Flowgraph Models and Analysis for Markov Jump Processes
  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. 
Muhammad Fikri Budiana, Murwan H. M. A. Siddig
stat.AP math.PR