On Woolhouse's Cotton-Spinning Problem

Abstract

In 1864 W.S.B. Woolhouse formulated the Cotton-Spinning problem. This problem boils down to the following. A piecer works at a spinning mule and walks back and forth to repair broken threads. The question is how far the piecer is expected to walk when the threads break at random. This problem can neatly be solved using process modelling and quantitative model checking, showing that Woolhouse's model led to an overestimation of the walking distance.