A production line that balances itself

In ‘bucket brigade’ manufacturing, such as recently introduced to the apparel industry, a production line has n workers moving among m stations, where each worker independently follows a simple rule that determines what to do next. Our analysis suggests and experiments confirm that if the workers are sequenced from slowest to fastest then, independently of the stations at which they begin, a stable partition of work will spontaneously emerge. Futhermore, the production rate will converge to a value that, for typical production lines, is the maximum possible among all ways of organizing the workers and stations.