## Section: New Results

### Performance Evaluation

#### Computing the Throughput of Probabilistic and Replicated Streaming Applications

In [8] , we investigate how to compute the throughput of probabilistic and replicated streaming applications. We are given (i) a streaming application whose dependence graph is a linear chain; (ii) a one-to-many mapping of the application onto a fully heterogeneous target platform, where a processor is assigned at most one application stage, but where a stage can be replicated onto a set of processors; and (iii) a set of random variables modeling the computation and communication times in the mapping. We show how to compute the throughput of the application, i.e., the rate at which data sets can be processed, under two execution models, the Strict model where the actions of each processor are sequentialized, and the Overlap model where a processor can compute and communicate in parallel. The problem is easy when application stages are not replicated, i.e., assigned to a single processor: in that case the throughput is dictated by the critical hardware resource. However, when stages are replicated, i.e., assigned to several processors, the problem becomes surprisingly complicated: even in the deterministic case, the optimal throughput may be lower than the smallest internal resource throughput. The first contribution of the paper is to provide a general method to compute the throughput when mapping parameters are constant or follow I.I.D. exponential laws. The second contribution is to provide bounds for the throughput when stage parameters (computation and communication times) form associated random sequences, and are N.B.U.E. (New Better than Used in Expectation) variables: the throughput is bounded from below by the exponential case and bounded from above by the deterministic case. An extensive set of simulation allows us to assess the quality of the model, and to observe the actual behavior of several distributions.

#### Optimization of Cloud Task Processing with Checkpoint-Restart Mechanism

In [17] , we explain how to optimize fault-tolerance techniques based on a checkpointing/restart mechanism, in the context of cloud computing. Our contribution is three-fold. (1) We derive a fresh formula to compute the optimal number of checkpoints for cloud jobs with varied distributions of failure events. Our analysis is not only generic with no assumption on failure probability distribution, but also attractively simple to apply in practice. (2) We design an adaptive algorithm to optimize the impact of checkpointing regarding various costs like checkpointing/restart overhead. (3) We evaluate our optimized solution in a real cluster environment with hundreds of virtual machines and Berkeley Lab Checkpoint/Restart tool. Task failure events are emulated via a production trace produced on a large-scale Google data center. Experiments confirm that our solution is fairly suitable for Google systems. Our optimized formula outperforms Young's formula by 3-10 percent, reducing wallclock lengths by 50-100 seconds per job on average.