  Group elevator scheduling is an NP-hard sequential decision-making problem
with unbounded state spaces and substantial uncertainty. Decision-theoretic
reasoning plays a surprisingly limited role in fielded systems. A new
opportunity for probabilistic methods has opened with the recent discovery of a
tractable solution for the expected waiting times of all passengers in the
building, marginalized over all possible passenger itineraries. Though
commercially competitive, this solution does not contemplate future passengers.
Yet in up-peak traffic, the effects of future passengers arriving at the lobby
and entering elevator cars can dominate all waiting times. We develop a
probabilistic model of how these arrivals affect the behavior of elevator cars
at the lobby, and demonstrate how this model can be used to very significantly
reduce the average waiting time of all passengers.
