## Abstract

Consider a regenerative storage process with a nondecreasing Levy 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.

Original language | American English |
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Pages (from-to) | 730-744 |

Number of pages | 15 |

Journal | Probability in the Engineering and Informational Sciences |

Volume | 35 |

Issue number | 3 |

DOIs | |

State | Published - Jul 2021 |

### Bibliographical note

Publisher Copyright:Copyright © Cambridge University Press 2020.

## Keywords

- Levy driven queues
- optimization with partial information
- output rate control
- queues with server vacations