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Consider a regenerative storage process with a nondecreasing L\'evy input(subordinator) such that every cycle may be split into two periods. In thefirst (off) the output is shut off and the workload accumulates. This continuesuntil some stopping time. In the second (on), the process evolves like asubordinator minus a positive drift (output rate) until it hits the origin. Inaddition, we assume that the output rate of every on period is a randomvariable which is determined at the beginning of this period. For example, ateach period, the output rate may depend on the workload level at the beginningof the corresponding busy period. We derive the Laplace-Stieltjes transform ofthe steady state distribution of the workload process and then apply thisresult to solve a steady-state cost minimization problem with holding, setupand output capacity costs. It is shown that the optimal output rate is anondecreasing deterministic function of the workload level at the beginning ofthe corresponding on period.

Steady-state optimization of an exhaustive Levy storage process with intermittent output and random output rate