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It is challenging to deal with the Internet congestion problem because of several factors such as ever-growing traffic and distributed network architecture. The congestion problem can be solved or alleviated by various methods, including rate control, bandwidth-guarantee routing and bandwidth reservation. We use the term broad-sensed Internet congestion control and avoidance (BICC&A) to generally denote all of the above methods. Most BICC&A solutions depend on or benefit from the knowledge of network conditions, including traffic status (type and volume), available bandwidth and topology. In this paper, we present a comprehensive survey of the applications of machine learning to network condition acquirement methods for BICC&A and specific BICC&A methods. First, we provide an overview of the background knowledge of BICC&A and machine learning. Then, we provide detailed reviews on the applications of machine learning techniques to network condition acquirement methods for BICC&A and to specific BICC&A methods. Finally, we outline important research opportunities.