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Admission Control (AC) has long been considered as a key mechanism to support Quality of Service objectives in networks. There is a significant base of literature in the area of admission control algorithms, but not all of these algorithms are directly comparable in terms of inputs, outputs or objectives. Current theory does not well describe the when, where, and how to best apply AC in designing network and service infrastructure for multi-service IP networks. This tutorial takes an ontological perspective within which to categorize admission control schemes. Industrystandard architectures (both core and access networks) are used to illustrate some of the key concepts. Two tables are provided to summarize the different approaches for categorization of admission control schemes.