On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A most probable path approach to queueing systems with general Gaussian input
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Advances in modeling and engineering of Longe-Range dependent traffic
Fast simulation of overflow probabilities in a queue with Gaussian input
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Gaussian tandem queues with an application to dimensioning of switch fabric interfaces
Computer Networks: The International Journal of Computer and Telecommunications Networking
An introduction to large deviations for communication networks
IEEE Journal on Selected Areas in Communications
On the use of fractional Brownian motion in the theory of connectionless networks
IEEE Journal on Selected Areas in Communications
IEEE Network: The Magazine of Global Internetworking
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The theory of large deviations refers to a collection of techniques for estimating properties of rare events such as their frequency and most likely manner of occurrence. Loosely speaking, LDT can be seen as a refinement of the classical limit theorems of probability theory and it is useful when simulation or numerical techniques become increasingly difficult as a parameter of interest tends to its limit. The first part of this tutorial deals with the behaviour of the empirical mean of IID RVs, the most natural framework to introduce the basic concepts and theorems of LDT and to highlight their heuristic interpretation. Then, the large deviation principle for the single server queue is presented and its implications on network dimensioning are discussed. Finally, the tutorial overviews the application of LDT to rare event simulation, for the choice of the optimal change of measure in Importance Sampling.