A versatile and accurate approximation for LRU cache performance

In a 2002 paper, Che and co-authors proposed a simple approach for estimating the hit rates of a cache operating the least recently used (LRU) replacement policy. The approximation proves remarkably accurate and is applicable to quite general distributions of object popularity. This paper provides a mathematical explanation for the success of the approximation, notably in configurations where the intuitive arguments of Che, et al clearly do not apply. The approximation is particularly useful in evaluating the performance of current proposals for an information centric network where other approaches fail due to the very large populations of cacheable objects to be taken into account and to their complex popularity law, resulting from the mix of different content types and the filtering effect induced by the lower layers in a cache hierarchy

The limiting move-to-front search-cost in law of large numbers asymptotic regimes

We explicitly compute the limiting transient distribution of the search-cost in the move-to-front Markov chain when the number of objects tends to infinity, for general families of deterministic or random request rates. Our techniques are based on a "law of large numbers for random partitions," a scaling limit that allows us to exactly compute limiting expectation of empirical functionals of the request probabilities of objects. In particular, we show that the limiting search-cost can be split at an explicit deterministic threshold into one random variable in equilibrium, and a second one related to the initial ordering of the list. Our results ensure the stability of the limiting search-cost under general perturbations of the request probabilities. We provide the description of the limiting transient behavior in several examples where only the stationary regime is known, and discuss the range of validity of our scaling limit.Comment: Published in at http://dx.doi.org/10.1214/09-AAP635 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Comparing Strength of Locality of Reference: Popularity, Temporal Correlations, and Some Folk Theorems for the Miss Rates and Outputs of Caches

The performance of demand-driven caching is known to depend on the locality of reference exhibited by the stream of requests made to the cache. In spite of numerous efforts, no consensus has been reached on how to formalize this notion, let alone on how to compare streams of requests on the basis of their locality of reference. We take on this issue with an eye towards validating operational expectations associated with the notion of locality of reference. We focus on two ``folk theorems," that is, (i) The stronger the locality of reference, the smaller the miss rate of the cache; and (ii) Good caching is expected to produce an output stream of requests exhibiting less locality of reference than the input stream of requests. These two folk theorems are explored in the context of demand-driven caching for the two main contributors of locality of reference, namely popularity and temporal correlations. We first focus exclusively on popularity by considering the situation where there are no temporal correlations in the stream of requests, as would be the case under the Independent Reference Model (IRM). As we propose to measure strength of locality of reference in a stream of requests through the skewness of its popularity distribution, we introduce the notion of majorization as a means for capturing this degree of skewness. We show that these folk theorems hold for caches operating under a large class of replacement policies, the so-called Random On-demand Replacement Algorithms (RORA), which includes the optimal policy $A_0$ and the random policy. However, counterexamples prove that this is not always the case under the (popular) Least-Recently-Used (LRU) and CLIMB policies. In such cases, conjectures are offered (and supported by simulations) as to when the folk theorems would hold under the LRU or CLIMB caching, given that the IRM input has a Zipf-like popularity pmf. To compare the strength of temporal correlations in streams of requests, we define the notion of Temporal Correlations (TC) ordering based on the so-called supermodular ordering, a concept of positive dependence which has been successfully used for comparing dependence structures in sequences of random variables. We explore how the TC ordering captures the strength of temporal correlations in several Web request models, namely the higher-order Markov chain model (HOMM), the partial Markov chain model (PMM) and the Least-Recently-Used stack model (LRUSM). We establish the folk theorem to the effect that the stronger the strength of temporal correlations, the smaller the miss rate for the PMM under certain assumptions on the caching policy. Conjectures and simulations are offered as to when this folk theorem would hold under the HOMM and under the LRUSM. In addition, the validity of this folk theorem for general request streams under the Working Set algorithm is studied. Lastly, we investigate how the majorization and TC orderings can be translated into comparisons of three well-known locality of reference metrics, namely the working set size, the inter-reference time and the stack distance

Stochastic ranking process with space-time dependent intensities

We consider the stochastic ranking process with space-time dependent jump rates for the particles. The process is a simplified model of the time evolution of the rankings such as sales ranks at online bookstores. We prove that the joint empirical distribution of jump rate and scaled position converges almost surely to a deterministic distribution, and also the tagged particle processes converge almost surely, in the infinite particle limit. The limit distribution is characterized by a system of inviscid Burgers-like integral-partial differential equations with evaporation terms, and the limit process of a tagged particle is a motion along a characteristic curve of the differential equations except at its Poisson times of jumps to the origin

Traffic and resource management in content-centric networks (design and evaluation)

Dans les dernières années, l utilisation d Internet a sensiblement changé en passant d un modèle de communication centré sur les machines á un centré sur les contenus. La plus part de services utilisés par les clients d Internet aujourd hui sont déjà centré sur les contenus même et pas sur leurs emplacement. Dans ce contexte, beaucoup de projets de recherche proposent un changement de l architecture de l Internet, en mettent des contenu identifié par leur nom au centre du réseau. Ce group de proposition est identifiés sous le nom de Information Centric Networking (ICN). Cette thèse se focalise sur la proposition Content-Centric Network (CCN). Dans une premier temps, nous analysons les performance du modèle de communication CCN en se concentrent sur le partage de la bande passante et de la mémoire et en proposant des formules pour la caractérisation du temps de transfert. Deuxièmement, nous proposons un protocole de contrôle de congestion et des mécanismes de forwarding pour CCN. En particulier on présent un premier mécanisme de contrôle de congestion, Interest Control Protocol (ICP), qui utilise une fenêtre contrôlé avec le mécanisme Additive Increase Multiplicative Decrease au récepteur. En complément avec ça, nous présentons un mécanisme distribué (hop-by-hop) pour obtenir une détection/réaction à la congestion plus rapide. Nous proposons aussi une modification d'ICP en implémentant le mécanisme Remote Adaptive Active Queue Management pour exploiter efficacement le multi-chemin. En fin, nous présentons un mécanisme de forwarding distribué qui base ses décisions sur des mesure de qualité d interface par chaque préfixe disponible dans les tableaux de routage.The advent of the World Wide Web has radically changed Internet usage from host-to-host to service access and data retrieval. The majority of services used by Internet s clients are content-centric (e.g. web). However, the original Internet revolves around host-to-host communication for which it was conceived. Even if Internet has been able to address the challenges offered by new applications, there is an evident mismatch between the architecture and its current usage. Many projects in national research agencies propose to redesign the Internet architecture around named data. Such research efforts are identified under the name of Information Centric Networking. This thesis focuses on the Content-Centric Networking (CCN) proposition. We first analyze the CCN communication model with particular focus on the bandwidth and storage sharing performance, We compute closed formulas for data delivery time, that we use in the second part of the thesis as guideline for network protocol design. Second, we propose some CCN congestion control and forwarding mechanisms. We present a first window based receiver driven flow control protocol, Interest Control Protocol (ICP). We also introduce a hop-by-hop congestion control mechanism to obtain early congestion detection and reaction. We then extend the original ICP congestion control protocol implementing a Remote Adaptive Active Queue Management mechanism in order to efficiently exploit heterogeneous (joint/disjoint) network paths. Finally, we introduce a distributed forwarding mechanism that bases its decisions on per prefix and per interface quality measurement without impacting the system scalability.PARIS-Télécom ParisTech (751132302) / SudocSudocFranceF