Fundamentals of simulation modeling

Fundamentals of simulation modeling

1. View simulation model as a black box which transforms inputs -> outputs

2. Background & terminology

   • System: set of emelemsts which interact in some fashion
     • elments
       • with no relationship to others: can not affect the system elements and are irrelevant to our goal.
       • that make up the system are named: entities
     • queueing system
       • a queue: a concept
       • a server: physical entities
     • sub-systems
     • deterministic
       • We try to produce state trajectories which are similar to those of the real system
     • stochastic
       • We do no t need to mach state trajectories directly; instead, we try to produce state trajectories which are plausibles realizations of what might be seen in the real system
   • Model: is a sustem which we use as a surrogate for anotehr system
     • Use models im an attempt to gain understanding and insights about some aspects of the real world.
       • Assume a priori the existence of undeniable truth
     • observability
     • controllabity

3. An overview of the modeling process

   • Stage 1
     • Identify what is meant by the system of interest
     • At the end we have a descriptive model
   • Stage 2
     • Describe the behaviors and interactions of all the entities
     • At the end we have a formal model
       • if it has a high degree of conformance with the real world, analytuc models and their solutions would allow us to obtain insights and draw inferences
       • Adding real-world features of other distributions, change the models, now they can not be solved analytically
         • Here is where simulation might enter
           • if the simulation model uses randomness as part of the modeling process; its output is a random variabla
             • The proper way to analize stochastic system is with stadistics
           • Simulatuib nidekubg ubvikves a longer chain of inference than does analytiical modeling
   • Feedback
     • Verification; feedback loop between the computer model and the formal model
       • Does my computer program do what I meant it to do?
     • Validation: a feedback loop between the computer model and reality
       • Does my computer program mimic reality adequatelu?
   • IRKs (Independent Rheostat Knobs)
   • Inputs
     • Simplify: There comes a point where you face diminishing returns. Sometimes, an addition produces no measurable benefit
     • Test frequently: after each of your incremental improvements, check the resulting model
     • Improve incrementally: you can add features to improve the representation of reality
     • Start small: simplest posssible model which captures the essence of the system

4. Discrete event systems

   • Where tje state changes occur at a discrete set of points along the time axis, rather than continuously
     • events
   • Works by advancing simulated tieme directly from one event to another.
     • Intervals of time between events are of no interes
       • Create event graph notation
   • Type III error
     • Choosing the wrong problem representtation
     • Domain Specific Languages (DSLs)
       • Very good at expressing problems within their chosen modeling framework
     • General-Purpose Programming Languages (GPPLs)
       • The oppositive to DSL s

5. Randomness

   • Importance
     • The system can be drastically affected by the presence or absence of randomness
   • Examples
     • Inversion
     • Convolution
     • Composition
     • Special Relationships
   • Random Numbers
     • Uniformly distributed between zero and one
   • Random Variables
     • Everything that is not a random number
     • We can generate them, by using a source of random numbers
   • Characteristics of a "source of randomness"
     • Independence: Easier to induce correlation from independent random numbers than to achieve independence from correlated ones
     • Known distribution: from there we can in turn map it to other distributions
     • Unlimited: we should be able to draw as many values from the source as we need
     • Minimal storage: the source should not be a drain on memory or other storage resources
     • Fast: getting them should be quick
     • Portable: our ability to create and run models should not be tied to a specific computing platform
     • Reproducible

6. Viewing the model as a model

   • Inputs
     • Parameterizations of each run of the model
     • Include the random number seeds
   • Simulation
     • If it is robust to the distribution of a particular component element, use a distribution which is easy to implement and computationally efficient
     • If your simulation results vary sifnigicantly based on the choice of distribution, this is a model component which is important for you to expend the effort to get right

7. Output analysis

   • classical statistics
     • describe the briad variety of statistical techniques which assume ind, ibservations
   • If there is no randomness in your model, youc an run it once to determine "the answer"
   • If your model is of a static system but has a well-defined terminating state: use replication to study it
     • Replication
       • first delete some initial portion of the simulation output to remove the effects of initialization
       • to obtain a suitable number of these estimates, which will be independent if the replications are independently seeded
   • The data can be collected and then analyzed using classical statistics