ANALYTICAL SOLUTION OF STEADY-STATE BEHAVIOR OF BERNOULLI PRODUCTION LINE WITH TWO FINITE BUFFERS

Production system engineering is strongly relied on mathematical models of systems under consideration and analytical solution of the problem has an important role in development and validation of more complex numerical tools. Analytical solution of steady state behavior of serial Bernoulli production line with three machines and two buffers is considered in this paper based on Markov chain approach. Transition matrices in general case, including three machines with different probabilities of failure and arbitrary occupancy of two buffers, are formulated along with equations for performance measures. The developed theory is illustrated using four different serial Bernoulli lines and the obtained results are compared to those determined using semi-analytical approach via aggregation procedure. Finally, the existing discrepancies are analyzed and pointed out for five different levels of buffers occupancy. From general perspective, good agreement has been found for most of the results within the examined space of system states.