Types of simulation and model, Lecture notes of Mathematical Modeling and Simulation

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CHAPTER TWO

TYPES OF SIMULATION

Simulation Intro

• (^) Simulation is a representation of a real world or hypothetical events or processes
• (^) It can be live, constructive and virtual
  • (^) “Live" simulation (where actual players use genuine systems in a real environment); Real entities included in the simulation
  • (^) “Virtual" simulation (where actual players use simulated systems in a synthetic environment,^ Real and computer generated entities are present and interact with environment
  • (^) “Constructive" simulation (where simulated players use simulated systems in a synthetic environment), all entities are computer generated.

• (^) Virtual: Simulation involving real people

operating simulated systems. Virtual

simulations inject Human-In-The-Loop in a

central role by exercising:

• (^) Motor control skills (e.g., flying an airplane)
• (^) Decision skills (e.g., committing fire control

resources to action)

• (^) Communication skills (e.g., members of a C4I

team)

• (^) Constructive: Simulation involving simulated people operating simulated systems. Real people can stimulate (make inputs) but are not involved in determining outcomes. Constructive simulations offer the ability to:Analyze concepts
• (^) Predict possible outcomes
• (^) Stress large organizations
• (^) Make measurements
• (^) Generate statistics
• (^) Perform analysis

Types of Simulation

Models

20  (^) Simulation models can be classified as being static or dynamic, deterministic or stochastic and discrete or continuous.  (^) A static simulation model represents a system, which does not change with time or represents the system at a particular point in time.  (^) Dynamic simulation models represent systems as they change over time.  (^) Deterministic models have a known set of inputs, which result into unique set of outputs.  (^) In stochastic model, there are one or more random input variables, which lead to random outputs.  (^) System in which the state of the system changes continuously with time are called continuous systems while the systems in which the state changes abruptly at discrete points in time called discrete systems.

Stochastic vs. Deterministic

 (^) Stochastic simulation: a simulation that contains random (probabilistic) elements, e.g.,  (^) Examples  (^) Inter-arrival time or service time of customers at a restaurant or store  (^) Amount of time required to service a customer  (^) Output is a random quantity (multiple runs required analyze output)  (^) Deterministic simulation: a simulation containing no random elements  (^) Examples  (^) Simulation of a digital circuit  (^) Simulation of a chemical reaction based on differential equations  (^) Output is deterministic for a given set of inputs

Continuous vs.

Discrete

 Discrete  (^) State of the system is viewed as changing at discrete points in time  (^) An event is associated with each state transition  (^) Events contain time stamp  Continuous  (^) State of the system is viewed as changing continuously across time  (^) System typically described by a set of differential equations

Types of models

Models Physical Mathematical Static Dynamic Static Dynamic Numerical Analytical Analytical Numerical System Simulation

Types of models

 Mathematical models use symbolic notation and mathematical equation to represent a system.  The system attributes are represented by variables, and the activities are represented by mathematical functions that interrelate the variables.

Differences between static modeling and dynamic modeling 

The most notable difference between static and

dynamic models of a system is that while a

dynamic model refers to runtime model of the

system, static model is the model of the system

not during runtime.



Another difference lies in the use of differential

equations in dynamic model



Dynamic models keep changing with reference

to time whereas static models are at

equilibrium of in a steady state.



Static model is more structural than behavioral

while dynamic model is a representation of the

behavior of the static components of the

system.

World Views of Simulation Model

• (^) Event-Scheduling View
  • (^) Focus on processing each event
• (^) Process-interaction View
  • (^) View model as a set of processes through which

an entity “flows”

• (^) Life-cycle approach – time-sequenced list of

events, activities, & delays

• (^) Common in simulation environments 16

World Views of Simulation Model

• (^) Activity Scanning Approach
  • (^) Focus on activities & conditions that allow it to begin
  • (^) At each clock advance, scan conditions to start any

activity that can begin

• (^) Approach is simple, but scan is slow
• (^) New 3-phase approach includes some event

scheduling – somewhat more complex but more

efficient

17

Human in the Loop Simul...

• (^) Simulations are performed for a variety of reasons, many of which involve creating experiences for people that are beneficial (such as training) or entertaining. Many of these applications require that a human be in the loop, that is, reacting to inputs from other simulation components, and generating outputs that affect the course of simulation.
• (^) Moreover, some simulations require representations of human behavior even if no live human is in the loop. These representations,if too simplistic, can restrict the validity of the simulation results.

• (^) Human-in-the-Loop (HITL) Modeling & Simulation (M&S) is a model type that requires human interaction during runtime. It employs one or more human operators in direct control of the simulation/simulator or in some key support function.
• (^) Human-in-the-Loop lends itself the ability for the user to change the outcome of an event or process. HITL is extremely effective for the purposes of training because it allows the trainee to immerse themselves in the event or process. The immersion effectively contributes to a positive transfer of skills acquired to the real world.