On the minimal travel time needed to collect n items on a circle

Details On the minimal travel time needed to collect n items on a circle On the minimal travel time needed to collect n items on a circle

2004-05-14

arxiv.org/abs/math/0405294v1

Annals of Applied Probability 2004, Vol. 14, No. 2, 881-902

Mathematics

Probability

Scientific paper

10.1214/105051604000000152

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 has to collect all n items by moving along the circle at unit speed in either direction. In this paper we study the minimal travel time of the picker. We obtain upper bounds and analyze the exact travel time distribution. Further, we derive closed-form limiting results when n tends to infinity. We determine the behavior of the limiting distribution in a positive neighborhood of zero. The limiting random variable is closely related to exponential functionals associated with a Poisson process. These functionals occur in many areas and have been intensively studied in recent literature.

Affiliated with

Also associated with

No associations

Rating

On the minimal travel time needed to collect n items on a circle does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the minimal travel time needed to collect n items on a circle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the minimal travel time needed to collect n items on a circle will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-671784