An Accurate and Robust Algorithm for Performance Evaluation of Exponential Serial Lines with Finite Buffers

Calculation of performance metrics as functions of machine and buffer parameters is one of the most important problems in production system research. In this paper, we study serial production lines with finite buffers and machines following the exponential reliability model. While such systems are characterized by continuous-time Markov processes, exact analysis is all but impossible due to high state space dimensionality. To overcome this problem, a recursive aggregation-based algorithm is proposed by representing a multi-machine line by a number of two-machine lines. Numerical experiments are used to justify the convergence of the algorithm and to evaluate the accuracy of the calculated performance metrics. The results show that the proposed algorithm significantly improve the approximation accuracy, compared to two commonly used aggregation-based methods in the literature.