On the Size of Buffers in an Assembly Line

We consider the design of a large assembly line with approximately 50 machines, in particular the question where intermediate buffers are necessary, and what size these buffers should have. If in a production or assembly line without buffers one of the machines fails, within a few minutes all machines in front of it will be blocked, and the machines after the one that failed are going to starve. Depending on the failure frequencies and failure times this may lead to an enormous loss of production capacity for the entire system. For the case of 50 machines, where each of the machines is down 2% of the time, the capacity of the whole system may reduce to 36% of the capacity without failures. With infinite buffers the capacity remains 98%.