Modeling and Analysis of Markovian Continuous Flow Production Systems with a Finite Buffer: Methodology and Applications

Fluid flow models have been used in performance evaluation of production, computer, and telecommunication systems. Currently, a general methodology to model and analyze a given continuous flow production system is not available. In order to develop a general methodology to analyze Markovian continuous material flow production systems with a finite buffer, we modelled the fluid flow system as a continuous time, continuous-discrete state space stochastic process and determined the steady state distributions by using a level crossing analysis. Various performance measures such as the production rate and the expected buffer level are also determined directly from the steady-state distributions. The flexibility of our methodology allows us to analyze a wide range of models including models with machines that have multiple up and down states, models with multiple unreliable machines in series or parallel in each stage, models with merge-type structures, and models with phase-type failure and repair-time distributions by using the same methodology. Therefore the method is proposed as a general tool for performance evaluation of continuous material flow production systems with a single buffer.