12/7/2015© 2008 raymond p. jefferis iii1 simulation of computer systems

04/21/23 © 2008 Raymond P. Jefferis III 1

Simulation of Computer Systems


Overview of Simulation

• Fundamentals of discrete system simulation

• Building a system model

• Gathering system data

• Fitting the model

• Simulating the system

• Evaluating what-if conditions

• Using simulation in training


Available Tools

• Commercial simulation packages - CACI– SIMPROCESS– SIMSCRIPT

• Student versions of commercial packages– Arena (Systems Modeling Corporation)– ProModel (Promodel Corporation)

• Network monitor to gather data files


Introduction to Simulation

System types

Definition

Reasons for simulation

Simulation components

Development of a simulation --from model to verified results


System Types• Continuous

– Variables take on quasi-continuous values– Described by ordinary differential equations– Example: Motion of objects

• Discrete– Variables take on discrete values– Described by difference equations– Example: Queuing systems and networks


Definition

Simulation is the study of a process through observation of the behavior of a model over time in response to a pattern of inputs.


Keywords

• process

• model

• pattern of inputs

• response - behavior over time

• observations

• study


Process

• system to be simulated - aspect of whole

• exists as a physical object or system

• obeys natural (possibly known) laws

• responds predictably to inputs (controllable)

• responds over time

• may be observed (observable)


Model

• mathematical representation of the process

• based upon natural laws

• usually built by engineering scientist

• based upon experimental data

• must be verified

• predicts behavior for known inputs


Pattern of Inputs

• inputs affect system

• may be a time sequence

• may be statistically distributed– time is random variable– magnitude is random variable


Response

• behavior over time– Example: queue length

• may be statistical– Examples: arrival time, service time


Observations

• Inputs– Examples: packets, frames and their lengths,

arrival times

• Outputs– Examples: packets, frames and their lengths,

service times, queue lengths


Study

• network monitor (“SnifferTM”)

• “smart” switches, routers, & hubs

• modeling of distribution functions• verification of traffic rates and queues

TM Trademark of Network Associates, Inc.


Why simulate?

• Mathematical intractability

• Process independence needed

• Change of time scale needed

• Design tool

• Training tool

• Inference tool


Mathematical Intractability

• nonlinear models (queuing problems)

• models too complex (combinatorics)

• microscopic details wanted (distributions)

• analytical methods inadequate

• non-steady state solutions desired


Process Independence

• high testing costs - many alternatives

• parametric studies - many variations

• inaccessible processes - scale issues

• measurements alter the process - monitors

• hazards


Time Scale Change

• very short times - expand (microscopic)

• very long times - compress (macroscopic)


Design

• Model– reduction of time and cost to develop model

• Process– reduction of time and cost to optimize process– performance by some criterion


Training

• reduction of time and cost to train operator

• elimination of off-spec production that would otherwise occur during training

• elimination of costly “crashes” that would otherwise occur during training

• preparation for events not yet experienced


Inference

• Learning about possible relationships in system from external behavior

• model-reference diagnostics (possibly on-line using validated model)


Simulation Components

• Queuing system model

• Probability distributions

• Random numbers (generators)

• Random variable distributions

• Experiments - system data


Model System


Model Development (scientist)

• Fixed input/output data sets

• Adjust model & parameters to give best fit


Process Development (engineer)

• Fixed model & parameters

• Vary inputs to give best output performance


Optimization (process mgmt.)

• Fixed model and input data

• Adjust some parameters

• Review simulation results

• Repeat parameter adjustment to optimize

• Hill-climbing method


Scenarios (What-ifs)

• Fixed model

• Adjust some parameters or inputs (what-if)

• Review simulation results

• Repeat adjustment to get desired performance

• Evolutionary algorithm approach


Inputs

• assumed known

• assumed to influence process

• time/event bases

• form a sequence

• may be affected by sampling effects


Time-based Inputs

• have time-to-go

• triggered by clock


Event-based Inputs

• have condition of occurrence(based on process variables)

• triggered by process (model) conditions or state


Generalized Events

• time can be an event

• all events queued in linked list


Other Forms

• State machine– events– actions

• Expert system– if– then


Responses

• process must be observable

• observation must not disturb process

• state variables (observable)(saving state allows rerun from halt)

• assumed predictable and stable

• may be affected by sampling rate

• have time course for each input


Observations

• must not affect the process

• suffer from sampling effects - aliasing

• used to validate the model

• used historically to diagnose process faults

• used currently to filter process data

• used predictively to optimize performance


Process Study by Simulation

generation of inference about process from observations of model behavior in response to known inputs


Implications (Problem Formulation)

• What is the process?– What aspect is to be simulated?– What laws govern its behavior?

• What form should simulation take?– Discrete?– Continuous?


Related Issues

• user interface

• data capture interface

• data storage (often large files)

• fitting of distributions & models

• data presentation

• programming requirements


Implications (Study Objectives)

• What should be the result?

• What will be the expected benefits?

• Who will be the users of the results?


Implications (Model)

• What natural laws are represented?

• What assumptions, goals, measures?

• What boundary (limiting) conditions?

• What form (package, language)?

• How is it to be validated?


Implications (Data Collection)

• What data (how much, what type)?

• How often?

• How executed?

• What conditions?

• How processed?

• What precision?

• What format?


Implications (Coding)

• Package or language?

• What speed desired?

• Graphical effects?

• Object oriented?

• What interfaces?– User– Network monitor


Implications (Verification)

• How will this be accomplished?

• Testing of random number generator?

• Testing of time function inputs?

• Testing of traffic generation model?

• Testing of network monitor?

• Check physical units?

• Verification of predicted values?


Implications (Experimental Design)

• For observability

• To validate the model

• To validate the simulation


Implications (Analysis of Results)

• Do results make sense?

• Is time/physical scale (detail) appropriate?

• What inferences can be drawn?

• Are further studies needed?


Implications (Documentation)

• How will models be documented?

• How will results be presented?

• Save all for further studies?


Validation of Simulation

Validation is the determination that the simulated system closely approximates the real system for the given scope.


Validation (Functional Approach)

Operate in linear and nonlinear regions and confirm conformity with real system behavior. Operations outside the validated region should be “flagged” with warning messages for the user.


Validation (Distribution Issues)

Real-world probability distributions do not always conform to ideal models. Determine the degree of approximation and the resultant error.

Determine what traffic can be ignored, to remove statistical “outliers”


Validation (Independence Issues)

Verify statistical independence - does the model assume independence? Lack of it can invalidate such a model.


Validation (Aggregation of Effects )

Can effects that are separate be lumped together - time, space, etc. Determine if the degree of aggregation is too great.


Validation (Stationarity Issues)

Validate the stationarity of parameters and probability distributions - are there variations and are they significant to the accuracy of the simulation results?


Verification

Verification is the determination that the model and simulation are operating in the manner intended - that the logic of the simulation program is correct and is correctly implemented.


Verification Steps

• Logic “walkthrough”

• Modular testing for correct I/O relationships

• Comparison with known results(Possibly compare with reduced system)

• Sensitivity testing (parameters output)

• Limit checking (inputs and parameters)

12/7/2015© 2008 raymond p. jefferis iii1 simulation of computer systems

Documents

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simulation of computer

queue lengths

queuing systems

conditionsusing simulation

known inputs

discrete valuesdescribed

inputs controllableresponds