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?