Chapter 17 Selecting the Best System

Question

1. What are the contributions in "Chapter 17: selecting the best system" ?

2. How many outputs are required under independent sampling?

3. Why is Fabian’s bound on PrICS useful?

4. What is the procedure for selecting the system?

Accepted Answer

The authors describe the basic principles of ranking and selection, a collection of experimentdesign techniques for comparing “ populations ” with the goal of finding the best among them.. The authors then describe the challenges and opportunities encountered in adapting ranking-and-selection techniques to stochastic simulation problems, along with key theorems, results and analysis tools that have proven useful in extending them to this setting.

Accepted Answer

For instance, if p2 = 4/5, p1 = 3/4, 1 − α = 0.95 and θ = 4/3, then the authors can show that the expected number of outputs that must be generated under independent sampling is about 357, while under CRN it is 400.

Accepted Answer

Fabian’s bound on Pr{ICS} is particularly useful because a is the term that depends on the sample variance (see Paulson’s a in Equation (8) for intuition).

Accepted Answer

The procedure is as follows: From each system, taken =⌈ 2h2σ2δ2⌉ (4)outputs, where h is an appropriate constant (determined below) and dxe means to round x up; then select the system with the largest sample mean as the best.

Accepted Answer

There exist at least four classes of comparison problems that arise in simulation studies: selecting the system with the largest or smallest expected performance measure (selection of the best), comparing all alternatives against a standard (comparison with a standard), selecting the system with the largest probability of actually being the best performer (multinomial selection), and selecting the system with the largest probability of success (Bernoulli selection).

Accepted Answer

In conjunction with a decomposition into pairwise comparisons, as in (7), this result can be used to derive R&S procedures for k ≥ 2.

Accepted Answer

0. Letl(t)=−a + λt u(t)= a − λtfor some a > 0 and λ = ∆/(2b) for some positive integer b. Let c(t) denote the continuation region (l(t), u(t)) and let T be the first time that B(t,∆) /∈ c(t).

Accepted Answer

as (1 − α) → 1, the expected sample size from system i 6= k is approximatelyri ≈ ln (k − 1 α) σ2(δ − λ)(µk − µi + λ)while for i = k it isrk ≈ ln (k − 1 α) σ2(δ − λ)(µk − µk−1 + λ) .

Accepted Answer

This is frequently the situation for socalled “terminating simulations” in which the initial conditions and stopping time for each replication are an inherent part of the definition of the system.

Accepted Answer

A hidden cost of using multi-stage procedures is the computational overhead in switching among the simulations of the k alternatives.

Chapter 17 Selecting the Best System

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Most frequently asked questions

1. What are the contributions in "Chapter 17: selecting the best system" ?

2. How many outputs are required under independent sampling?

3. Why is Fabian’s bound on PrICS useful?

4. What is the procedure for selecting the system?

5. What are the four classes of comparison problems that arise in simulation studies?

6. What is the simplest way to derive R&S procedures for k 2?

7. What is the probability of a b being the first time that B(t,?

8. What is the expected sample size from system i 6= k?

9. What is the common scenario for a so called “terminating simulation”?

10. What is the hidden cost of using multi-stage procedures?

Figures

Citations

Multiple Comparisons: Theory and Methods

Stochastic Simulation Optimization: An Optimal Computing Budget Allocation

Recent advances in ranking and selection

Stochastically Constrained Ranking and Selection via SCORE

Approximate Simulation Budget Allocation for Selecting the Best Design in the Presence of Stochastic Constraints

References

Simulation Modeling and Analysis

Discrete-Event System Simulation

Introduction to Probability Models.

Simulation Modeling And Analysis

Introduction to Probability Models.

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