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Systems Simulation Midterm
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Key Concepts:
Terms in this set (28)
Simulation
Defining, designing, and constructing a model or representation; defining the experiments to be conducted; collecting and analyzing data to drive model; and analyzing and interpreting the Results.
Type 1 Error
Falsely reject the null hypothesis
false postive or alpha
Type 2 Error
Falsely Accept the Null Hypothesis
False Negative or Beta Error
Modeling
starting points with physical or mathematical description of an event
Static Model
a specific structure of the object that exist in the complex problem under study. Time and random events had no meaning to those models. These are expressed using class, object and USECASE diagrams.
Physical Working Models
such as architectural model of a building
Mathematical Models
discrete event systems and queuing theory
Discrete event Systems
events that occur at asynchronous distinct points in time and changing a state of a system
Queuing Theory
-Using queuing theory random processes are described in terms of different assumed probabilities distributions. As a results, performance measures are calculated directly
-Performance measures such as time in the queue, mean time in designing a product and so on.
-How long do customers have to wait at the checkouts? What happens with the waiting 7 time during peak-hours? Are there enough checkouts?
Discrete system
a set of data where the values belonging to the set are distinct and separate
-example is a roll of a dice [ 1,2,3,4,5,6]
-counted
-quantitative
-data that has distinguishable spaces between possible values
Continuous System
a set of data where the values that belong to the set can take on any value within a finite or infinite interval
-example is a measurement of temperature [50-100F]
-Measured
-Example speed of a train
- data that can be measured as finely as is practical (no spaces between values)
Basic parameters of queuing models
1. Arrival Rate
- Ex: Customers may arrive one by one or in batches
2. The Behavior of Customers
-Ex: In call centers, customers will hang up when they to wait too long
3. Service Times
- Ex: The Processing rates of the machines in a production system can be increased once the number of jobs waiting to be processed becomes too large
Nominal Data
Assign number to objects where different numbers indicate different objects. the numbers have no real meaning other than differentiating between objects. Order of numbers is not important
-EX: Gender: Male 1 Female 2
Ordinal Data
Assign numbers to objects, but the number also have meaningful order
-Ex: Level of Education, Work Experience
Interval Data
Number have order like ordinal, but there are also equal intervals between adjacent categories
-Ex: temperature in Degrees Farenheit: the difference between 78 & 79 degrees is the same as 45 & 46 degrees
Stochastic systems
systems that are dynamic and unpredictable because of the occurrence of the random events
Stochastic system consists of 3 components
1. Noise Factors: Uncontrollable Factors
2. Controllable Factors: decision variables that you can manipulate in the model in order to improve a system's performance (# of processors, transporters, etc)
3. Output of the model: since the input to a modal are stochastic, the output or performance measures are also stochastic
How can we control noise factors in an experiment?
Factorial Analysis is a good way to minimize noise factors
System- as - is
the system as it exists now
system - to - be
the system as it is envisioned or desired
Verification
-asks "Was the system built right?"
-asks "Were the requirements formulated right?"
-involves satisfying customer intent
Validation
- asks "Was the Right system built?"
- asks "Where the right requirements formulated?"
- involves fully understanding customer intent
Poisson Distribution
Given an average arrival ( ) the Poisson distribution give the probability a certain number of customers (x) arrive in a given time window
- Poisson distribution is a Discrete distribution
-Time between customer arrivals usually (inter-arrival time) is exponentially distributed conversely, arrival rate is Poisson distributed
-service rate is Poisson distribution
Exponential Distribution
Given an average service time (mu), the exponential distribution gives the probability service will exceed specific time (t)
-continuous distribution
-service time is usually exponentially distributed
FIFO
first in first out
FILO
first in last out
Arrival Rate
Poisson Distribution
Service Time
Exponential Distributions
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