Simulating a Markov model is the method of choice when analytic or numerical approaches are not possible. Basically, the former happens when the model is not regular enough, meaning that it does not have enough structure, the latter when its size precludes the use of numerical procedures. We also use the term Monte Carlo to refer to these simulation methods, using the term in its most common meaning, i.e. the use of randomness to solve deterministic problems. There are many important subfields in this wide area that have been the object of concerted research efforts, for instance the MCMC [83], [31] or the perfect simulation [81] approaches, and many procedures designed for specific application areas, such as queuing [52], [38], [109], financial problems [37], physics [40], and many more [45], [35], [4]. Monte Carlo techniques are extremely powerful, and they can deal, in principle, with any kind of model. They are not limited by the lack of structure in the model, nor by the model's size. However, they have their own difficulties, the main one being the case of rare events. If you want to analyze a specific metric quantifying some aspect of this rarity, the fact that the focused event appears with very small probability means that it will also be hard to observe in the simulation.