Abstract
Abstract The infinite version of the generalized secretary problem is here combined with the random duration time of the process in a natural way. A traveler, starting at t=0, going towards to the destination t= 1, and observing relative ranks of objects that appear one by one according to a non-homogeneous Poisson stream, hopes to select the best object (in the classical secretary problem), and “win” if the selected one is the best among all objects which appear untill the process terminates or until the final time 1 comes, whichever occurs first. We are asked to find the stopping policy that maximizes the probability of “win”. Three problems with different objectives of the traveler’s decision of stopping are analysed. In these problems the traveler’s objectives are to select: (1) the best by three stops, (2) the best and the second best by three stops, (3) the best, the second best and the third best by three stops. For each of these the optimal policy and the probability of win under this policy are explicitly derived when the duration time of the process is uniformly distributed in [0, 1].
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