The goal of the POLARIS project is to contribute to the understanding (from the observation, modeling and analysis to the actual optimization through adapted algorithms) of the performance of very large scale distributed systems by applying original ideas from various research fields and application domains. Studying all these different aspects at once without restricting to specific systems is the key to push forward our understanding of such challenges and propose innovative solutions. If large computing infrastructures are naturally among our targets, the synergies with other data intensive sciences leads us to consider other kind of big data processing infrastructures as well. This is why we investigate problems arising from application domains as varied as large computing infrastructures, wireless networks, smart grids or transportation systems. The POLARIS team works in close cooperation with other research teams on a continuum of five research themes including measurement and experimentation, statistical trace analysis and visualization, discrete-event and perfect simulation, asymptotic modeling, stochastic optimization and game theory.