tie up (traffic) - to slow down traffic, to cause road traffic to stop The accident tied up the highway traffic for two hours last night. tie up with (someone or something) - to enter into an association or partnership with someone or something Our company decided to tie up with a company from Sweden to make the pollution equipment. . tied to one's mother's apron strings - to be dominated or dependent on one's mother The boy is tied to his mother's apron strings and he never wants to leave home. tied up - to be busy I was tied up yesterday and did not have enough.