Lecture 16 - Simulation and Random Numbers

Lecture 16 - Simulation and Random Numbers - Lecture 16...

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1 Lecture 16 Simulation Analysis and Random Number Generation DADSS
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2 Administrative Details Homework 7 Due Tuesday Term Project Progress? Questions from last class?
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3 What is Simulation? “A mathematical model that is studied by  means of simulation” Question:  Why? To “simulate” is to replicate or copy the process  of something – in our case, for the sake of  studying it Many mathematical models are so complicated  that it is impossible or impractical to “solve”  them via a  closed-form  or analytic solution
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4 Analytical vs Computational An example:  d  =  r   ×   t What happens to distance traveled if I double my speed? If we want to study the behavior of distance, we have a  simple mathematical model with which to do that Sensitivity of distance with respect to the rate Sensitivity of distance with respect to the time Both Because this model is simple, we can develop an  explicit understanding analytically
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5 Analytical vs Computational Another example: A check-out line in a supermarket What happens to the amount of time I spend in line if the  supermarket opens another register? Even if we could set out a system of equations that  represented this situation (“queueing theory”), it would  be very difficult to analyze analytically Instead, we can analyze the  actual  problem by building  replica  (or simulation) of the problem and studying  that The difference? Control We get to “play god”
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6 Possible Future States Simulation models are useful primarily for  allowing examination of what  could  happen or  what  could have  happened Two roles for simulation analysis: Studying uncertainty Think of a decision tree with an infinite number of  branches Studying complex systems Systems for which an analytical representation is  impractical or impossible
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7 Simulation Analysis in General Describe the problem AS ALWAYS
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