JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Mathematical Association of America is collaborating with JSTOR to digitize, preserve and extend access to Mathematics Magazine.http://www.jstor.org VOL. 84, NO. 4, OCTOBER 2011 283 with a buffer of limited capacity, and data packets arrive online and can be stored in the buffers. In each time slot the switch can transmit packets from some of the buffers to the output channel, and all decisions must be based on the current state without knowledge of future events. We stress that in practice, greedy strategies are very important because they are fast and use little extra memory. In our game, Cinderella's buckets model the buffers, the water models the data that arrives continuously over time, and Cinderella models a scheduling procedure that tries to keep the system stable by preventing buffer overflows.Finally let us make the connection to the standard language of game theory [3]. If we change the game so that the Stepmother scores points according to the maximum amount she can ever get into a bucket, then the game has a value and optimal strategies. (Actually the Stepmother only has a sequence of strategies, whose results converge; this often happens with non-compact strategy spaces.) We have established that the value of this game is 2, and that in the case where Cinderella follows the sub-optimal GREEDY strategy, the Stepmother can achieve a score of 17/8.
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