Synonyms of 'tied up'
Copyright © 2016 by HarperCollins Publishers. All rights reserved.
Someone who is engaged in or engaged on a particular activity is doing that thing.
the various projects he was engaged on
If you are engrossed in something, it holds your attention completely.
He didn't notice because he was too engrossed in his work.
Thesaurus for tied up from the Collins English Thesaurus
If someone or something is tied up , they are busy or being used, with the result that they are not available for anything else.