The current global pandemic crisis has unquestionably disrupted the higher education sector, forcing educational institutions to rapidly embrace technology-enhanced learning. However, the COVID-19 containment measures that forced people to work or stay at home, have determined a significant increase in the Internet traffic that puts tremendous pressure on the underlying network infrastructure. This affects negatively content delivery and consequently user perceived quality, especially for video-based services. Focusing on this problem, this paper proposes a machine learning-based resource allocation solution that improves the quality of video services for increased number of viewers. The solution is deployed and tested in an educational context, demonstrating its benefit in terms of major quality of service parameters for various video content, in comparison with existing state of the art. Moreover, a discussion on how the technology is helping to mitigate the effects of massively increasing internet traffic on the video quality in an educational context is also presented.