Reservation strategies for stochastic jobs

In this paper, we are interested in scheduling stochastic jobs on a reservation-based platform. Specifically, we consider jobs whose execution time follows a known probability distribution. The platform is reservation-based, meaning that the user has to request fixed-length time slots. The cost then depends on both (i) the request duration (pay for what you ask); and (ii) the actual execution time of the job (pay for what you use). A reservation strategy determines a sequence of increasing-length reservations, which are paid for until one of them allows the job to successfully complete. The goal is to minimize the total expected cost of the strategy. We provide some properties of the optimal solution, which we characterize up to the length of the first reservation. We then design several heuristics based on various approaches, including a brute-force search of the first reservation length while relying on the characterization of the optimal strategy, as well as the discretization of the target continuous probability distribution together with an optimal dynamic programming algorithm for the discrete distribution. We evaluate these heuristics using two different platform models and cost functions: The first one targets a cloud-oriented platform (e.g., Amazon AWS) using jobs that follow a large number of usual probability distributions (e.g., Uniform, Exponential, LogNormal, Weibull, Beta), and the second one is based on interpolating traces from a real neuroscience application executed on an HPC platform. An extensive set of simulation results show the effectiveness of the proposed reservation-based approaches for scheduling stochastic jobs.