Introduction to Modeling & Simulation PDF

INTRODUCTION TO MODELING & SIMULATION WHAT IS MONTE CARLO SIMULATION?  Monte Carlo simulation is a computational method that uses random sampling to approximate the outcomes of a system. It is particularly useful when analytical or deterministic methods are not feasible or when uncert...

INTRODUCTION TO MODELING & SIMULATION WHAT IS MONTE CARLO SIMULATION?  Monte Carlo simulation is a computational method that uses random sampling to approximate the outcomes of a system. It is particularly useful when analytical or deterministic methods are not feasible or when uncertainty needs to be accounted for. The technique is named after the famous Monte Carlo casino in Monaco, known for its games of chance. INTRO TO MODELING & SIMULATION 2 BASIC PRINCIPLES OF MONTE CARLO SIMULATION  All models are a simplified representation of reality, an abstraction.  Simulation is just one type of model, a numerical model which presumes experimentation.  A DES simulation model is discrete, stochastic and dynamic.  Since it moves over time it must, therefore, include facilities for the collection of output measures that change over time. INTRO TO MODELING & SIMULATION 3 TITLE: STEPS IN MONTE CARLO SIMULATION 1. Define the problem: Clearly define the system or process to be modeled and identify the variables and parameters involved. 2. Define probability distributions: Assign probability distributions to the variables based on available data or expert knowledge. 3. Generate random samples: Generate a large number of random samples for each variable based on their assigned probability distributions. 4. Perform simulations: Use the generated random samples as inputs to simulate the system or process multiple times. 5. Analyze results: Analyze the simulated results using statistical techniques to estimate the behavior and outcomes of the system. 6. Validate and refine: Validate the simulation results against real-world data and refine the model if necessary. INTRO TO MODELING & SIMULATION 4 GENERATING RANDOM NUMBERS Random numbers are generated using pseudorandom number generators (PRNGs). PRNGs produce sequences of numbers that exhibit statistical properties similar to true randomness. Careful selection of PRNGs is important to ensure randomness and avoid biases in the simulation results. INTRO TO MODELING & SIMULATION 5 PROBABILITY DISTRIBUTIONS Statistical techniques such as descriptive statistics, regression analysis, confidence intervals, and hypothesis testing are employed to analyze the results of Monte Carlo simulations. These techniques help estimate the central tendency, variability, and uncertainty of the simulated outcomes. Probability distributions play a crucial role in Monte Carlo simulation. Common distributions used include: Uniform distribution: Equally likely outcomes within a specified range. Normal (Gaussian) distribution: Bell-shaped curve describing many natural phenomena. Exponential distribution: Describes the time between events occurring in a Poisson process. Random samples are generated from these distributions to represent uncertainty in the model. INTRO TO MODELING & SIMULATION 6 ESTIMATING UNKNOWN QUANTITIES While Monte Carlo simulation is a versatile technique, it has certain limitations. Some limitations include the assumption of independence among variables, the need for adequate sample sizes, and the computational resources required for large-scale simulations. Additionally, the accuracy of the simulation depends on the quality of the probability distributions assigned to the variables. Monte Carlo simulation allows us to estimate unknown quantities with statistical inference. By running a large number of iterations, we obtain a distribution of possible outcomes. Confidence intervals provide a measure of uncertainty around the estimated values. INTRO TO MODELING & SIMULATION 7