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There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
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Consider n items located randomly on a circle of length 1. The locations of the items are assumed to be independent and uniformly distributed on [0,1). A picker starts at point 0, and he has to collect all the n items moving along the circle at unit speed in either direction. We study the travel time of the picker. The problem is motivated by performance analysis of carousel systems which are widely used automated warehousing systems. The travel time highly depends on the pick strategy. For example, the picker may use the 'greedy' strategy: always travel to the nearest item to be picked. This simple algorithm is often used in practice. One can also
consider so-called m-step strategies: the picker chooses the shortest route among the ones that change direction at most once after collecting at most m items. Already for small values of m, the travel time under the m-step strategies is very close to the optimal (minimal) one. It is a non-trivial problem to find the travel time distribution under the strategies mentioned above. We develop an approach based on the well-known
relations between exponential random variables and uniform spacings. We first prove two distributional identities which are of pure mathematical interest as new peculiar properties of exponentials. Using these results, we derive the travel time distribution under the 'greedy' and the m-step strategy provided 2m
counterintuitive) results on collecting n items on a circle.
