We study the problem of online peak minimization under inventory constraints. It is motivated by the emerging scenario where large-load customers utilize energy storage to reduce the peak procurement from the grid, which accounts for up to 90% of their electric bills. The problem is uniquely challenging due to (i) the coupling of online decisions across time imposed by the inventory constraints and (ii) the noncumulative nature of the peak procurement. In this paper, we develop an optimal online algorithm for the problem that attains the best possible competitive ratio (CR) among all deterministic and randomized algorithms. We show that the optimal CR can be computed in polynomial time, by solving a linear number of linear-fractional problems. We also generalize our approach to develop an anytime-optimal online algorithm that achieves the best possible CR at any epoch, given the inputs and online decisions so far. The algorithm retains the optimal worst-case performance and achieves adaptive average-case performance. Simulation results based on real-world traces show that our algorithms improve peak reduction by more than 19% as compared to baseline alternatives.

中文翻译：

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利用储能实现在线高峰需求最小化

我们研究了在库存限制下在线高峰期最小化的问题。它受到新兴场景的激励，在这种场景中，大负载客户利用储能来减少从电网的高峰采购，这占到了他们电费的90％。由于（i）由于库存限制而跨时间跨在线决策，以及（ii）高峰采购的非累积性质，因此该问题具有独特的挑战性。在本文中，我们针对所有确定性和随机算法中的最佳问题开发了一种在线最优算法。我们表明，通过求解线性分数线性问题，可以在多项式时间内计算出最佳CR。考虑到到目前为止的输入和在线决策，我们还将概括我们的方法以开发一种随时最佳的在线算法，该算法可在任何时期实现最佳CR。该算法保留了最佳的最坏情况性能，并实现了自适应的平均情况性能。基于真实世界轨迹的仿真结果表明，与基准方案相比，我们的算法将峰值降低幅度提高了19％以上。