Sensitivity analysis of Stochastic Fluid Models: Stationary and transient quantities with applications

TL;DR

This paper develops the first sensitivity analysis methods for stochastic fluid models, providing formulas for stationary and transient quantities, with applications demonstrated in queueing and risk systems.

Contribution

It introduces novel sensitivity analysis expressions for SFMs and lays the groundwork for extending these methods to other Markovian modulated models.

Findings

Derived formulas for sensitivity of stationary quantities

Derived formulas for sensitivity of transient quantities

Numerical examples demonstrate application in queueing and risk models

Abstract

We establish results for the first sensitivity analysis of the stochastic fluid models (SFMs). We derive expressions for the sensitivity analysis of the key stationary and transient (time-dependent) quantities of this class of models. We also construct numerical examples to demonstrate the application potential of our methodology in queueing systems, such as deteriorating systems and insurance risk processes. This work forms foundation for the sensitivity analysis of other Markovian modulated models, which are generalisations of the SFMs, and have widespread applications.