This document validates the f^2 rule-of-thumb for determining the length of batches in a simulation. It compares the confidence intervals of load, loss, and queuing ratios for groups with different batch lengths. The results show that confidence interval sizes decrease by a factor of f^2 as batch length increases, validating the rule-of-thumb. It also finds that confidence interval sizes are nearly equal when comparing groups with the same batch length. This confirms that longer batch lengths lead to more precise estimates as predicted by the f^2 rule-of-thumb.

1. ET2534 Simulation VT17 LP4
Group 10
Ivvala Venkata Sai Krishna Chaitanya
Mamidi Sai Prakash
Peteti sridhar

2. Description of the Task:
• Validate the 𝑓2 rule-of-thumb for the length of batches.
• Rule of thumb: Reduction of CI size by factor f means 𝑓2 more effort
• Here we consider groups 1,2,3,4,5 and compare their confidence
intervals (Relative half sizes) based on the length of the batches.
Relative Confidence Interval: = 1 ±
𝑍
1−
∝
2
𝑛
𝑆
𝑋

3. How to perform the task?
• Here we compare confidence intervals(Relative half sizes) for Load,
Loss and Queuing of the groups 1,2,3,4 by varying the length of the
batches.
• Then we compare confidence intervals(Relative half sizes) for Load,
Loss and Queuing for the groups 5 and 2 for the same length of the
batches.
• From the above comparisons we can validate the 𝑓2 rule-of-thumb
for the length of batches.

4. Input parameters:
Group 1 Group 2 Group 3 Group 4 Group 5
Seed 2017 2017 2017 2017 2017
Arr. proc M M M M M
Mean inter
arrival time
100 100 100 100 100
Buffer size 0-10 0-10 0-10 0-10 0-10
Serv. proc M M M M M
Mean service
time
60 60 60 60 60
Warm up? 1 1 1 1 1
#bat.n 100 100 100 100 10000
#arr.k 100 1000 10000 100000 10

5. COMPARISON OF AVERAGE LOAD RATIO CI RELATIVE HALF SIZES

6. K group1 group2 group3 group4
0
2.18% 0.80% 0.24% 0.07%
1
2.43% 0.71% 0.20% 0.08%
2
2.48% 0.75% 0.20% 0.07%
3
2.39% 0.57% 0.26% 0.08%
4
2.72% 0.75% 0.24% 0.08%
5
2.80% 0.80% 0.25% 0.08%
6
2.80% 0.89% 0.23% 0.09%
7
2.48% 0.81% 0.27% 0.09%
8
2.69% 0.90% 0.24% 0.09%
9
2.47% 0.77% 0.28% 0.09%
10
2.78% 0.86% 0.27% 0.09%
CI Relative half size vs Buffer size K for load estimation

7. COMPARISON OF AVERAGE LOSS RATIO CI RELATIVE HALF SIZES

8. CI Relative half size vs Buffer size K for loss estimation
K group1 group2 group3 group4
0
2.55% 0.85% 0.25% 0.08%
1
5.10% 1.56% 0.51% 0.17%
2
8.78% 2.72% 0.84% 0.26%
3
12.64% 3.83% 1.30% 0.43%
4
18.35% 5.86% 1.80% 0.56%
5
25.73% 7.55% 2.75% 0.72%
6
35.50% 9.33% 3.50% 1.07%
7
41.43% 12.50% 4.40% 1.46%
8
59.88% 19.60% 5.80% 1.91%
9
64.32% 23.64% 6.90% 2.71%
10
81.41% 31.21% 10.05% 3.23%

9. COMPARISON OF AVERAGE QUEUING RATIO CI RELATIVE HALF SIZES

10. CI Relative half size vs Buffer size K for Queuing estimation
K group1 group2 group3 group4
0
0% 0% 0% 0%
1
2.78% 0.77% 0.21% 0.08%
2
2.23% 0.83% 0.21% 0.07%
3
2.54% 0.78% 0.26% 0.08%
4
2.72% 0.78% 0.27% 0.09%
5
2.83% 0.78% 0.30% 0.08%
6
2.73% 1.00% 0.27% 0.09%
7
2.76% 0.89% 0.31% 0.09%
8
2.83% 1.01% 0.26% 0.10%
9
2.79% 0.94% 0.33% 0.10%
10
2.79% 0.93% 0.30% 0.09%

11. Comparison of the groups with the same length of batches
K group2 group5 group3 group6 group4 group7
0 0.80% 0.67% 0.24% 0.22% 0.07% 0.07%
1 0.71% 0.66% 0.20% 0.22% 0.08% 0.07%
2 0.75% 0.67% 0.20% 0.23% 0.07% 0.07%
3 0.57% 0.68% 0.26% 0.24% 0.08% 0.08%
4 0.75% 0.68% 0.24% 0.25% 0.08% 0.08%
5 0.80% 0.68% 0.25% 0.26% 0.08% 0.08%
6 0.89% 0.68% 0.23% 0.26% 0.09% 0.08%
7 0.81% 0.68% 0.27% 0.27% 0.09% 0.08%
8 0.90% 0.69% 0.24% 0.27% 0.09% 0.08%
9 0.77% 0.69% 0.28% 0.27% 0.09% 0.09%
10 0.86% 0.69% 0.27% 0.27% 0.09% 0.09%

12. Observations
• Load ratio increases with increases in the buffer size.
• From the comparisons of load ratio for group 1, 2, 3,4 in slide 6, we
conclude that the CI Relative Half Size decreases with increase in
length of batches, hence the 𝑓2 rule-of-thumb is valid.
• For group 2 and 5 , group 3 and 6 , group 4 and 7 we observe the CI
Relative half Size is almost equal because length of batches are also
equal.
• Loss ratio decreases with increases in the buffer size.
• From the comparisons of loss ratio for group 1, 2, 3,4 in slide 8, we
conclude that the CI Relative Half Size decreases with increase in
length of batches, hence the 𝑓2 rule-of-thumb is valid.

13. Observations
• Queuing ratio increases with increases in the buffer size.
• From the comparisons of Queuing ratio for group 1, 2, 3,4 in slide 6,
we conclude that the CI Relative Half Size decreases with increase in
length of batches, hence the 𝑓2 rule-of-thumb is valid.

14. THANK YOU !