Introduction to rare event simulation

This monograph deals with the analysis by simulation of ‘rare situations’ in systems of quite different types, that is, situations that happen very infrequently, but important enough to justify their study. A rare event is an event occurring with a very small probability, the definition of ‘small’ depending on the application domain. These events are of interest in many areas. Typical examples come, for instance, from transportation systems, where catastrophic failures must be rare enough. For instance, a representative specification for civil aircraft is that the probability of failure must be less than, say, 10−9 during an ‘average-length’ flight (a flight of about 8 hours). Transportation systems are called critical in the dependability area because of the existence of these types of failures, that is, failures that can lead to loss of human life if they occur. Aircraft, trains, subways, all these systems belong to this class. The case of cars is less clear, mainly because the probability of a catastrophic failure is, in many contexts, much higher. Security systems in nuclear plants are also examples of critical systems. Nowadays we also call critical other systems where catastrophic failures may lead to significant loss of money rather than human lives (banking information systems, for example). In telecommunications, modern networks often offer very high speed links. Since information travels in small units or messages (packets in the Internet world, cells in asynchronous transfer mode infrastructures, etc.), the saturation of the memory of a node in the network, even during a small amount of time, may induce a huge amount of losses (in most cases, any unit arriving at