On a class of order pick strategies in paternosters

We study the travel time needed to pick n items in a paternoster, operating under the m-step strategy. This means that the paternoster chooses the shortest route among the ones that change direction at most once, and after collecting at most m items. For random pick positions, we find the distribution and moments of the travel time, provided n > 2m. It appears that, already for m = 2, the m-step strategy is very close to optimal, and better than the nearest item heuristic.