Consider a regenerative storage process with a nondecreasing Lévy input (subordinator) such that every cycle may be split into two periods. In the first (off), the output is shut off and the workload accumulates. This continues until some stopping time. In the second (on), the process evolves like a subordinator minus a positive drift (output rate) until it hits the origin. In addition, we assume that the output rate of every on period is a random variable, which is determined at the beginning of this period. For example, at each period, the output rate may depend on the workload level at the beginning of the corresponding busy period. We derive the Laplace–Stieltjes transform of the steady-state distribution of the workload process and then apply this result to solve a steady-state cost minimization problem with holding, setup and output capacity costs. It is shown that the optimal output rate is a nondecreasing deterministic function of the workload level at the beginning of the corresponding on period.

中文翻译：

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具有间歇输出和随机输出速率的详尽 LÉVY 存储过程的稳态优化

考虑一个具有非递减 Lévy 输入（从属子）的再生存储过程，这样每个周期都可以分为两个周期。在第一个（关闭）中，输出被关闭并且工作量累积。这种情况一直持续到某个停止时间。在第二个（on）中，该过程像从属器减去正漂移（输出率）一样演变，直到它到达原点。另外，我们假设每个on周期的产出率是一个随机变量，它是在这个周期开始时确定的。例如，在每个时段，输出率可能取决于相应繁忙时段开始时的工作负载水平。我们推导出工作负载过程的稳态分布的 Laplace-Stieltjes 变换，然后应用这个结果来解决持有的稳态成本最小化问题，设置和输出能力成本。结果表明，最佳输出率是相应开启期开始时工作量水平的非减确定性函数。