A Poisson Arrival Selection Problem for Gamma Prior Density with Parameter R=2
Katsunori Ano · 1999
. Bruss #1987# studied a continuous-time generalization of the so-called secretary problem, where options arise according to a homogeneous Poisson process of unknown intensity # having an exponential prior density, G#1; 1=a#. This article shows that this problem is monotone in the sense of Chow, Robbins, and Siegmund, and that the monotonicity remains for the secretary problem with Gamma prior intensity, G#2; 1=a#. The optimal strategy for the problem is shown to be a threshold rule. 1. Introduction. Bruss #1987# studied a continuous-time generalization of the so-called secretary problem which is as follows: A man has been allowed a #xed time T in which to #nd an apartment. Opportunities to inspect apartments occur at the epochs of a homogeneous Poisson process of unknown intensity #. He inspects each apartment when the opportunity arises, and he must decide immediately whether to accept or not. Atany epoch he is able to rank a given apartment amongst all those inspected to date, where...