LECTURE NOTES ON SIMULATION AND MODELING
Course Content: Introduction and basic simulation procedures. Model
classification: Monte Carlo
simulation, discrete-event simulation, continuous system simulation, mixed
continuous/discrete-event
simulation. Queui
Object1
Object2
Object4
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Waiting Line Models
The M/Ek/1 ( /FIFO) system
It is a queuing model where the arrivals follow a Poisson process, service time follows an Erlang (k) probability
distribution
Object1
Object3
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Waiting Line Models
In this section and the subsequent sections of this chapter, we explain several models. In presenting the models
below, we start slowly and provide several exampl
QUEUE NOTES
Terminology
Calling population. Total number of distinct potential arrivals (The size of the calling
population may be assumed to be finite (limited) or infinite (unlimited).
Arrivals. Let
A(t) := No of arrivals during [0, t]
:= lim
A(t)/t
(Me
Object1
Object3
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Waiting Line Models
The M/M/C ( /FIFO) system
It is a queuing model where the arrivals follow a Poisson process, service times are exponentially distributed and
there are C servers.
Object1
Object3
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Waiting Line Models
The M/M/1 (N/FIFO) system
It is a queuing model where the arrivals follow a Poisson process, service times are exponentially distributed and
there is only one ser
10.2
Functions - Algebra of Functions
Several functions can work together in one larger function. There are 5 common
operations that can be performed on functions. The four basic operations on functions are adding, subtracting, multiplying, and dividing.
10.5
Functions - Exponential Functions
As our study of algebra gets more advanced we begin to study more involved
functions. One pair of inverse functions we will look at are exponential functions
and logarithmic functions. Here we will look at exponentia
10.3
Functions - Inverse Functions
Objective: Identify and find inverse functions.
When a value goes into a function it is called the input. The result that we get
when we evaluate the function is called the output. When working with functions
sometimes w
Simulation
Based on
Law & Kelton, Simulation Modeling &
Analysis, McGraw-Hill
?Why Simulation
Test design when cannot analyze
System too complex
Can analyze only for certain cases (Poisson
arrivals, very large N, etc.)
Verify analysis
Fast production
Midterm Exam for Simulation (CAP 4800)
Summer 2013
> SOLUTIONS <
Welcome to the Midterm Exam for Simulation. Read each problem carefully. There are 10 required problems
where each problem is worth 10 points. There is also an additional extra credit proble
8.2
Radicals - Higher Roots
Objective: Simplify radicals with an index greater than two.
While square roots are the most common type of radical we work with, we can
take higher roots of numbers as well: cube roots, fourth roots, fth roots, etc. Following
8.1
Radicals - Square Roots
Objective: Simplify expressions with square roots.
Square roots are the most common type of radical used. A square root unsquares a number. For example, because 52 = 25 we say the square root of 25 is 5.
The square root of 25 i
6.2
Factoring - Grouping
Objective: Factor polynomials with four terms using grouping.
The rst thing we will always do when factoring is try to factor out a GCF. This
GCF is often a monomial like in the problem 5x y + 10xz the GCF is the monomial 5x, so w
8.8
Radicals - Complex Numbers
Objective: Add, subtract, multiply, rationalize, and simplify expressions using complex numbers.
World View Note: When mathematics was rst used, the primary purpose was
for counting. Thus they did not originally use negative
3.1
Inequalities - Graphing and Solving
When we have an equation such as x = 4 we have a specic value for our variable.
With inequalities we will give a range of values for our variable. To do this we
will not use equals, but one of the following symbols:
2.3
Graphing - Slope-Intercept Form
Objective: Give the equation of a line with a known slope and y-intercept.
When graphing a line we found one method we could use is to make a table of
values. However, if we can identify some properties of the line, we
6.3
Factoring - Trinomials where a = 1
Objective: Factor trinomials where the coecient of x2 is one.
Factoring with three terms, or trinomials, is the most important type of factoring
to be able to master. As factoring is multiplication backwards we will
6.4
Factoring - Trinomials where a
1
Objective: Factor trinomials using the ac method when the coecient
of x2 is not one.
When factoring trinomials we used the ac method to split the middle term and
then factor by grouping. The ac method gets its name fro
2.1
Graphs - Points and Lines
Often, to get an idea of the behavior of an equation we will make a picture that
represents the solutions to the equations. A graph is simplify a picture of the
solutions to an equation. Before we spend much time on making a
2.5
Graphing - Parallel and Perpendicular Lines
Objective: Identify the equation of a line given a parallel or perpendicular line.
There is an interesting connection between the slope of lines that are parallel and
the slope of lines that are perpendicula
2.2
Graphing - Slope
Objective: Find the slope of a line given a graph or two points.
As we graph lines, we will want to be able to identify dierent properties of the
lines we graph. One of the most important properties of a line is its slope. Slope
is a
6.1
Factoring - Greatest Common Factor
Objective: Find the greatest common factor of a polynomial and factor
it out of the expression.
The opposite of multiplying polynomials together is factoring polynomials. There
are many benits of a polynomial being f
2.4
Graphing - Point-Slope Form
Objective: Give the equation of a line with a known slope and point.
The slope-intercept form has the advantage of being simple to remember and use,
however, it has one major disadvantage: we must know the y-intercept in or
10.6
Functions - Logarithms
The inverse of an exponential function is a new function known as a logarithm.
Lograithms are studied in detail in advanced algebra, here we will take an introductory look at how logarithms works. When working with radicals we
10.6
Functions - Compound Interest
Objective: Calculate nal account balances using the formulas for compound and continuous interest.
An application of exponential functions is compound interest. When money is
invested in an account (or given out on loan)
8.7
Radicals - Mixed Index
Knowing that a radical has the same properties as exponents (written as a ratio)
allows us to manipulate radicals in new ways. One thing we are allowed to do is
reduce, not just the radicand, but the index as well. This is shown
9.10
Quadratics - Revenue and Distance
Objective: Solve revenue and distance applications of quadratic equations.
A common application of quadratics comes from revenue and distance problems.
Both are set up almost identical to each other so they are both