Insights of the Intersection of Phase-Type Distributions and Positive Systems

TL;DR

This paper explores the relationship between phase-type distributions and positive systems, demonstrating their interconnectedness and potential applications through practical examples to enhance understanding of their dynamic behavior.

Contribution

It establishes clear connections between phase-type distributions and positive systems, highlighting their relevance and utility across various disciplines.

Findings

Phase-type distributions can effectively model positive system dynamics.

The paper provides practical examples illustrating the application of phase-type in positive systems.

It opens new avenues for interdisciplinary research in system modeling.

Abstract

In this paper, we consider the relationship between phase-type distributions and positive systems through practical examples. Phase-type distributions, commonly used in modelling dynamic systems, represent the temporal evolution of a set of variables based on their phase. On the other hand, positive systems, prevalent in a wide range of disciplines, are those where the involved variables maintain non-negative values over time. Through some examples, we demonstrate how phase-type distributions can be useful in describing and analyzing positive systems, providing a perspective on their dynamic behavior. Our main objective is to establish clear connections between these seemingly different concepts, highlighting their relevance and utility in various fields of study. The findings presented here contribute to a better understanding of the interaction between phase-type distribution theory and positive system theory, opening new opportunities for future research in this exciting interdisciplinary field.