 1  GSLM System Simulation Yat-wah Wan Room: B317; ywan; Ext: 3166

 2  Agenda  house keeping issues  introduction  applications  definition  systems, models, and solution  states

 3  House-Keeping Issues  prerequisite/background: undergraduate probability and statistics  aims and objectives: hand-on experience on system modeling, statistical theory, and programming

 4  Content  introduction  overview of simulation and relevant theory  modeling  discrete-event simulation  simulation by spreadsheet  simulation by programming language  ARENA ARENA  basic models, detailed operations, optimization  analysis  input, output, random variate generation

 5  Textbooks and References  Hoover, Stewart V. and Ronald F. Perry [1989] Simulation: A Problem-Solving Approach  Kelton, W. David, Randall P. Sadowski, and David T. Sturrock [2004] Simulation with Arena  Law, Averill M. and W. David Kelton [2000] Simulation Modeling and Analysis  Ripley, Brian D. [2006] Stochastic Simulation  Ross, Sheldon M. [2006] Simulation

 6  Assessments  Assignments30%  Project30%  Final Examination40%

 7  Examples of Simulation  If we search for “ simulation ” on web  Simulation Games Simulation Games  Solar System Simulator Solar System Simulator  Simulating Fire Patterns in Heterogeneous Landscapes Simulating Fire Patterns in Heterogeneous Landscapes  Advanced Simulation Systems Advanced Simulation Systems  Arena Software Arena Software  Example 1, Example 2 Example 1Example 2  ….. etc. etc.

 8  Definition of Simulation  Wikipedia Wikipedia  simulation = ???  simulation software?  computer languages  statistical analysis?  computers?  queueing systems? ….….

 9  Applications of Simulation Applications of Simulation  Interfaces Interfaces  simulation papers in 2007 & 2008 simulation papers in 2007 & 2008  15 (out of 172) titles in two years 15 (out of 172) titles in two years market- ing SCMNLPStatistic fore- casting Invent- ory DPLP logisticsIPnetwork15simulat- ion

 10  Common Characteristics of Different Types of Simulation  …..  mimic reality when the real system is  not available  costly to build  dangerous to operate  difficult to visualize  slow in evolution  difficult to predict  both deterministic and stochastic systems how about analytical methods?

 11  Summary of Introduction  many types of simulation  wide spread applications in various contexts

 12  From System to Simulation From System to Simulation

 13  System, Model, & Solution systemmodel solution Role of models: describe, explain, predict, control, optimize Simulation: a special way to find the solution of a model

 14  Our Simulation computer simulation, after all most stochastic systems, though …  required knowledge in  modeling (state, dynamics, etc.)  analysis (input, output, verification and validation, variance reduction, optimization)  a computer language and a simulation software

 15  Pillars of Simulation simulation  Which is the most important? modeling computer: languages & software analysis: probability & statistics

 16  System, Model, & Solution systemmodel solution  how to represent a real system?  stochastic inputs  what information to carry  model correctly (setting the model right)?  correct model (setting the right model) ? art  how to analyze?  how to optimize?

 17  Issues to Simulate a System  first: the amount of information to carry to represent the system (i.e., the state of the system)  second: the evolution of the state of the system (i.e., the system dynamics of the system)  third: the medium to realize the (evolution of the) system  fourth: the method to represent the system dynamics in the selected medium  fifth: the analysis, control, and optimization of the simulation model

 18  Summary of the Relationship Among Systems, Models, and Solution Methods  pillars of simulation  modeling, analysis, programming skills  issues in simulation  defining the state of system  tracing the evolution of the state  selecting the medium to simulate  building the simulation model in the selected medium  analyzing, controlling, and optimizing the simulation model

 19  Amount of Information to Represent a System  sufficient to trace the history of the system  sufficient to calculate performance measures  sufficient for future evolution of the system feasible trajectory of system

 20  amount of details: application dependent The State of a System  …..  the collection of variables that  given their evolution up to time t, give any relevant information of the system up to t  characterize the future evolution of the system including performance measures driven by performance measures

 21  The System Dynamics of a System  physical and natural relationship among variables  represented usually by tracing the evolution of the system

 22  Medium to Represent a System  any and many  generally one to one correspondence between actions in any two media  e.g., the correspondence between human and computer actions  best medium being application dependent

 23  Example 1  Type A machine  alternatively “ on ” for one time unit and “ off ” for 3 time units  start with the beginning of an “ on ” period at epoch 0  the first three issues in simulating the system  defining the state of the system  tracing the evolution of states  selecting the medium to simulate

 24  Example 1 (Continued)  defining the state: trivial, completely determined by the initial condition  tracing the evolution of the state (system dynamics)  on at t: for t  (4n, 4n+1)  off at t: for t  (4n+1, 4n+4)  selecting the medium to simulate: many  paper and pencil  how about computer?

 25  Example 1 (Continued)  paper and pencil  record the system dynamics  give formulas to calculate various performance measures for any epoch t  computer  record similar quantities and formulas as by paper and pencil  provide interfaces for users to interact with computer