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Comparing Alternative system Configurations - Ranking and Selection

12 important questions on Comparing Alternative system Configurations - Ranking and Selection

How does the two-stage sampling from each of the k systems look like?

1) In the first stage we make a fixed number of replications of each system
2), then use the resulting variance estimates to determine how many more replications from each system are necessary in a second stage of sampling in order to reach a decision.
(one policy is chosen as the best)

Why would we select a subset of size m containing best of k systems?

Useful in the initial stages of a simulation study, where there may be a large number of alternative systems and we would like to perform an initial screening to eliminate those that appear to be clearly inferior. Thus, we could avoid expending a large amount of computer time getting precise estimates of the behaviour of these inferior systems.

What is a problem with the smallest mean out of k systems?

It does not make use of any sample-mean information from the first stage in deciding how many replications to make in the second stage, which seems inefficient.

Optimal computing budget allocation multistage approach:

maximizes the probability of correct selection given that a total budget B of replications is available to simulate the k systems.

In the case of a steady-state parameter for a non-terminating simulation, unbiased independent observations do not come as easily. What are approaches to selection for steady-state parameters?

1. Replication/deletion approach to produce Xij's that are independent and approximately unbiased for the steady-state mean of system i.
2. Make a single long run of system i and then let Xij be the sample mean of the observations in the jth batch within this run.

What is the tradeoff for specifying n0?

- If n0 too small, it could be that Si^2(n0) is much greater than sigmai^2, leading to an unnecessarily large value of Ni.
- If n0 too large, we could overshoot the necessary numbers of replications for some of the system, which is wasteful.

What is the goal of ranking and selection?

Select one of the k systems as the best one and control the probability that the selected system really is the best one

(in other words: Select the best of k systems with prescribed probability P∗ of
correct selection and with indifference amount (distance) d∗)

What is the correct selection (CS)

select mu_il, the l'th smallest of the mu_i's

Alternative Ranking and selection goals and procedures are?

Select a subset of size m containing the best of k systems with prescribed probability P∗ of correct selection and with indifference amount (distance) d∗
– Similar procedure (Dudewicz and Dalal), other constants
– Less ambitious, requires less runs
– Apply in initial stage of study when k is large
(e.g more policies are chosen as best)

Select the m best of k systems (not ranked) with pre-scribed probability P∗ of correct selection and with indifference amount (distance) d∗
– Similar procedure (Dudewicz and Dalal), other constants
– More ambitious, requires more runs

What is the 2-stage procedure of Dudwicz and Dalal?

Pilot stage: n_0≥ 20 runs of each system
• Use variance estimates to compute sample size N_i for system i (constant depends on P∗, d∗, k, n_0)
•Final stage:N_i − n_0 additional runs for system i
• Compute weighted sample means of 2 stages (w_i)
• Select the best system

Which problems can occur by ranking and selection?

* Correlation between alternatives
* Cororelation within an alternative

What do we mean as we define a system as the "best" system?

We define this system as the system that has the largest probability of producing a "good" outcome

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The question on the page originate from the summary of the following study material:

Simulation Modeling and Analysis | 9781259254383 | Averill M Law

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Comparing Alternative system Configurations - Ranking and Selection

12 important questions on Comparing Alternative system Configurations - Ranking and Selection

How does the two-stage sampling from each of the k systems look like?

Why would we select a subset of size m containing best of k systems?

What is a problem with the smallest mean out of k systems?

Optimal computing budget allocation multistage approach:

In the case of a steady-state parameter for a non-terminating simulation, unbiased independent observations do not come as easily. What are approaches to selection for steady-state parameters?

What is the tradeoff for specifying n0?

What is the goal of ranking and selection?

What is the correct selection (CS)

Alternative Ranking and selection goals and procedures are?

What is the 2-stage procedure of Dudwicz and Dalal?

Which problems can occur by ranking and selection?

What do we mean as we define a system as the "best" system?

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