Section: New Results

Performance Evaluation of Distributed Systems

Participants : Bruno Sericola, Gerardo Rubino, Laura Aspirot, Romaric Ludinard.

In [92] and [13] , we consider the behavior of a stochastic system composed of several identically distributed, but non independent, discrete-time absorbing Markov chains competing at each instant for a transition. The competition consists in determining at each instant, using a given probability distribution, the only Markov chain allowed to make a transition. We analyze the first time at which one of the Markov chains reaches its absorbing state. We obtain its distribution and its expectation and we propose an algorithm to compute these quantities. We also exhibit the asymptotic behavior of the system when the number of Markov chains goes to infinity. Actually, this problem comes from the analysis of large-scale distributed systems and we show how our results apply to this domain.

In [14] , we present an in-depth study of the dynamicity and robustness properties of large-scale distributed systems, and in particular of peer-to-peer systems. When designing such systems, two major issues need to be faced. First, population of these systems evolves continuously (nodes can join and leave the system as often as they wish without any central authority in charge of their control), and second, these systems being open, one needs to defend against the presence of malicious nodes that try to subvert the system. Given robust operations and adversarial strategies, we propose an analytical model of the local behavior of clusters, based on Markov chains. This local model provides an evaluation of the impact of malicious behaviors on the correctness of the system. Moreover, this local model is used to evaluate analytically the performance of the global system, allowing to characterize its global behavior with respect to its dynamics and to the presence of malicious nodes, and then to validate our approach.

Monitoring a system is the ability of collecting and analyzing relevant information provided by the monitored devices so as to be continuously aware of the system's state. However, the ever growing complexity and scale of systems makes both real time monitoring and fault detection a quite tedious task. The usually adopted option is to focus solely on a subset of information states, so as to provide coarse-grained indicators. As a consequence, detecting isolated failures or anomalies is a quite challenging issue. In [34] , we propose to address this issue by pushing the monitoring task at the edge of the network. We present a peer-to-peer-based architecture, which enables nodes to self-organize according to their “health” indicators. By exploiting both temporal and spatial correlations that exist between a device and its vicinity, our approach guarantees that only isolated anomalies (an anomaly is isolated if it impacts solely a monitored device) are reported on the fly to the network operator. We show that the end-to-end detection process, i.e., from the local detection to the management operator reporting, requires a logarithmic number of messages in the size of the network. This work led to the patent [91] with Technicolor.

In [66] we continued previous efforts in the design of peer-to-peer networks for transmitting video content. In the past, we develop tools allowing a perceptual quality-based design tool. In [66] , we explore an architectural idea where the video stream is decomposed in sequential sets of chunks that we call “windows”. The paper explores some aspects of the performance of such a transmission scheme. The techniques used are Markovian models which are simulated, and deterministic dynamical systems that allow for some equilibrium analysis.