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Summary  Simulation Modeling and Analysis

1.1 The Nature of Simulation

Simulation:to imitate the operations of a facility or process based on a model of the system.

For what kinds of problems has simulation been found a useful and powerful tool?1. Designing and analyzing manufacturing systems.
2. Analyzing supply chains.
3. DeDesigning and operating transportation systems such as airports, freeways, ports and subways. 
Objections against simulation:1. Models used to study largescale systems tend to be very complex, and writing computer programs to execute them can be an arduous task indeed.
2. A large amount of computer time is sometimes required.
3. There appears to be an unfortunate impressions that simulation is just an exercise in computer programming, albeit a complicated one. 
What's a system in the simulation
the facility process of interest 
What's a modelSet of assumptions about how the system works

Analytic SolutionFound by using mathematical methods to obtain exact information

1.2 Systems, Models and Simulations

System:a collection of entities, that act and interact together toward the accomplishment of some logical end.

State of a system:collection of variables necessary to describe a system at a particular time, relative to the objectives of a study.

Discrete system:System for which the state variables change instantaneously at separated points in time.

Continuous system:System for which the state variables change continuously with respect to time.

Ways to study a system:Look at figure.

Static Model:Representation of a system at a particular time, or one that may be used to represent a system in which time simply plays no role.

Dynamic model:Represents a system as it evolves over time.

Deterministic Model:A simulation model that does not contain any probabilistic components. The output is determined once the set of input quantities and relationships in the model have been specified, even though it might take a lot of computer time to evaluate what it is.

Stochastic model:Modes having at least some random input components. They produce output that is itself random, which must therefore be treated as only an estimate of the true characteristics of the model.

Continuous Model:State can change continuously over time.

Discrete Model:State can change at discrete points (Events) in time.

What type are most operational models?Dynamic, discreteevent, stochastic.

1.3 DiscreteEvent Simulation

Discreteevent simulation:Concerns the modeling of a system as it evolves over time by a representation in which the state variables change instantaneously at separate points in time.

Event:Instantaneous occurence that may change the state of the system.

Simulation clock:variable that keeps the current value of simulated time in the model.

What are two principal approaches for advancing the simulation clock?1. Nextevent time advance
2. Fixedincrement time advance 
Event list:List containing the next time when each type of event will occur.

Statistical counters:Variables used for storing statistical information about system performance.

Initialization routine:Subprogram to initialize the simulation model at time 0.

Timing routine:Subprogram that determines the next event from the event list and then advances the simulation clock to the time when that event is to occur.

Event routine:Subprogram that updates the system state when a particular type of event occurs.

Library routines:Set of subprograms used to generate random observations from probability distributions that were determined as part of the simulation model.

Report generator:Subprogram that computes estimates (from the statistical counters) of the desired measures of performance and produces a report when the simulation ends.

Main program:Subprogram that invokes the timing routine to determine the next event and then transfers contrl to the corresponding event routine to update the system state appropriately. The main program may also check for termination and invoke the report generator when the simulation is over.

If the main program invokes event routine i, what are the activities that occur?1. The system state is updated to account for the fact that an event of type i has occurred.
2. Information about system performance is gathered by updating the statistical counters.
3. The times of occurrence of future events are generated, and this information is added to the event list.
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Latest added flashcards
What is an agent?
an entity that senses environment and makes decisions based on that information
What is the goal of spacefilling design
Spread design points "uniformly" over the experimental region
What is the central Composite Design (CCD)
augment the existing design points with 4 axial points:
2^k design points
1 center point
2k axial points
2^k design points
1 center point
2k axial points
Formulate a test of quality of approximate response surface of metamodel
1) Simulate system at center point
2) Construct (paired t) confidence interval for differences between simulated values and estimated values from metamodel
3) if CI does not contain 0m difference in statistically significant
2) Construct (paired t) confidence interval for differences between simulated values and estimated values from metamodel
3) if CI does not contain 0m difference in statistically significant
Multiple metamodels can be fit by using the same set of simulation runs if?
I All factors that are significant for any of the responses are included in the design
II all responses are recorded for each run
II all responses are recorded for each run
What is is a response surface?
Plot of response values versus input parameters
Does effect insignificant imply corresponding regression to be insignificant and vice versa?
No this does not imply.
> Do regression directly on raw simulation data
> Do regression directly on raw simulation data
When is factor y more important than factor x?
If slope in direction y < slope in direction x at x but e_y > e_x
Give the regression in coded variables and in natural variables with the corresponding coefficients.
See picture
How do metamodels look like?
Usually takes the form of a first or secondorder regression equation