Rare events in queueing systems?A survey

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Several practical approaches have been used to estimate the probabilities of rare events occurring in queueing processes. Rare events of practical interest can be considered as large deviations for a fixed queueing process (such as level crossing by the waiting time, or the queue length) or as those for a limiting triangular scheme. This paper is a survey of the literature devoted to the regenerative analysis of rare events. Because of the importance of busy period parameters, rare events within a busy period are discussed. A number of small parameter theorems useful in rare events analysis are outlined, including singular states aggregation theorems. Simulation methods for rare events analysis and other numerical methods are also presented.