A cloud scheduler packs tasks onto machines with contradictory goals of (1) using the machines as efficiently as possible while (2) avoiding overloading that might result in CPU throttling or out-of-memory errors. We take a stochastic approach that models the uncertainty of tasks' resource requirements by random variables. We focus on a little-explored case of items, each having a Bernoulli distribution that corresponds to tasks that are either idle or need a certain CPU share. RPAP, our online approximation algorithm, upper-bounds a subset of items by Poisson distributions. Unlike existing algorithms for Bernoulli items that prove the approximation ratio only up to a multiplicative constant, we provide a closed-form expression. We derive RPAPC, a combined approach having the same theoretical guarantees as RPAP. In simulations, RPAPC's results are close to FFR, a greedy heuristic with no worst-case guarantees; RPAPC slightly outperforms FFR on datasets with small items.

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