---
title: "Need for replications of runs"
subject: "Simulation and Modeling"
chapter: 8
key: "semester_8/simulation_and_modeling:replications-of-runs"
source: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/replications-of-runs
site: BCT Engineering
---

# Need for replications of runs

Simulation and Modeling · Chapter 8: Analysis of simulation output

- Asked in: 2074 Magh, 5 marks
- Video: [Replication Number Simul8 Simulation Trial Setup, Number of Runs 95% confidence Interval](https://www.youtube.com/watch?v=cycByv3kQRs) — Ramzi Fayad
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/replications-of-runs
- Whole chapter: https://www.bctengineer.com/md/semester_8/simulation_and_modeling/chapter-8

## Question

Why do we need replications of runs? Explain with example.

## Short answer

Replications provide independent runs with different random number seeds, enabling confidence interval estimation and accounting for randomness. One run may be atypical. With five replications, 95% CI for mean delay is (1.86, 2.74) min, showing variation hidden in a single run.

## Answer

A **replication** is a complete, independent run of the simulation using the same model and input parameters but a different stream of random numbers (different seeds). Replications are needed because one run gives only one random sample of the output.

#### Reasons for replications
1. **Randomness**: the output of a run is a random variable. One run may be unusually good or bad, and its value alone is not reliable.
2. **Independent observations**: observations inside one run are autocorrelated (a long queue now means a long queue a moment later), so the classical formulas for variance and confidence intervals do not apply. Averages of whole runs are independent and identically distributed.
3. **Confidence intervals**: with R replications, Ȳ ± t(α/2, R-1)·S/√R can be computed. A single run gives no estimate of variance.
4. **Precision control**: more replications reduce the half-width in proportion to 1/√R.
5. **Initial bias**: each replication starts afresh, so the effect of start-up conditions can be examined, and a warm-up can be applied.
6. **Comparing alternatives**: reliable comparison of two designs needs several runs of each.

#### Conditions
- Same model, parameters and run length in every replication.
- Different random-number seeds or non-overlapping streams, so that runs are independent.
- Run length and number of replications chosen from the required accuracy.

#### Example
Mean customer delay in a single-teller bank model from one run is 2.1 min. Four more runs with different seeds give 2.5, 1.9, 2.8 and 2.2 min. The single value 2.1 hides the variation; the five runs show Ȳ = 2.30 and S = 0.354. The 95% confidence interval is 2.30 ± 2.776 × 0.354/√5 = 2.30 ± 0.44, i.e. (1.86, 2.74) min. A manager can now see that the true delay may be anywhere from about 1.9 to 2.7 min, which is not visible from one run.

For a half-width of 0.1 min, about (1.96 × 0.354 / 0.1)² ≈ 48, so around 50 replications are required.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What defines a replication?
   A. A run with the same seed repeated
   B. A run of a different model
   C. A shorter run with deleted data
   D. An independent run of the same model using a different random number stream
   Answer: D. Replications use the same model and parameters but different seeds or streams. (Key point: Replication definition)

2. Why can observations from one run not be used with classical CI formulas?
   A. They are autocorrelated, whereas run averages from replications are independent and identically distributed
   B. They are always normal
   C. They have zero variance
   D. They are too few
   Answer: A. Autocorrelation breaks the formulas; averages of whole replications are iid. (Key point: Why independent runs)

3. What does a single run fail to provide?
   A. A mean value
   B. An estimate of variance, hence no confidence interval
   C. Any output
   D. A random number stream
   Answer: B. One run is one random sample, so variance and CI cannot be computed. (Key point: Single run limitation)

4. Using R >= (1.96 S / epsilon)^2 with S = 0.354 and epsilon = 0.1, about how many replications are needed?
   A. 5
   B. 15
   C. About 48 (around 50)
   D. 500
   Answer: C. (1.96 x 0.354 / 0.1)^2 is about 48. (Key point: Number needed)

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