Monte Carlo Simulations

Most real world processes have some random components in them. That is why we have to investigate the statistical properties of such systems/processes. For example, we may be interested in computing the expected performance of a system or the expected distance in a random walk process, or the mean power of a received signal or the expected number of people in a waiting room (see the last example in Chapter 5). Many mathematical tools have been derived to compute such metrics, however in most cases the systems are too complex to derive any tractable results. In such scenarios, simulations with random sampling, also known as Monte Carlo simulations, can provide the desired analysis. This technique is based on the assumption that if we perform random sampling of a random variable sufficiently many times, we can derive the approximate statistical properties of it. On the other hand, we sometimes add the random component into a computation or algorithm deliberately when deterministic computation is very extensive or difficult. Monte Carlo simulations are also very useful in such cases.