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Modeling and Simulation

The Way of Systems

Modeling & Simulation

An Introduction

After some consideration regarding a meaningful way of putting System, Model, and Simulation in an appropriate perspective I arrived at the following distinction.


  • A system exists and operates in time and space.
  • Model

  • A model is a simplified representation of a system at some particular point in time or space intended to promote understanding of the real system.
  • Simulation

  • A simulation is the manipulation of a model in such a way that it operates on time or space to compress it, thus enabling one to perceive the interactions that would not otherwise be apparent because of their separation in time or space.
  • Modeling and Simulation is a discipline for developing a level of understanding of the interaction of the parts of a system, and of the system as a whole. The level of understanding which may be developed via this discipline is seldom achievable via any other discipline.

    A system is understood to be an entity which maintains its existence through the interaction of its parts. A model is a simplified representation of the actual system intended to promote understanding. Whether a model is a good model or not depends on the extent to which it promotes understanding. Since all models are simplifications of reality there is always a trade-off as to what level of detail is included in the model. If too little detail is included in the model one runs the risk of missing relevant interactions and the resultant model does not promote understanding. If too much detail is included in the model the model may become overly complicated and actually preclude the development of understanding. One simply cannot develop all models in the context of the entire universe, of course unless you name is Carl Sagan.

    A simulation generally refers to a computerized version of the model which is run over time to study the implications of the defined interactions. Simulations are generally iterative in there development. One develops a model, simulates it, learns from the simulation, revises the model, and continues the iterations until an adequate level of understanding is developed.

    Modeling and Simulation is a discipline, it is also very much an art form. One can learn about riding a bicycle from reading a book. To really learn to ride a bicycle one must become actively engaged with a bicycle. Modeling and Simulation follows much the same reality. You can learn much about modeling and simulation from reading books and talking with other people. Skill and talent in developing models and performing simulations is only developed through the building of models and simulating them. It's very much a learn as you go process. From the interaction of the developer and the models emerges an understanding of what makes sense and what doesn't.

    I am repeatedly amazed at the ability of my models to point out my own ignorance. Through the activity of developing the model and then simulating it, the simulation says, "Based on your model and your set of assumptions, reality is absurd!" Often times the model is grossly incorrect, and other times the model produces great leaps in my understanding of how things actually work, and, quite often contrary to common sense. It is an amazingly wonderful journey my models and I are undertaking.

    Peter Senge, in "The Fifth Discipline: The Art & Practice of the Learning Organization" talks about two types of complexity, detail and dynamic. Detail complexity is associated with systems which have many component parts. Dynamic complexity is associated with systems which have cause and effect separated by time and or space. The understanding is that it is dynamic complexity that we have great difficulty dealing with because we are unable to readily see the connections between the parts of the system and their interactions. One of the great values of simulation is its ability to effect a time and space compression on the system, essentially allowing one to perceive, in a matter of minutes, interactions that would normally unfold over very lengthy time periods. This is probably best demonstrated by an example. The following example is an elaboration of one of the introductory models in the ithink documentation from isee Systems.

    Consider a consulting company which has 120 employees. These 120 employees are composed of 60 rookies and 60 professionals. The company wishes to maintain the total number of employees at 120 so it hires a new rookie for each professional who quits. Rookies don't quit! Professionals quit at a rate of 10 per month and it takes 6 months to develop a professional from a rookie. Additionally, the company bills out rookies at $10k/month and professionals at $15k/month. All 120 employees are fully applied (I know it's a pipe dream).

    An ithink model for this system might look like the following:

    If you run this model you find it exists in essentially a steady state, and is about as exciting as watching paint dry!

    Now, in the 10th month the company notices its revenue has dropped from $1.5m/month to $1.35m/month and it wonders what has happened. And where do you think it looks for the problem? All around the 10th month of course. And what does it find? The company finds that it still has 120 employees, yet there are now 30 professionals and 90 rookies. A most puzzling situation!

    As it turns out, there was an organizational policy change made in month 3 which seemed to annoy professionals more than in the past, and the quit rate jumped from 10 to 15 professionals a month. The system, with it's built in hiring rule, essentially an auto pilot no thought action, hired one rookie for each professional that quit. What this one time transition in quit rate actually did was set off a 6 month transition within the organization leading to a new equilibrium state with 30 professionals and 90 rookies. The following graph represents this transition.

    Thus, one of the real benefits of modeling and simulation is its ability to accomplish a time and space compression between the interrelationships within a system. This brings into view the results of interactions that would normally escape us because they are not closely related in time and space. Modeling and simulation can provide a way of understanding dynamic complexity!

    The model used for this example was done in ithink. [, 2k]

    Simulation is not the Answer

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