Approximate analysis of LRU in the case of short term correlations

Panagakis, Antonis; Vaios, Athanasios; Stavrakakis, Ioannis

doi:10.1016/j.comnet.2007.12.006

Cited by 9 publications

(10 citation statements)

References 14 publications

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“…In particular, [17] studies the performance of a LRU cache fed by correlated requests, where the instantaneous request distribution depends on a stationary modulating Markov process; the asymptotic performance is identical to that under IRM, showing that such a short-term correlation does not fully capture the content dynamics. [21] also estimates the performance of a LRU cache when the requests form a Markov chain, but no closed-form formula is provided. [10] and [19] provide a theoretical analysis of a network of LRU cache, when requests for a given document form an arbitrary renewal process; correlation among requests can thus be incorporated, but the catalog of document remains static.…”

Section: Related Workmentioning

confidence: 99%

Catalog dynamics: Impact of content publishing and perishing on the performance of a LRU cache

Olmos

Kauffmann

Simonian

et al. 2014

2014 26th International Teletraffic Congress (ITC)

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The Internet heavily relies on Content Distribution Networks and transparent caches to cope with the ever-increasing traffic demand of users. Content, however, is essentially versatile: once published at a given time, its popularity vanishes over time. All requests for a given document are then concentrated between the publishing time and an effective perishing time.In this paper, we propose a new model for the arrival of content requests, which takes into account the dynamical nature of the content catalog. Based on two large traffic traces collected on the Orange network, we use the semi-experimental method and determine invariants of the content request process. This allows us to define a simple mathematical model for content requests; by extending the so-called "Che approximation", we then compute the performance of a LRU cache fed with such a request process, expressed by its hit ratio. We numerically validate the good accuracy of our model by comparison to tracebased simulation.

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Section: Related Workmentioning

confidence: 99%

Catalog dynamics: Impact of content publishing and perishing on the performance of a LRU cache

Olmos

Kauffmann

Simonian

et al. 2014

2014 26th International Teletraffic Congress (ITC)

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“…al. [31] present approximate analysis for streams that have short term correlations for requests. Since in cache network we see the opposite effect, with content requested recently less likely to be requested next, this approach is less useful here without modifications.…”

Section: A Irm Exogenous Request Streamsmentioning

confidence: 99%

On the steady-state of cache networks

Rosensweig

Menasché

Kurose

2013

2013 Proceedings IEEE INFOCOM

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Abstract-A shift has recently begun taking place regarding the manner in which researchers are thinking about networking in the Internet. In addition to the traditional host-to-host communication that has endured for more than four decades, many researchers have begun to focus on Content Networking -a networking model in which host-to-content interaction is the norm. A central component of such an architecture is a large-scale interconnected caching system. To date, very little is understood about the way these networks of such caches behave and perform.In this work, we demonstrate that certain cache networks are non-ergodic in that their steady-state characterization depends on the initial state of the system. We then establish several important properties of cache networks, in the form of three sufficient conditions for a cache network to be ergodic. Each property targets a different aspect of the system -topology, admission control and cache replacement policies. Perhaps most importantly we demonstrate that cache replacement can be grouped into equivalence classes, such that the ergodicity (or lack-thereof) of one policy implies the same property holds for all policies in the class.

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“…We are not aware of any prior stochastic analysis of offline optimal caching. In the context of online caching policies, there is an extensive body of work using stochastic assumptions similar to ours [58,43,25,65,20,45,29,82,38,37,52,31,76,26,53,73,75,41,86,72,40,63,15,14,42,80,54,12], of which five prove optimality results [2,6,72,36,49]. Unfortunately, these results are only for objects with equal sizes, and these policies perform poorly in our experiments because they do not account for object size.…”

Section: Prior Bounds On Opt With Variable Object Sizes Are Impracticalmentioning

confidence: 98%

“…To do this, our approach is two-fold. First, we prove that FOO gives tight bounds on traces that obey the independent reference model (IRM), the most common assumptions used in prior analysis of online policies [2,58,43,25,65,20,45,29,82,38,37,52,31,76,26,53,73,75,41,86,72,40,63,15,14,42,80,54]. The IRM assumption is only needed for the proof; FOO is designed to work on any trace and does not itself rely on any properties of the IRM.…”

Section: Offline Bounds Are More Robust Than Online Boundsmentioning

confidence: 99%

Practical Bounds on Optimal Caching with Variable Object Sizes

Berger

Beckmann

2018

Proc. ACM Meas. Anal. Comput. Syst.

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Many recent caching systems aim to improve miss ratios, but there is no good sense among practitioners of how much further miss ratios can be improved. In other words, should the systems community continue working on this problem?Currently, there is no principled answer to this question. In practice, object sizes often vary by several orders of magnitude, where computing the optimal miss ratio (OPT) is known to be NP-hard. The few known results on caching with variable object sizes provide very weak bounds and are impractical to compute on traces of realistic length.We propose a new method to compute upper and lower bounds on OPT. Our key insight is to represent caching as a min-cost flow problem, hence we call our method the flow-based offline optimal (FOO). We prove that, under simple independence assumptions, FOO's bounds become tight as the number of objects goes to infinity. Indeed, FOO's error over 10M requests of production CDN and storage traces is negligible: at most 0.3%. FOO thus reveals, for the first time, the limits of caching with variable object sizes.While FOO is very accurate, it is computationally impractical on traces with hundreds of millions of requests. We therefore extend FOO to obtain more efficient bounds on OPT, which we call practical flow-based offline optimal (PFOO). We evaluate PFOO on several full production traces and use it to compare OPT to prior online policies. This analysis shows that current caching systems are in fact still far from optimal, suffering 11-43% more cache misses than OPT, whereas the best prior offline bounds suggest that there is essentially no room for improvement.

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Approximate analysis of LRU in the case of short term correlations

Cited by 9 publications

References 14 publications

Catalog dynamics: Impact of content publishing and perishing on the performance of a LRU cache

Catalog dynamics: Impact of content publishing and perishing on the performance of a LRU cache

On the steady-state of cache networks

Practical Bounds on Optimal Caching with Variable Object Sizes

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