Production Line Analysis by Bounding Discretization

In this paper, we present a new modeling method for production lines with stochastic working times. To analyze the behavior of lines, we discretize the working time distributions, in order to use discrete Markov chains. The goal is to get weakly restrictive assumptions on the lines configuration : working times are described by general distributions and buffers are of arbitrary finite size. Our originality mostly lies in the discretization method we use, which aims to conserve the shape of the distributions and to maintain an intelligible link with the original distributions. At this stage, the main, theoretical, contributions consists in upper and lower bounds for the productivity, which can be computed by the method. These bounds are proved using tools, the covering sequence in particular, which should be applicable to other cases. In a second part, we open the door to a more practical use of the method and give a lot of possible extensions.