Efficiency and production rate of a transfer line with two machines and a finite storage buffer

A markov model for a transfer line with two unreliable machines separated by a finite storage size buffer is introduced. Service time distribution for the two machines is Erlang whereas failure and repair times are assumed to be exponential random variables. The paper presents an efficient method to solve analytically the steady state probabilities of the system. This method is independent of the buffer size. We also include in the paper a study of the behavior of some systems performance measures such as the efficiency of the two machines and the production rate of the system.