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

## TL;DR

This paper analyzes a regenerative storage process with random output rates, deriving the steady-state workload distribution and optimizing output rates to minimize costs, with the optimal policy depending on workload levels.

## Contribution

It introduces a model with random output rates in a Levy storage process and derives the steady-state distribution and optimal output policy.

## Key findings

- Derived the Laplace-Stieltjes transform of the workload distribution.
- Identified the optimal output rate as a nondecreasing function of workload.
- Provided a cost minimization framework for the storage process.

## Abstract

Consider a regenerative storage process with a nondecreasing L\'evy 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.