A five-story office building is served by a single elevator. People arrive to the ground floor (floor 1) with independent exponential interarrival times having mean 1 minute. A person will go to each of the upper floors with probability 0.25. It takes the elevator 15 seconds to travel one floor. Assume, however, that there is no loading or unloading time for the elevator at a particular floor. A person will stay on a particular floor for an amount of time that is distributed uniformly between 15 and 120 minutes. When a person leaves floor i (where i = 2, 3, 4, 5), he or she will go to floor 1 with probability 0.7, and will go to each of the other three floors with probability 0.1. The elevator can carry six people, and starts on floor 1. If there is not room to get all people waiting at a particular floor on the arriving elevator, the excess remain in queue. A person coming down to floor 1 departs from the building immediately. The following control logic also applies to the elevator:
• When the elevator is going up, it will continue in that direction if a current passenger wants to go to a higher floor or if a person on a higher floor wants to get on the elevator.
• When the elevator is going down, it will continue in that direction if it has at least one passenger or if there is a waiting passenger at a lower floor.
• If the elevator is at floor i (where i = 2, 3, 4) and going up (down), then it will not immediately pick up a person who wants to go down (up) at that floor.
• When the elevator is idle, its home base is floor 1.
• The elevator decides at each floor what floor it will go to next. It will not change directions between floors.
Use the following random-number stream assignments:
1, interarrival times of people to the building
2, next-floor determination (generate upon arrival at origin floor)
3, length of stay on a particular floor (generate upon arrival at floor)
Run a simulation for 20 hours and gather statistics on:
(a) Average delay in queue in each direction (if appropriate), for each floor
(b) Average of individual delays in queue over all floors and all people
(c) Proportion of time that the elevator is moving with people, is moving empty, and is idle (on floor 1)
(d) Average and maximum number in the elevator
(e) Proportion of people who cannot get on the elevator since it is full, for each floor Rerun the simulation if the home base for the elevator is floor 3. Which home base gives the smallest average delay [output statistic (b)]?
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