Flowgraph Models and Analysis for Markov Jump Processes

TL;DR

This paper introduces flowgraph models as an effective alternative for analyzing Markov jump processes, simplifying the derivation of waiting time distributions and demonstrating practical advantages over traditional methods.

Contribution

It develops the theory and computational techniques for flowgraph analysis of Markov jump processes, highlighting its efficiency and practicality.

Findings

Flowgraph analysis simplifies the computation of waiting time distributions.

Flowgraph method is more practical than traditional Markov process construction.

The paper demonstrates the effectiveness of flowgraph models through comparative analysis.

Abstract

Flowgraph models provide an alternative approach in modeling a multi-state stochastic process. One of the most widely used stochastic processes that have many real-world applications especially in actuarial models is the Markov jump process or continuous- time Markov chain. However, finding waiting time distributions between any two states in a Markov jump process can be very difficult. Flowgraph analysis for Markov jump process comprises of modeling the possible states of the process, the interstates waiting time distribution, and working on the moment generating function domain to obtain the total waiting time distribution in form of density or survival function. This paper gives the theory and computational method of flowgraph analysis, uses it in Markov process problems, and compares the traditional Markov process construction method with the flowgraph method to demonstrate the convenience and practicality of flowgraph analysis.