MIE360 10 Pilot Runs - MIE360 Computer Modeling and Simulation Lecture Notes Lecture 10 Make Pilot Runs Yes Determine of replications Yes Include

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MIE360 Computer Modeling and Simulation Lecture Notes Lecture 10– Make Pilot Runs Yes Determine # of replications No Determine the run lengths Terminating Simulation Determine the Warm-up period No Include Transient Yes Determine # of replications The Warm-Up period In many real life situations we rarely start the system from scratch. When plants close, its status is frozen as is until it opens up again the next day. Or it runs 24/7 shifts. When we simulate such systems in a computer model, there is an initial period which resembles the operation of the plant when it first started many years ago. In order to ensure that the initial simulation period is representative of the steady state operation of a system, we have to wait some time until the simulation itself reaches this steady state. Until it reaches steady-state the results have to be ignored. We can only start tracking the states and counters once this stead state period is reached. Computer simulation languages always allow a user to specify a warm-up period. For now we delay dealing with this issue, by assuming that we wish to include the transient. Terminating vs. Non-terminating Simulations A terminating simulation is one that has a natural end point, such as a closing time or natural cycle. A non-terminating simulation is one that has no such natural end-point. Clearly the problem of the run length only exists for non-terminating simulations - for terminating simulation the run length is decided upon by the user or situation. While there are very sophisticated methods for determining the run lengths for non-terminating simulations, these are beyond the scope of introductory simulation courses, and common practice. The standard practice in simulation is for the analyst to negotiate a run-length with the client that is considered “appropriate” and thus to negotiate the client into using a terminating simulation. Daniel Frances © 2010 1
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MIE360 Computer Modeling and Simulation Lecture Notes Using Replications to derive confidence intervals Consider simulation results in the table above i 123456789 1 0 1 1 1 2 1 3A v g X i 143 7 8 41 27 5 9 81 1 7 6 . 6 2 What about reporting a confidence interval for the average of 6.62? Perhaps we can calculate a sample standard deviation for these observations, and then create a confidence interval around the 6.62 average! DEFINITELY NO! Outputs of simulation models are notoriously auto-correlated! Large readings tend to come in bunches, and so do small readings. It is the same reason why waiting lines randomly grow, stay long for a while, and then randomly return to shorter lines. The theory behind confidence intervals requires the data to be IID, and assumes no autocorrelation. With this assumption blatantly violated reporting confidence intervals based on a stream of simulation outputs would be totally invalid!
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This note was uploaded on 09/20/2011 for the course MIE 360 taught by Professor D.frances during the Fall '10 term at University of Toronto- Toronto.

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MIE360 10 Pilot Runs - MIE360 Computer Modeling and Simulation Lecture Notes Lecture 10 Make Pilot Runs Yes Determine of replications Yes Include

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