Simulating rare events in queues via neural networks

Excerpt

Queueing models form an ideal ‘sandbox’ for the study of complex random systems. Some of these models are simple enough to allow a detailed analysis to reveal interesting mathematical properties, whereas highly intricate queueing models can be studied through simulation. One of the intriguing problems to study is how certain rare events happen in queueing systems. For example, in [8] a tandem queue is analysed under the rare event that the second buffer reaches a high level. It is found that when the first queue is the bottleneck, the system behaves as if the interarrival rate and the slowest (second) service rates are interchanged. However, when the second queue is the bottleneck, the first queue has to build up first before the second queue hits the high level. …