For a single elevator building:

Consider a set of floors {C_i} such that the time it takes to travel between floors 

T(i,j) = k|i-j|

for some constant k. 

Furthermore, let the presses on up and down buttons for each floors C_i be modelled with an exponential distribution. 

Given the set of moves an elevator can make

M={Stay, Up, Down}

find 

best_move = argmin(M_i) E[ total time spent in or waiting for elevator of all users]

I'm hoping one of you can provide some advice for how to formulate the expression for best_move. Obviously it can't be defined for all time because that would blow to infinity. So what can I write down?

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