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The theory of large deviations provides a simple unified basis for statistical mechanics, information theory and queueing theory. The objective of this paper is to use large deviation theory and the Laplace method of integration to provide an simple intuitive overview of the theory of effective bandwidth for high-speed digital networks, especially ATM networks. This includes (1) identification of the appropriate energy function, entropy function and effective bandwidth function of a source, (2) the calculus of the effective bandwidth functions, (3) bandwidth allocation and buffer management, (4) traffic descriptors, and (5) envelope processes and conjugate processes for fast simulation and bounds