The transposition replacement policy with a partial memory
Peter R. Nelson · Journal of Applied Probability · 1982
Consider as a model for any serial list a bookshelf with books B1, ···, Bn. At each unit of time book is demanded with probability pi and is replaced one position to the left of where it was removed (or in the same position if it is already at the left-hand end). If this transposition is made only when Bi has been demanded k times in a row, we show that the average position of the next book demanded is a monotone decreasing function of k.