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

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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

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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

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Introduction to Simulation

System types

Definition

Reasons for simulation

Simulation components

Development of a simulation --from model to verified results

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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

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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.

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Keywords

• process

• model

• pattern of inputs

• response - behavior over time

• observations

• study

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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)

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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

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Pattern of Inputs

• inputs affect system

• may be a time sequence

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

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Response

• behavior over time– Example: queue length

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

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Observations

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

arrival times

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

service times, queue lengths

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Study

• network monitor (“SnifferTM”)

• “smart” switches, routers, & hubs

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

TM Trademark of Network Associates, Inc.

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Why simulate?

• Mathematical intractability

• Process independence needed

• Change of time scale needed

• Design tool

• Training tool

• Inference tool

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Mathematical Intractability

• nonlinear models (queuing problems)

• models too complex (combinatorics)

• microscopic details wanted (distributions)

• analytical methods inadequate

• non-steady state solutions desired

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Process Independence

• high testing costs - many alternatives

• parametric studies - many variations

• inaccessible processes - scale issues

• measurements alter the process - monitors

• hazards

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Time Scale Change

• very short times - expand (microscopic)

• very long times - compress (macroscopic)

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Design

• Model– reduction of time and cost to develop model

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

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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

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Inference

• Learning about possible relationships in system from external behavior

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

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Simulation Components

• Queuing system model

• Probability distributions

• Random numbers (generators)

• Random variable distributions

• Experiments - system data

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Model System

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Model Development (scientist)

• Fixed input/output data sets

• Adjust model & parameters to give best fit

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Process Development (engineer)

• Fixed model & parameters

• Vary inputs to give best output performance

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Optimization (process mgmt.)

• Fixed model and input data

• Adjust some parameters

• Review simulation results

• Repeat parameter adjustment to optimize

• Hill-climbing method

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Scenarios (What-ifs)

• Fixed model

• Adjust some parameters or inputs (what-if)

• Review simulation results

• Repeat adjustment to get desired performance

• Evolutionary algorithm approach

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Inputs

• assumed known

• assumed to influence process

• time/event bases

• form a sequence

• may be affected by sampling effects

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Time-based Inputs

• have time-to-go

• triggered by clock

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Event-based Inputs

• have condition of occurrence(based on process variables)

• triggered by process (model) conditions or state

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Generalized Events

• time can be an event

• all events queued in linked list

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Other Forms

• State machine– events– actions

• Expert system– if– then

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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

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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

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Process Study by Simulation

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

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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?

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Related Issues

• user interface

• data capture interface

• data storage (often large files)

• fitting of distributions & models

• data presentation

• programming requirements

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Implications (Study Objectives)

• What should be the result?

• What will be the expected benefits?

• Who will be the users of the results?

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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?

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Implications (Data Collection)

• What data (how much, what type)?

• How often?

• How executed?

• What conditions?

• How processed?

• What precision?

• What format?

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Implications (Coding)

• Package or language?

• What speed desired?

• Graphical effects?

• Object oriented?

• What interfaces?– User– Network monitor

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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?

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Implications (Experimental Design)

• For observability

• To validate the model

• To validate the simulation

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Implications (Analysis of Results)

• Do results make sense?

• Is time/physical scale (detail) appropriate?

• What inferences can be drawn?

• Are further studies needed?

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Implications (Documentation)

• How will models be documented?

• How will results be presented?

• Save all for further studies?

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Validation of Simulation

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

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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.

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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”

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Validation (Independence Issues)

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

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Validation (Aggregation of Effects )

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

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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?

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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.

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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)