I am currently retired but have spent considerable time teaching high rise fire operations. (1981 to1992) This tactic for high rise opertions comes form the LACITYFD. and is used successfully in actual fires.
Myself and Bob Ramirez travelled across the U.S. presenting high rise seminars.
Regarding the hose lays in stairshafts. Using 1 1/2 or 1 3/4 attack lines we found that it is very effective to lay the lines up the stairway on the fire floor and then back down to the doorway. Do not load the line until the fire attack team is ready to enter the fire floor. When the line is loaded it will come back down as the line is extended. This will be an easier pull into the fire area rather then pulling the line up from the floor below. This operation is better then pulling all of the hose from the stairway as it comes out of the hose pack or bundle. Some firefighters call this the "loop" method.