as the th century progressedthe limitations of this approach became increasingly clear reasons for this includean increased interest in the social sciencese economicsled to desire to construct good models of systems that were not mathematically tractable as the systems to be modeled grew increasingly complexit seemed easier to successively refine series of simulation models than to construct accurate analytic models it is often easier to extract useful intermediate results from simulation than from an analytical modele to play "what ifgames the availability of computers made it feasible to run large-scale simulations until the advent of the modern computer in the middle of the th century the utility of simulation was limited by the time required to perform calculations by hand simulation attempts to build an experimental devicecalled modelthat will provide useful information about the possible behaviors of the system being modeled it is important to remember that these modelslike all modelsare only an approximation of reality one can never be sure that the actual system will behave in the way predicted by the model in factone can usually be pretty confident that the actual system will not behave exactly as predicted by the model it is commonly quoted truism that "all models are wrongbut some are useful " simulation models are descriptivenot prescriptive they tell how system works under given conditionsnot how to arrange the conditions to make the system work best simulation does not optimizeit merely describes that is not to say that simulation cannot be used as part of an optimization process for examplesimulation is often used as part of search process in finding an optimal set of parameter settings simulation models can be classified along three dimensionsdeterministic versus stochasticstatic versus dynamicand discrete versus continuous the behavior of deterministic simulation is completely defined by the model rerunning simulation will not change the outcome deterministic simulations are typically used when the system being modeled is too complex to analyze analyticallye the performance of processor chip stochastic simulations incorporate randomness in the model multiple runs of the same model may generate different values this random element forces us to generate many outcomes to see the range of possibilities the question of whether to generate or or , outcomes is statistical questionas discussed earlier usually attributed to the statistician george box