Section: New Results

Content-Oriented Systems

Participants : Sara Alouf, Eitan Altman, Konstantin Avrachenkov, Nicaise Choungmo Fofack, Abdulhalim Dandoush, Majed Haddad, Alain Jean-Marie, Philippe Nain, Giovanni Neglia, Marina Sokol.

Modeling modern DNS caches

N. Choungmo Fofack and S. Alouf have pursued their study of the modern behavior of DNS (Domain Name System) caches. The entire set of traces collected in 2013 by Inria's IT services in Sophia Antipolis at one of the Inria's DNS caches have been processed and analyzed with the help of N. Nedkov (4-month intern in Maestro ). This allowed to strengthen the validation of the theoretical models developed in 2013 (see [86] ). On the other hand, parts of [86] have been revisited and derived under more general assumptions. As a direct consequence, the exact analysis derived on linear cache networks is extended to a large class of hierarchical cache networks called linear-star networks which include linear and two-level tree/star networks. In addition, closed-form expressions for the cache consistency measures (refresh rate and correctness probability) are provided under the assumption that contents requests and updates occur according to two independent renewal processes.

Analysis of general and heterogeneous cache networks

There has been considerable research on the performance analysis of on-demand caching replacement policies like Least-Recently-Used (LRU), First-In-First-Out (FIFO) or Random (RND). Much progress has been made on the analysis of a single cache running these algorithms. However it has been almost impossible to extend the results to networks of caches. In [22] , N. Choungmo Fofack, P. Nain and G. Neglia, in collaboration with D. Towsley (Univ. of Massachusetts, Amherst, USA), introduce a Time-To-Live (TTL) based caching model, that assigns a timer to each content stored in the cache and redraws it every time the content is requested (at each hit/miss). They derive the performance metrics (hit/miss ratio and rate, occupancy) of a TTL-based cache in isolation fed by stationary and ergodic request processes with general TTL distributions. Moreover they propose an iterative procedure to analyze TTL-based cache networks under the assumptions that requests are described by renewal processes (that generalize Poisson processes or the standard IRM assumption). They validate the theoretical findings through event-driven and Monte-Carlo simulations based on the Fourier Amplitude Sensitivity Test to explore the space of the input parameters. The analytic model predicts remarkably well all metrics of interest with relative errors smaller than $1\%$.

Jointly with M. Badov, M. Dehghan, D. L. Goeckel and D. Towsley (all with the Univ. of Massachusetts, Amherst, USA), N. Choungmo Fofack proposes in [81] 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. The authors take 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. This approach is validated through event-driven simulations, and when possible, compared to the existing a-NET model.

Data placement and retrieval in distributed/peer-to-peer systems

Distributed systems using a network of peers have become an alternative solution for storing data. These systems are based on three pillars: data fragmentation and dissemination among the peers, redundancy mechanisms to cope with peers churn and repair mechanisms to recover lost or temporarily unavailable data. In previous years, A. Dandoush, S. Alouf and P. Nain have studied the performance of peer-to-peer storage systems in terms of data lifetime and availability using the traditional redundancy schemes. This work has now been published in [23] .

A. Jean-Marie and O. Morad (Univ. Montpellier 2) have proposed a control-theoretic model for the optimization of prefetching in the context of hypervideo or, more generally, connected documents. The user is assumed to move randomly from document to document, and the controller attempts at downloading in advance the documents accessed. A penalty is incurred when the document is not completely present. The model is flexible in the sense that it allows several variants for the network model and the cost metric [63] . They have proposed exact algorithms and heuristics for the solution of this problem, and compared them on a benchmark of different user behaviors [62] .

The question of whether it is possible to prefetch documents so that the user never experiences blocking, has been modeled with a “cops-and-robbers” game jointly with F. Fomin (Univ. Bergen), F. Giroire and N. Nisse (both from Inria project-team Coati ) and D. Mazauric (former PhD student in Maestro and Mascotte ) [24] (see also Maestro 's 2011 activity report).

Streaming optimization

In streaming applications such as youtube, packets have to be played at the destination at the same rate they were created. If a packet is not available at the destination when it has to be played then a starvation occurs. This results in an unpleasant frozen screen and in an interruption in the video. To decrease the probability of a starvation the destination first waits till it has received some target number of packets and only then starts to play them. In [32] , E. Altman and M. Haddad together with Y. Xu (Fudan Univ. China), R. El-Azouzi and T. Jimenez (Univ. of Avignon), and S.-E. Elayoubi (Orange Labs, Issy les Moulineaux) compute the starvation probability as a function of the initial buffering and study tradeoffs between the two performance measures: starvation probabilities and the pre-buffering delay.

Stochastic geometry and network coding for distributed storage

In [37] E. Altman and K. Avrachenkov in collaboration with J. Goseling (Twente Univ., The Netherlands) consider storage devices located in the plane according to a general point process and specialize the results for the homogeneous Poisson process. A large data file is stored at the storage devices, which have limited storage capabilities. Hence, they can only store parts of the data. Clients can contact the storage devices to retrieve the data. The expected costs of obtaining the complete data under uncoded or coded data allocation strategies are compared. It is shown that for the general class of cost measures where the cost of retrieving data is increasing with the distance between client and storage devices, coded allocation outperforms uncoded allocation. The improvement offered by coding is quantified for two more specific classes of performance measures. Finally, the results are validated by computing the costs of the allocation strategies for the case that storage devices coincide with currently deployed mobile base stations.