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Maria Hybinette, UGA
CSCI: 4210/
Simulation & Modeling
Event-Oriented Simulations
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Outline
! Simulation modeling characteristics
! Concept of Time
! A DES computation
! DES System = model + simulation executive
! Data structures
! Program (Code)
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Simulation Model Characteristics
Today we will look at:
! Static or dynamic models
! Stochastic, deterministic or chaotic models
! Discrete or continuous change/models
! Aggregates or Individuals
C formapcuttaelr wAirtth: a Bdreonwdnriiatni (^) cT rseter (^) u-cture. Generated stochastically Maria Hybinette, UGA 4 Static Dynamic Discrete Time Continuous Time Deterministic Stochastic Mo nte Ca rlo sim ula tio ns
Static or Dynamic Models
! Dynamic:
Ā» State variables change over time
Ā» System Dynamics, Discrete Event, Agent-Based
! Static:
Ā» Snapshot at a single point in time
Ā» Monte Carlo simulation, optimization models
yi Response Xi,2 X 3 i, ā¦ Xi,j ā¦ Xi,p n . . . 3 2 1 Repetitions^ X 1 i, Inputs
Deterministic, Stochastic or Chaotic
! Deterministic:
Ā» Predictive behavior. The system is perfectly understood, then it is possible to predict precisely what will happen. Ā» Repeatable
! Stochastic:
Ā» behavior cannot be entirely predicted.
! Chaotic:
Ā» deterministic model with a behavior that cannot be entirely predicted. Depends so sensitively on the systemās initial conditions so that in effect it cannot be predicted.
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Discrete or Continuous Models
! Discrete model:
Ā» state variables change only at a countable
number of points in time.
- These points in time are the ones at which the event occurs/change in state.
! Continuous model:
Ā» state variables change in a continuous way,
and not abruptly from one state to another.
Ā» infinite number of states.
Maria Hybinette, UGA 8 State variables Time Continuous: State variables change continuously as a function of time State variables = f( t ) State variables Time Discrete: State variables change at discrete times Maria Hybinette, UGA 9 Static Dynamic Discrete Time Continuous Time Deterministic Stochastic One or more random parameters Fixed inputs yield fixed outputs Fixed inputs yield different outputs System description at one point in time System state changes at distinct times System description as it changes in time Model allows system state to change at any time Mo nte Ca rlo sim ula tio ns Maria Hybinette, UGA 10
Simulation
Actual System Simulated System
! Simulated system imitates operations of actual system over time ! Artificial history of system can be generated and observed ! Internal (perhaps unobservable) behavior of system can be studied ! Time scale can be altered as needed ! Conclusion about actual system characteristics can be inferred inputs (t) Parameters outputs (t) outputs (t)
What is a Simulation Model?
! An abstraction of a real system
! Simplified assumptions are used to capture (only)
important behaviors
Actual System Parameters (^) EnvirSoynsmteemnt inputs (t) outputs (t) Model (simplified) Parameters (^) EnviroMnmodeenlt inputs (t) outputs (t)
Systemās Modeling
System
Interactive
objects
System Environment
Placing the system boundary is the first difficult task in modeling
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How to Create a DES?
! DES Modeling raises the following questions?
Ā» How does each event affect system state and
attributes?
Ā» How are activities defined?
- What events mark beginning and the end?
- What condition (if any) most hold?
Ā» How are delays defined?
Ā» How is the simulation initialized?
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A Simulation Example
! Single-server Queue at a bank
! One possible problem formulation:
Ā» ācustomer have to wait too long in my bankā
! Objective:
Ā» Determine the effect of an additional cashier
! Data needed:
Ā» inter-arrival time of customers
Ā» Service times
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Simulation Results
Queue Length Time Maria Hybinette, UGA 22 Moving Image
Movie
! Series of still images, sufficient to convey
recognizable motion
System Snapshots
System Simulation
! Series of system snapshot
Ā» system state
Ā» activities in progress
Ā» end time
System Snapshots
Moving Image System Simulation
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Time
! Physical system: actual or imagined system being modeled
! Simulation : a system that emulates the behavior of a physical system
physical system simulation
main() { ... double clock; ... } ! physical time: time in the physical system Ā» Noon, December 31 , 1999 to noon January 1 , 2000 ! simulation time: representation of physical time within the simulation Ā» floating point values in interval [ 0. 0 , 24. 0 ] ! wallclock time: time during the execution of the simulation, usually output from a hardware clock Ā» 9 : 00 to 9 : 15 AM on September 10 , 1999 Maria Hybinette, UGA 26
Simulation Time
Simulation time is defined as a totally ordered set of values
where each value represents an instant of time in the
physical system being modeled.
! For any two values of simulation time T 1 representing
instant P 1 , and T 2 representing P 2 :
! Correct ordering of time instants
Ā» If T 1 < T 2 , then P 1 occurs before P 2 Ā» 9.0 represents 9 PM, 10.5 represents 10:30 PM
! Correct representation of time durations
Ā» T 2 - T 1 = k (P 2 - P 1 ) for some constant k Ā» 1.0 in simulation time represents 1 hour of physical time Maria Hybinette, UGA 27
Modes of Execution
! As-fast-as-possible execution (unpaced): no fixed
relationship necessarily exists between advances in
simulation time and advances in wallclock time
! Real-time execution (paced): each advance in simulation
time is paced to occur in synchrony with an equivalent
advance in wallclock time
! Scaled real-time execution (paced): each advance in
simulation time is paced to occur in synchrony with S * an
equivalent advance in wallclock time (e.g., 2 x wallclock
time)
Converting from wallclock to Simulation Time:
Simulation Time = W2S(W) = T 0 + S * (W - W 0 ) W = wallclock time; S = scale factor W 0 (T 0 ) = wallclock (simulation) time at start of simulation (assume simulation and wallclock time use same time units) Maria Hybinette, UGA 28
Discrete Event Simulation
Discrete event simulation: computer model for a
system where changes in the state of the system
occur at discrete points in simulation time.
Fundamental concepts:
- system state (state variables)
- state transitions (events)
A DES computation: can be viewed as a sequence of
event computations , with each event computation is
assigned a (simulation time) time stamp. Each event
computation can
- modify state variables
- schedule new events
Discrete Event Simulation
Computation
! Unprocessed events are stored in a pending event list
! Events are processed in time stamp order
example: air traffic at an airport
events: aircraft arrival, landing, departure
arrival 8: departure 9: landed 8: schedules^ arrival 9:30^ processed event^ current event unprocessed event schedules
Discrete Event Simulation
System
model of the
physical
system
Simulation Application
ā¢ state variables
ā¢ code modeling system behavior
ā¢ I/O and user interface software
Simulation Executive
ā¢ event list management
ā¢ managing advances in simulation time
calls to
schedule
events
calls to event
handlers
Independent
of the
simulation
application
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Summary
! Simulation modeling characteristics ! Time Ā» Important to distinguish among simulation time, wallclock time, and time in the physical system Ā» Paced execution (e.g., immersive virtual environments) vs. unpaced execution (e.g., simulations to analyze systems) ! DES computation: sequence of event computations Ā» Modify state variables Ā» Schedule new events ! DES System = model + simulation executive ! Data structures Ā» Pending event list to hold unprocessed events Ā» State variables Ā» Simulation time clock variable ! Program (Code) Ā» Main event processing loop Ā» Event procedures Ā» Events processed in time stamp order
