Scheduling Jobs Under a Variable Number of Processors

Even though it is usually assumed that data centers can always operate at maximum capacity, there have been recent scenarios where the amount of electricity that can be used by data centers evolve over time. Hence, the number of available processors is not a constant anymore. In this work, we assume that jobs can be checkpointed before a resource change. Indeed, in the scenarios that we consider, the resource provider warns the user before a change in the number of processors. It is thus possible to anticipate and take checkpoints before the change happens, such that no work is ever lost. The goal is then to maximize the goodput and/or the minimum yield of jobs within the next section (time between two changes in the number of processors). We model the problem and design greedy solutions and sophisticated dynamic programming algorithms with some optimality results for jobs of infinite duration, and adapt the algorithms to finite jobs. A comprehensive set of simulations, building on real-life job sets, demonstrates the performance of the proposed algorithms. Most algorithms achieve a useful platform utilization (goodput) of over 95%. With infinite jobs, the algorithms also keep fairness by having a relative minimum yield above 0.8, meaning that each job gets a good access to the platform (80% of the time that it would have had if each job had its perfect share of the platform). For finite jobs, the minimum yield can be low since very short new jobs may have to wait until the beginning of the next section to start (and finish), significantly impacting their yield. However, for 75% of the jobs within each workload, the yield ratio between these jobs is at most at a factor two, hence demonstrating the fairness of the proposed algorithms.