Simulation Modeling

Simulation Modeling

1. System

   • Elements that interact
     • Entities
   • Made by sub-systems

2. Queue

3. Model

   • Analogic circuitry
   • Mathematical equations
   • Physical duplicates
   • Computer programs
   • Describe the behavior of a system

4. State of the system

   • Total of entities and attributes
   • Deterministic
     • No random elements
     • Trajectories- Real system
   • Stochastic
     • No need to match trajectories
   • Trajectories
     • Plausible realizations of what might be in real system
   • Observability
     • Assume that by observing the system we can infer the state
   • Controllability
     • Current state -> Desire state
       • Finite times
       • Finite inputs

5. Modeling Process

   • Stage 1
     • Identify what is meant by the system
     • Descriptive model
   • Stage 2
     • Behavior and interactions
       • Mathematical
       • Differential equations
       • Constrains (optimization)
       • Distribution modeling
     • Formal model
   • Verification
     • Feedback between computer model and formal model
   • Validation
     • Feedback between computer model and reality

6. Discrete Event Systems

   • State changes occur at a discrete set of points
     • Events
   • Process model
     • Requirements
       • Activities
         • Delays
           • Decisions
   • Type III Error
     • Choosing the wrong problem representation
   • Event Graphs
     • Provide a description of how events change system

7. Randomness

   • Random presence or absence may affect system behavior
   • Independence
   • Known distribution
   • Unlimited
   • Fast
   • Reproducible
   • PRNG
     • Pseudo-Random Number Generators

8. Model as a model

   • Inputs into outputs
   • Inputs
     • Parameterizations of each run
   • Distribution
   • Output Analysis
     • Make it work
   • Replication
     • Static system, time dependency
   • Replication/Delation
     • Delete some of the outputs