Introduction

# Introduction - Control of Discrete-Event Systems Introduction What is simulation and what is it used for Simulation is a method of predicting the

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Control of Discrete-Event Systems Introduction What is simulation and what is it used for Simulation is a method of predicting the future given the situation set forth in the model. It is used to run a make believe system in order to predict how the real system will perform. In many application an analytical solution can not be found and one must resort to simulation. With simulation one only has to specify the model in terms of how the system works. The constraints do not need to be identified since they are imbedded in the model. The analytical solution requires identifying and expressing each constraint in a precise mathematical form. Deterministic simulation The first type of simulation that will be looked at is of a simple deterministic model. Deterministic means that we can determine what the simulation output will be. If we run the simulation two times we get the same results. No random inputs are used. This type of simulation is used for systems that have no random events associated with it. On the other hand non-deterministic simulation is when there is a random component to the model and the exact output can not be determined but rather estimated. This is used to simulate processes that involve random events. The following is an example of a deterministic system we wish to analyze. We will use both the analytical and numerical approach. Suppose you are to invest \$40 per week for a 50-week year, a total investment of \$2000, to put it into an IRA account. The IRA account requires a minimum of \$2000 so you save the money in a savings account in the mean time. Since the IRA account has a much higher interest rate than the savings account we will consider borrowing \$2000 to invent, along with the money in the saving account, into the IRA. The question is when do we make this transaction. Do not consider the deferred tax property of the IRA account of the effects of compounding the interest.

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Analytical Solution: IRA b s I t I t t tI t y ) 1 ( 2000 ) 1 ( 2 ) 1 ( 2000 2 2000 ) ( - + - - + = s b IRA b I I I I T dt t dy - - = = 0 ) ( if % 6 %, 8 %, 2 = = = IRA b s I I I then T = 120 days. This means the optimal time to make the transaction is in 120 days. Numerical Solution: We will simulate the system using the algorithm below. The simulation will be given T and the interest rates and will return the amount of money made. We then run the simulation for several values of T and chose the best one. int day = 0; double savings = 0; double longterm = 0; double petty = 0; for (day = 0; day < 365; day++) { savings = savings + (2000.0 / 365); if (savings >= 0) petty = petty + savings * (IS / 365); else petty = petty + savings * (IB / 365); petty = petty + longterm * (IIRA / 365); if (day == TDAY) { longterm = 2000; savings = savings - 2000; } } Notice that the petty account does not earn interest. This simulation yields the optimal time to make the transaction is as 121 days.
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## This note was uploaded on 09/13/2011 for the course EEL 5937 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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Introduction - Control of Discrete-Event Systems Introduction What is simulation and what is it used for Simulation is a method of predicting the

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