The loss of serving in the dark
Yossi Azar, Ilan Reuven Cohen, Iftah Gamzu · 2013
We study the following balls and bins stochastic process: There is a buffer with B bins, and there is a stream of balls X = {X1, X2, ... ,XT} such that Xi is the number of balls that arrive before time i but after time i-1. Once a ball arrives, it is stored in one of the unoccupied bins. If all the bins are occupied then the ball is thrown away. In each time step, we select a bin uniformly at random, clear it, and gain its content. Once the stream of balls ends, all the remaining balls in the buffer are cleared and added to our gain. We are interested in analyzing the expected gain of this randomized process with respect to that of an optimal gain-maximizing strategy, which gets the same online stream of balls, and clears a ball from a bin, if exists, at any step. We name this gain ratio the loss of serving in the dark.