12/7/2015© 2008 Raymond P. Jefferis III1 Simulation of Computer Systems

12/7/2015© 2008 Raymond P. Jefferis III2 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

12/7/2015© 2008 Raymond P. Jefferis III3 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

12/7/2015© 2008 Raymond P. Jefferis III4 Introduction to Simulation System types Definition Reasons for simulation Simulation components Development of a simulation -- from model to verified results

12/7/2015© 2008 Raymond P. Jefferis III5 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

12/7/2015© 2008 Raymond P. Jefferis III6 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.

12/7/2015© 2008 Raymond P. Jefferis III7 Keywords process model pattern of inputs response - behavior over time observations study

12/7/2015© 2008 Raymond P. Jefferis III8 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)

12/7/2015© 2008 Raymond P. Jefferis III9 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

12/7/2015© 2008 Raymond P. Jefferis III10 Pattern of Inputs inputs affect system may be a time sequence may be statistically distributed –time is random variable –magnitude is random variable

12/7/2015© 2008 Raymond P. Jefferis III11 Response behavior over time –Example: queue length may be statistical –Examples: arrival time, service time

12/7/2015© 2008 Raymond P. Jefferis III12 Observations Inputs –Examples: packets, frames and their lengths, arrival times Outputs –Examples: packets, frames and their lengths, service times, queue lengths

12/7/2015© 2008 Raymond P. Jefferis III13 Study network monitor (“Sniffer TM ”) “smart” switches, routers, & hubs modeling of distribution functions verification of traffic rates and queues TM Trademark of Network Associates, Inc.

12/7/2015© 2008 Raymond P. Jefferis III14 Why simulate? Mathematical intractability Process independence needed Change of time scale needed Design tool Training tool Inference tool

12/7/2015© 2008 Raymond P. Jefferis III15 Mathematical Intractability nonlinear models (queuing problems) models too complex (combinatorics) microscopic details wanted (distributions) analytical methods inadequate non-steady state solutions desired

12/7/2015© 2008 Raymond P. Jefferis III16 Process Independence high testing costs - many alternatives parametric studies - many variations inaccessible processes - scale issues measurements alter the process - monitors hazards

12/7/2015© 2008 Raymond P. Jefferis III17 Time Scale Change very short times - expand (microscopic) very long times - compress (macroscopic)

12/7/2015© 2008 Raymond P. Jefferis III18 Design Model –reduction of time and cost to develop model Process –reduction of time and cost to optimize process –performance by some criterion

12/7/2015© 2008 Raymond P. Jefferis III19 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

12/7/2015© 2008 Raymond P. Jefferis III20 Inference Learning about possible relationships in system from external behavior model-reference diagnostics (possibly on- line using validated model)

12/7/2015© 2008 Raymond P. Jefferis III21 Simulation Components Queuing system model Probability distributions Random numbers (generators) Random variable distributions Experiments - system data

12/7/2015© 2008 Raymond P. Jefferis III22 Model System

12/7/2015© 2008 Raymond P. Jefferis III23 Model Development (scientist) Fixed input/output data sets Adjust model & parameters to give best fit

12/7/2015© 2008 Raymond P. Jefferis III24 Process Development (engineer) Fixed model & parameters Vary inputs to give best output performance

12/7/2015© 2008 Raymond P. Jefferis III25 Optimization (process mgmt.) Fixed model and input data Adjust some parameters Review simulation results Repeat parameter adjustment to optimize Hill-climbing method

12/7/2015© 2008 Raymond P. Jefferis III26 Scenarios (What-ifs) Fixed model Adjust some parameters or inputs (what-if) Review simulation results Repeat adjustment to get desired performance Evolutionary algorithm approach

12/7/2015© 2008 Raymond P. Jefferis III27 Inputs assumed known assumed to influence process time/event bases form a sequence may be affected by sampling effects

12/7/2015© 2008 Raymond P. Jefferis III28 Time-based Inputs have time-to-go triggered by clock

12/7/2015© 2008 Raymond P. Jefferis III29 Event-based Inputs have condition of occurrence (based on process variables) triggered by process (model) conditions or state

12/7/2015© 2008 Raymond P. Jefferis III30 Generalized Events time can be an event all events queued in linked list

12/7/2015© 2008 Raymond P. Jefferis III31 Other Forms State machine –events –actions Expert system –if –then

12/7/2015© 2008 Raymond P. Jefferis III32 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

12/7/2015© 2008 Raymond P. Jefferis III33 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

12/7/2015© 2008 Raymond P. Jefferis III34 Process Study by Simulation generation of inference about process from observations of model behavior in response to known inputs

12/7/2015© 2008 Raymond P. Jefferis III35 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?

12/7/2015© 2008 Raymond P. Jefferis III36 Related Issues user interface data capture interface data storage (often large files) fitting of distributions & models data presentation programming requirements

12/7/2015© 2008 Raymond P. Jefferis III37 Implications (Study Objectives) What should be the result? What will be the expected benefits? Who will be the users of the results?

12/7/2015© 2008 Raymond P. Jefferis III38 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?

12/7/2015© 2008 Raymond P. Jefferis III39 Implications (Data Collection) What data (how much, what type)? How often? How executed? What conditions? How processed? What precision? What format?

12/7/2015© 2008 Raymond P. Jefferis III40 Implications (Coding) Package or language? What speed desired? Graphical effects? Object oriented? What interfaces? –User –Network monitor

12/7/2015© 2008 Raymond P. Jefferis III41 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?

12/7/2015© 2008 Raymond P. Jefferis III42 Implications (Experimental Design) For observability To validate the model To validate the simulation

12/7/2015© 2008 Raymond P. Jefferis III43 Implications (Analysis of Results) Do results make sense? Is time/physical scale (detail) appropriate? What inferences can be drawn? Are further studies needed?

12/7/2015© 2008 Raymond P. Jefferis III44 Implications (Documentation) How will models be documented? How will results be presented? Save all for further studies?

12/7/2015© 2008 Raymond P. Jefferis III45 Validation of Simulation Validation is the determination that the simulated system closely approximates the real system for the given scope.

12/7/2015© 2008 Raymond P. Jefferis III46 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.

12/7/2015© 2008 Raymond P. Jefferis III47 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”

12/7/2015© 2008 Raymond P. Jefferis III48 Validation (Independence Issues) Verify statistical independence - does the model assume independence? Lack of it can invalidate such a model.

12/7/2015© 2008 Raymond P. Jefferis III49 Validation (Aggregation of Effects ) Can effects that are separate be lumped together - time, space, etc. Determine if the degree of aggregation is too great.

12/7/2015© 2008 Raymond P. Jefferis III50 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?

12/7/2015© 2008 Raymond P. Jefferis III51 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.

12/7/2015© 2008 Raymond P. Jefferis III52 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)