79 research outputs found
TTL Approximations of the Cache Replacement Algorithms LRU(m) and h-LRU
International audienceComputer system and network performance can be significantly improved by caching frequently used information. When the cache size is limited, the cache replacement algorithm has an important impact on the effectiveness of caching. In this paper we introduce time-to-live (TTL) approximations to determine the cache hit probability of two classes of cache replacement algorithms: h-LRU and LRU(m). These approximations only require the requests to be generated according to a general Markovian arrival process (MAP). This includes phase-type renewal processes and the IRM model as special cases. We provide both numerical and theoretical support for the claim that the proposed TTL approximations are asymptotically exact. In particular, we show that the transient hit probability converges to the solution of a set of ODEs (under the IRM model), where the fixed point of the set of ODEs corresponds to the TTL approximation. We use this approximation and trace-based simulation to compare the performance of h-LRU and LRU(m). First, we show that they perform alike, while the latter requires less work when a hit/miss occurs. Second, we show that as opposed to LRU, h-LRU and LRU(m) are sensitive to the correlation between consecutive inter-request times. Last, we study cache partitioning. In all tested cases, the hit probability improved by partitioning the cache into different parts—each being dedicated to a particular content provider. However, the gain is limited and the optimal partition sizes are very sensitive to the problem's parameters
A unified approach to the performance analysis of caching systems
We propose a unified methodology to analyse the performance of caches (both
isolated and interconnected), by extending and generalizing a decoupling
technique originally known as Che's approximation, which provides very accurate
results at low computational cost. We consider several caching policies, taking
into account the effects of temporal locality. In the case of interconnected
caches, our approach allows us to do better than the Poisson approximation
commonly adopted in prior work. Our results, validated against simulations and
trace-driven experiments, provide interesting insights into the performance of
caching systems.Comment: in ACM TOMPECS 20016. Preliminary version published at IEEE Infocom
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Adaptive TTL-Based Caching for Content Delivery
Content Delivery Networks (CDNs) deliver a majority of the user-requested
content on the Internet, including web pages, videos, and software downloads. A
CDN server caches and serves the content requested by users. Designing caching
algorithms that automatically adapt to the heterogeneity, burstiness, and
non-stationary nature of real-world content requests is a major challenge and
is the focus of our work. While there is much work on caching algorithms for
stationary request traffic, the work on non-stationary request traffic is very
limited. Consequently, most prior models are inaccurate for production CDN
traffic that is non-stationary.
We propose two TTL-based caching algorithms and provide provable guarantees
for content request traffic that is bursty and non-stationary. The first
algorithm called d-TTL dynamically adapts a TTL parameter using a stochastic
approximation approach. Given a feasible target hit rate, we show that the hit
rate of d-TTL converges to its target value for a general class of bursty
traffic that allows Markov dependence over time and non-stationary arrivals.
The second algorithm called f-TTL uses two caches, each with its own TTL. The
first-level cache adaptively filters out non-stationary traffic, while the
second-level cache stores frequently-accessed stationary traffic. Given
feasible targets for both the hit rate and the expected cache size, f-TTL
asymptotically achieves both targets. We implement d-TTL and f-TTL and evaluate
both algorithms using an extensive nine-day trace consisting of 500 million
requests from a production CDN server. We show that both d-TTL and f-TTL
converge to their hit rate targets with an error of about 1.3%. But, f-TTL
requires a significantly smaller cache size than d-TTL to achieve the same hit
rate, since it effectively filters out the non-stationary traffic for
rarely-accessed objects
An approximate analysis of heterogeneous and general cache networks
In this paper, we propose approximate models to assess the performance of a cache network with arbitrary topology where nodes run the Least Recently Used (LRU), First-In First-Out (FIFO), or Random (RND) replacement policies on arbitrary size caches. Our model takes advantage of the notions of cache characteristic time and Time-To-Live (TTL)-based cache to develop a unified framework for approximating metrics of interest of interconnected caches. Our approach is validated through event-driven simulations; and when possible, compared to the existing a-NET model [23].Dans ce travail, nous proposons des modèles approximatifs pour évaluer les performances d'un réseau de caches ayant une topologie arbitraire où les noeuds exécutent les politiques Least Recently Used (LRU), First In First Out (FIFO), ou Random replacement (RND) sur des caches de taille quelconque. Notre modèle tire parti des notions de temps caractéristique d'un cache et des modèles Time-To-Live (TTL) de cache pour développer une approche unifiée pour l'approximation des métriques de performance sur des caches interconnectés. Notre approche est validée par des simulations événementielles; et, si possible, comparée au modèle existant a-NET [23]
Stationary Distribution of a Generalized LRU-MRU Content Cache
Many different caching mechanisms have been previously proposed, exploring
different insertion and eviction policies and their performance individually
and as part of caching networks. We obtain a novel closed-form stationary
invariant distribution for a generalization of LRU and MRU caching nodes under
a reference Markov model. Numerical comparisons are made with an "Incremental
Rank Progress" (IRP a.k.a. CLIMB) and random eviction (a.k.a. random
replacement) methods under a steady-state Zipf popularity distribution. The
range of cache hit probabilities is smaller under MRU and larger under IRP
compared to LRU. We conclude with the invariant distribution for a special case
of a random-eviction caching tree-network and associated discussion
On Resource Pooling and Separation for LRU Caching
Caching systems using the Least Recently Used (LRU) principle have now become
ubiquitous. A fundamental question for these systems is whether the cache space
should be pooled together or divided to serve multiple flows of data item
requests in order to minimize the miss probabilities. In this paper, we show
that there is no straight yes or no answer to this question, depending on
complex combinations of critical factors, including, e.g., request rates,
overlapped data items across different request flows, data item popularities
and their sizes. Specifically, we characterize the asymptotic miss
probabilities for multiple competing request flows under resource pooling and
separation for LRU caching when the cache size is large.
Analytically, we show that it is asymptotically optimal to jointly serve
multiple flows if their data item sizes and popularity distributions are
similar and their arrival rates do not differ significantly; the
self-organizing property of LRU caching automatically optimizes the resource
allocation among them asymptotically. Otherwise, separating these flows could
be better, e.g., when data sizes vary significantly. We also quantify critical
points beyond which resource pooling is better than separation for each of the
flows when the overlapped data items exceed certain levels. Technically, we
generalize existing results on the asymptotic miss probability of LRU caching
for a broad class of heavy-tailed distributions and extend them to multiple
competing flows with varying data item sizes, which also validates the Che
approximation under certain conditions. These results provide new insights on
improving the performance of caching systems
Exact Analysis of TTL Cache Networks: The Case of Caching Policies driven by Stopping Times
TTL caching models have recently regained significant research interest,
largely due to their ability to fit popular caching policies such as LRU. This
paper advances the state-of-the-art analysis of TTL-based cache networks by
developing two exact methods with orthogonal generality and computational
complexity. The first method generalizes existing results for line networks
under renewal requests to the broad class of caching policies whereby evictions
are driven by stopping times. The obtained results are further generalized,
using the second method, to feedforward networks with Markov arrival processes
(MAP) requests. MAPs are particularly suitable for non-line networks because
they are closed not only under superposition and splitting, as known, but also
under input-output caching operations as proven herein for phase-type TTL
distributions. The crucial benefit of the two closure properties is that they
jointly enable the first exact analysis of feedforward networks of TTL caches
in great generality
Cache Miss Estimation for Non-Stationary Request Processes
The aim of the paper is to evaluate the miss probability of a Least Recently
Used (LRU) cache, when it is offered a non-stationary request process given by
a Poisson cluster point process. First, we construct a probability space using
Palm theory, describing how to consider a tagged document with respect to the
rest of the request process. This framework allows us to derive a general
integral formula for the expected number of misses of the tagged document.
Then, we consider the limit when the cache size and the arrival rate go to
infinity proportionally, and use the integral formula to derive an asymptotic
expansion of the miss probability in powers of the inverse of the cache size.
This enables us to quantify and improve the accuracy of the so-called Che
approximation
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