Fundamental principles of Modeling

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Fundamental principles of Modeling Analysis
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Purposeful Representation

• A model is a representation of the system that is
  built to serve a purpose
• E.g. An artists rendering of a building gives
  customer an idea of the look-and-feel
• Architects building plan focuses on layout
• A cutaway might focus on building materials and
  construction
• Modeling starts with identifying the purpose of
  the model
• Multiple models for different purposes
• The key characteristic of a model is not accuracy
  but usefulness

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Level of detail

• The key decision in modeling is what and how much
  to leave out
• Eliminating distracting detail enables focus on
  aspects of interest, get higher level
  perspectives
• E.g. street maps for navigation mostly do not
  show buildings and topography
• More detail is NOT necessarily better
• If a street map showed every curve in the road,
  it could be harder to use
• A city map that shows every lane and alley less
  useful to get across city than one that shows
  just major roads

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Abstraction

• Modeling is about abstraction building generic,
  high-level concept pictures
• Good models often abstract out variation to
  facilitate analysis
• E.g. Authentication abstraction filters out
  whether it is login-password, questions,
  knowledgehardware, fingerprint recognition
• Different abstractions, levels of abstraction
  depending on aspects of interest

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Fidelity

• All models are approximations of reality
• Can build models of different fidelity
• Higher fidelity models have more details, more
  accurate representations, facilitate more
  accurate understanding/analysis
• Take significantly more effort to build, analysis
  may be more complex
• Choose fidelity depending on how much time
  effort you are willing to invest, how much
  accuracy of results you need

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Value of Modeling

• The primary purpose of modeling is to improve
  understanding
• The process of building the model itself focuses
  attention on the aspects of interest and gives us
  insights
• Observing differences between the model and
  reality (other than differences due to fidelity)
  shows us gaps in our understanding
• Models provide us the basis for analysis

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Analysis

• Systematic approach to understanding properties
  of the system
• Mathematical analysis involves using equations to
  derive properties from the model
• Statistical analysis and simulation involve
  observing the behavior of the model for different
  inputs/situations and drawing (probabilistic)
  conclusions
• Qualitative analysis derives properties results
  from a detailed examination of the model
• Route planning with a street map is qualitative
  analysis

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Tradeoffs between approaches

• Mathematical analysis
• more comprehensive (considers all possible
  situations).
• Intermediate results of equations may show
  relative magnitude of influencers which factors
  contribute more to the problem
• Cannot handle high complexity (intractable)
• Good for quick, approximate results
• Statistical analysis
• Can deal with considerable complexity
• Can do what if scenario analysis examine
  alternatives
• Can examine behavior of different components,
  find bottlenecks
• Example-based. Validity may be limited by
  situations that did not happen to occur. Also
  usually much more effort to construct simulation.
• Qualitative analysis
• Can take many more (intangible)
  considerations into account that may be very
  difficult to model
• - Limited in fidelity

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Types of Analysis

• Best-case analysis Most optimistic assumptions /
  situations, identify maximum (best) obtainable
  results
• Rarely useful, except to establish minimum
  feasibility (will this ever work) and to
  understand under what circumstances things work
  better
• Average-case analysis The most common. Behavior
  under typical circumstances.
• Worst-case Most pessimistic assumptions,
  identify situations of maximum stress
• Useful for determining needed capacities,
  identify potential failure scenarios
• Mathematical analysis good at determining
  worst-case. Simulation produces average-case,
  but can identify best and worst case among the
  cases seen.

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Other types of analysis

• Bottleneck analysis Used in analysis of
  transaction flow. Figure out which components or
  attributes impose the tightest constraints on
  what system can accomplish
• Improving behavior of a component / attributes
  other than the bottleneck has little impact on
  overall system behavior
• Sensitivity analysis Study change in system
  behavior when specific parameters are modified.
• Useful to figure out pressure points where a
  little additional effort can make a large impact
• Scenario analysis Try alternative configurations
  and study the properties of each.

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Summary

• The key to modeling is determining the right
  level of detail deciding what to leave out
• Creating the right abstraction facilitates
  understanding and analysis
• Can do modeling and analysis at different levels
  of fidelity.
• Different analysis approaches have different
  purposes, strengths and limitations