence Analysis

2021

Preprint

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Bilevel optimization has become a powerful framework in a variety of machine learning applications including signal processing, meta-learning, hyperparameter optimization, reinforcement learning and network architecture search. There are generally two classes of bilevel optimization formulations for modern machine learning: 1) problem-based bilevel optimization, whose inner-level problem is formulated as finding a minimizer of a given loss function; and 2) algorithm-based bilevel optimization, whose inner-level solution is an output of a fixed algorithm. For the first problem class, two popular types of gradient-based algorithms have been proposed to estimate the gradient of the outer-level objective (hypergradient) via approximate implicit differentiation (AID) and iterative differentiation (ITD). Algorithms for the second problem class include the popular model-agnostic meta-learning (MAML) and almost no inner loop (ANIL). Although bilevel optimization algorithms have been widely used, their convergence rate and fundamental limitations have not been well explored.

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On Resource Pooling and Separation for LRU Caching

Cited by 2 publications

References 1 publication

Asymptotic Miss Ratio of LRU Caching with Consistent Hashing

Asymptotic Miss Ratio of LRU Caching with Consistent Hashing

Bilevel Optimization for Machine Learning: Algorithm Design and Convergence Analysis

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