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## Section: New Results

### Data Aware Batch Scheduling

#### Batch Scheduling for Energy

The project COSMIC [24], [22], [16], [17], in collaboration with Myriads team in Inria Rennes-Atlantique, targets the optimization of green energy usage in Clouds. The project considers a geographically distributed cloud, with each data center associated with a local photovoltaic (PV) farm. The objective is to maximize the photovoltaic energy by allocation the computing workload to the data centers according to its energy production. The production forecasting is modeled with a truncated normal law, permitting to consider the uncertainty of the forecast.

Chapter [24] considers a simple model with homogeneous Virtual Machines submitted at unpredictable rate. This study has resulted in a scheduling algorithm for task allocation. The chapter demonstrates the optimality of this algorithm at current time slot according to production forecast parameters.

Paper [22] extends these results to heterogeneous VM. Each VM is defined by its arrival date, its execution time, its memory requirement and its CPU usage. In this model, due to execution time durations, the possibility to migrate running VM was considered. An algorithm is detailed in the paper that is compared to standard algorithm through simulations.

A third study [16], [17] has carefully modeled the interactions between the Cloud and the energy supplier. Due to variability of PV production and workload submission, each data center will alternatively inject energy into the electricity grid or purchase energy. The energy model considers a virtual energy pool mitigating the surplus and deficit of the different data center, with reduced costs regarding the difference between electricity cost and electricity injection tariff. The algorithm detailed in this paper outperforms well-known round-robin approaches, as shown by simulations.

#### Learning Methods for Batch Scheduling

Most of Job Scheduling algorithms apply greedy tasks ordering, as First Come First Served (FCFS) or Shortest Processing time First (SPF). They give simple methods, highly practical with certain guarantees. They are however far from optimal. Mixed methods, combining many of this basic methods permit to improve their performance. DataMove has developed [27] a learning method permitting to adapt the Mixed method to benchmarks. An extensive experimental campaign has permitted to determine the possibilities of basic and mixed methods according to the benchmarks characteristics, enhancing the efficiency of mixed methods.

#### Reproducibility

Related to batch scheduling experimentation, DataMove has led investigations on reproducibility [23]. Existing approaches focus on repeatability, but this is only the first step to reproducibility: Continuing a scientific work from a previous experiment requires to be able to modify it. This ability is called reproducibility with Variation. We show that capturing the environment of execution is necessary but not sufficient ; we also need the environment of development. The variation also implies that those environments are subject to evolution, so the whole software development lifecycle needs to be considered. To take into account these evolutions, software environments need to be clearly defined, reconstructible with variation, and easy to share. In this context, we propose new way of seeing reproducibility through the scientific software development lifecycle. Each step in this lifecycle requires a software environment. We define a software environment by a set of applications and libraries, with all their dependencies, and their configurations, required to achieve a step in a scientific workflow.

#### Online Algorithms

Rob van Stee wrote a review of 2018 online algorithms including our recent contributions on resource augmentation (Rob van Stee. 2018. SIGACT News Online Algorithms Column 34: 2018 in review. SIGACT News 49, 4 (December 2018), 36-45.) We quote him here:

Progress was also made on scheduling to minimize weighted flow time on unrelated machines. In ESA 2016, Giorgio Lucarelli et al. [1] had considered a version where the online algorithm can reject some ${\epsilon }_{r}>0$ fraction (by weight) of the jobs and have machines that are $1+{\epsilon }_{s}$ as fast as the offline machines, for some ${\epsilon }_{s}>0$. They showed that this is already enough to achieve a competitive ratio of $O\left(1/\left({\epsilon }_{s}{\epsilon }_{r}\right)\right)$.

In SPAA 2018, Giorgio Lucarelli et al.[20] (a superset of the previous authors) showed that it is in fact sufficient to reject a $2\epsilon$ fraction of the total number of jobs to achieve a competitive ratio of $2\left(\frac{1+\epsilon }{\epsilon }\right)$ for minimizing the total flow time. This algorithm sometimes rejects a job other than the one that has just arrived. The authors show that this is necessary, as otherwise there is a lower bound of $\Omega \left(\Delta \right)$ even on a single machine. Here $\Delta$ is the size ratio (the ratio of largest to smallest job size). (Obviously this lower bound also holds if you cannot reject jobs at all.)

They also consider the speed scaling model, in which machines can be sped up if additional energy is invested, and the goal is to minimize the total weighted flow time plus energy usage. If the power function of machine $i$ is given by $P\left({s}_{i}\left(t\right)\right)={s}_{i}{\left(t\right)}^{\alpha }$, where ${s}_{i}\left(t\right)$ is the current speed of machine $i$, there is an algorithm which is $O\left({\left(1+1/\epsilon \right)}^{\alpha /\left(\alpha -1\right)\right)}$-competitive that rejects jobs of total weight at most a fraction $\epsilon$ of the total weight of all the jobs. They also give a positive result for jobs with hard deadlines, where the goal is to minimize the total energy usage and no job may be rejected.

In ESA 2018, the same set of authors [11] improved/generalized these results by showing that rejection alone is sufficient for an algorithm to be competitive even for weighted flow time. They presented an $O\left(1/{\epsilon }^{3}\right)$-competitive algorithm that rejects at most $O\left(\epsilon \right)$ of the total weight of the jobs. In this algorithm, jobs are assigned (approximately) greedily to machines, and each machine runs the jobs assigned to it using Highest Density First. A job may be rejected if it is running while much heavier jobs arrive or if it is in the queue while very many jobs arrive. The second rule simulates the resource augmentation on the speed.