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Simulation

Minimalist Description

Simulation mimics the operation of a real-world process or system, usually in its behavior over time. Usually, we simulate a system to understand how it will respond to different situations. There are two main cases.
  1. Deterministic Simulation: The dynamics of the system are well known, but too complex to know analytically (i.e. by solving an equation) what state the system will end up in. Say, for instance, you want to understand what happens when small particle grains of metal or silica get very hot, their surfaces begin to melt, and the particles bond. That process is called sintering, and it is the reason ceramics get hard when they are fired in a kiln. Particle sinter simulations are deterministic. The surfaces evolve in a specific way. But we need to simulate the process to know what that specific way is. 
  2. Stochastic Simulations: There is uncertainty in the dynamics. Say for instance your submarine warfare model says that in any one hour, you have an 8% chance of killing the enemy sub by listening for their propeller, and a 12% chance of killing the sub by trying to locate it with a sonar ping, but pinging increases your vulnerability by 4%. When you simulate your battle strategy, there will be several possible outcomes, and you will want to report the likelihood of each in your results. That is to say, the job of a stochastic simulation is to report the probability distributions for the quantities of interest. In the image to the right, for instance, the red quantity probably has a value of -3, but might also be +3, and the blue quantity is probably +3 but might be -3.
Because stochastic simulations support a range of possible outcomes, we are often most interested in the worst cases rather than the most likely. In the submarine battle, the sub captain may favor the strategy with the least likelihood of being destroyed, even if that strategy is less likely than some other to destroy the enemy sub (in some outcomes, neither or both subs are destroyed). Similarly, if a business plans for the worst case, it may be able to survive indefinitely but if it plans for the most likely case it may do very well for a few periods but then unravel at the first catastrophe. A startup may be far more tolerant of risking catastrophe than a mature business because they have less legacy to protect. And so the same simulation may support different business decisions in different climates of risk tolerance. Click here for detail


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