Properties of continuous models of transfer lines with unreliable machines and finite buffers

The authors consider a transfer line consisting of a series of machines separated by buffers of finite capacity. The processing of a part on a machine requires a fixed amount of time. In these systems, blocking and starvation, which occur as a consequence of machine failures, are important phenomena. Except for transfer lines without buffer storage, no exact models of such systems have been reported in the literature, even in the case of two-machine lines. Two approximate models have been proposed: the discrete-time model and the continuous-flow model. Exact solutions of these models have been reported in the case of two-machine lines, and approximations have been proposed for longer lines. The purpose of this paper is to provide properties of the continuous-flow model. The main result of the paper is to show that lower and upper bounds on the exact production rate of the transfer line can be obtained using the continuous flow model. These bounds are obtained by making an appropriate choice of the buffer capacities.