7 Analysis
For each Controller type and Idle Configuration type, we ran a simulation of 72000 units of time and collated the following statistics:
- Wait Time Per Passenger
- Proportion of Idle Time per Elevator
Calculations are defined as shown in Section 5 under the calculations section All code used to generate these plots are found in analysis notebook
We then plot these results on a scatter plot as shown below:
For the Uniform Arrival Pattern
For the Ground Floor Heavy Arrival Pattern
We see that among all the controllers, the Nearest Elevator policy works the best and is able to minimize both the idle time and wait times the best, regardless of the arrival pattern.
The top combinations and some of their statistics are shown in the tables below
Uniform Arrival Pattern:
| controller | idle floor config | num cycles | wait time | idle time | |
|---|---|---|---|---|---|
| 1 | Nearest | (3, 3, 4) | 375 | 3.211126 | 0.117448 |
| 2 | Nearest | (3, 4, 4) | 391 | 3.217938 | 0.119769 |
| 3 | Nearest | (3, 3, 3) | 390 | 3.240747 | 0.116447 |
| 4 | Nearest | (4, 4, 4) | 398 | 3.258347 | 0.119106 |
| 5 | Nearest | (3, 4, 5) | 400 | 3.266873 | 0.120828 |
Ground Floor Heavy Arrival Pattern:
| controller | idle floor config | num cycles | wait time | idle time | |
|---|---|---|---|---|---|
| 1 | Nearest | (3, 3, 3) | 310 | 3.211491 | 0.106031 |
| 2 | Nearest | (3, 3, 4) | 322 | 3.238365 | 0.109021 |
| 3 | Nearest | (2, 3, 3) | 316 | 3.251655 | 0.105699 |
| 4 | Nearest | (2, 3, 4) | 312 | 3.256100 | 0.108547 |
| 5 | Nearest | (3, 4, 4) | 294 | 3.257771 | 0.112682 |
We then focus on the various idle floor configurations for the Nearest Elevator policy and see which performs the best.
Uniform Arrival Pattern:
Ground Floor Heavy Arrival Pattern:
Strangely, it seems that the configurations that have the lift between the 3rd and 4th floor are able to minimize the wait time the most.
For the Uniform Arrival pattern, this makes sense since the arrivals are evenly distributed over all the floors.
It is clear that idle floor configurations that are on the extreme ends such as (1,1,1) and (6,6,6) are heavily penalized.
However, for the Ground Floor Heavy pattern, this might be because the distribution of arrivals among the floors are not that significant. This potentially results in the elevators being in motion most of the time and hence not leading to a very significant improvement to have the elevators idle at lower floors. However compared to the Uniform Arrival pattern, we do see that for example, the idle floor configuration (1,1,1) does perform better than the (6,6,6) configuration. This does make sense since the arrivals and departures are primarily from the first floor.
We also decided to look closer and compare the results betwen group controllers for the same idle configuration.
Uniform Arrival Pattern, with the idle configuration (3,3,4):
Ground Floor Heavy Arrival Pattern, with the idle configuration (3,3,3):
Upon closer inspection, we see that perhaps the Nearest Elevator policy may not be the best policy for all floors. It is able to significantly decrease the wait time for the floors closest to its idle floors, but for floors that are further away (e.g. Floor 6), the difference between the controller policies are not that significant. We can see that since the confidence intervals of the steady state averages overlap. This shows that the difference between the wait times is not significant enough.
Comparing the Idle Time of each elevator
Uniform Arrival Pattern:
Ground Floor Heavy Arrival Pattern:
For the Uniform Arrival pattern, it is interesting to observe that elevator 2 for the zoning policy has significantly more idle time, than the other two elevators. This could be due to how it has to move a lot less distance. However, for the Random and Nearest Elevator policies, the idle time of the elevators are about the same across the board. But the Nearest Elevator policy is still the best at maximizing utility.
We see that for the Ground Floor Heavy Arrival pattern, the idle time for elevator 1 is significantly lower than the rest for the Zoning policy, this makes sense since its the only one that can service the first floor. The disparity between the elevator usage under the Zoning policy is very drastic compared to the distribution of usage in the case of the Random and Nearest Elevator policies.
Overall, we still see that the Nearest Elevator policy is the best at minimizing the idle time of the elevators.
Table: Average Wait Times for Passengers (Uniform Arrival Pattern, idle floors (3,3,4))
| controller | steady state average | floor | lower interval | upper interval | |
|---|---|---|---|---|---|
| 0 | Random | 4.514733 | 1 | 4.436524 | 4.592942 |
| 1 | Random | 4.328387 | 2 | 4.246462 | 4.410311 |
| 2 | Random | 4.017742 | 3 | 3.925416 | 4.110068 |
| 3 | Random | 4.097837 | 4 | 4.017382 | 4.178292 |
| 4 | Random | 4.342061 | 5 | 4.268983 | 4.415139 |
| 5 | Random | 4.504800 | 6 | 4.422835 | 4.586765 |
| 6 | Zoning | 4.299805 | 1 | 4.204307 | 4.395303 |
| 7 | Zoning | 4.319049 | 2 | 4.230318 | 4.407779 |
| 8 | Zoning | 3.530067 | 3 | 3.436947 | 3.623187 |
| 9 | Zoning | 3.744073 | 4 | 3.665780 | 3.822365 |
| 10 | Zoning | 4.304167 | 5 | 4.217810 | 4.390525 |
| 11 | Zoning | 4.295804 | 6 | 4.210875 | 4.380732 |
| 12 | Nearest | 3.297615 | 1 | 3.247971 | 3.347260 |
| 13 | Nearest | 2.971286 | 2 | 2.915278 | 3.027295 |
| 14 | Nearest | 2.439912 | 3 | 2.376684 | 2.503140 |
| 15 | Nearest | 2.588583 | 4 | 2.535020 | 2.642147 |
| 16 | Nearest | 3.494518 | 5 | 3.420404 | 3.568632 |
| 17 | Nearest | 4.448232 | 6 | 4.367788 | 4.528677 |
Table: Average Wait Times for Passengers (Ground Floor Heavy Arrival Pattern, idle floors (3,3,3))
| controller | steady state average | floor | lower interval | upper interval | |
|---|---|---|---|---|---|
| 0 | Random | 3.923278 | 1 | 3.855924 | 3.990633 |
| 1 | Random | 4.108038 | 2 | 4.002431 | 4.213645 |
| 2 | Random | 4.006417 | 3 | 3.902961 | 4.109872 |
| 3 | Random | 4.443174 | 4 | 4.348035 | 4.538312 |
| 4 | Random | 4.688774 | 5 | 4.588069 | 4.789478 |
| 5 | Random | 4.867173 | 6 | 4.772555 | 4.961792 |
| 6 | Zoning | 4.170334 | 1 | 4.112916 | 4.227752 |
| 7 | Zoning | 4.783515 | 2 | 4.670011 | 4.897019 |
| 8 | Zoning | 3.144472 | 3 | 3.041916 | 3.247028 |
| 9 | Zoning | 3.753227 | 4 | 3.674988 | 3.831467 |
| 10 | Zoning | 4.800358 | 5 | 4.706400 | 4.894316 |
| 11 | Zoning | 4.846862 | 6 | 4.747227 | 4.946497 |
| 12 | Nearest | 2.763881 | 1 | 2.723896 | 2.803867 |
| 13 | Nearest | 2.758057 | 2 | 2.689239 | 2.826874 |
| 14 | Nearest | 2.322586 | 3 | 2.253161 | 2.392011 |
| 15 | Nearest | 3.085365 | 4 | 3.014425 | 3.156305 |
Table: Proportion of Idle Time per elevator (Uniform Arrival Pattern, idle floors (3,3,4))
| controller | steady state average | elevator | lower interval | upper interval | |
|---|---|---|---|---|---|
| 0 | Random | 0.206831 | 1 | 0.197204 | 0.216459 |
| 1 | Random | 0.203371 | 2 | 0.194265 | 0.212477 |
| 2 | Random | 0.205077 | 3 | 0.195406 | 0.214748 |
| 3 | Zoning | 0.140108 | 1 | 0.133369 | 0.146847 |
| 4 | Zoning | 0.205334 | 2 | 0.197046 | 0.213621 |
| 5 | Zoning | 0.134887 | 3 | 0.127606 | 0.142167 |
| 6 | Nearest | 0.116262 | 1 | 0.111128 | 0.121396 |
| 7 | Nearest | 0.116788 | 2 | 0.111514 | 0.122062 |
| 8 | Nearest | 0.119295 | 3 | 0.113849 | 0.124740 |
Table: Proportion of Idle Time per elevator (Ground Floor Heavy Arrival Pattern, idle floors (3,3,3))
| controller | steady state average | elevator | lower interval | upper interval | |
|---|---|---|---|---|---|
| 0 | Random | 0.228695 | 1 | 0.219485 | 0.237905 |
| 1 | Random | 0.236762 | 2 | 0.226188 | 0.247335 |
| 2 | Random | 0.237784 | 3 | 0.227073 | 0.248494 |
| 3 | Zoning | 0.071350 | 1 | 0.066629 | 0.076071 |
| 4 | Zoning | 0.298642 | 2 | 0.289694 | 0.307589 |
| 5 | Zoning | 0.202257 | 3 | 0.192961 | 0.211553 |
| 6 | Nearest | 0.123840 | 1 | 0.118438 | 0.129241 |
| 7 | Nearest | 0.124041 | 2 | 0.118681 | 0.129402 |
| 8 | Nearest | 0.123259 | 3 | 0.117790 | 0.128728 |