busy

crowded with or characterized by much activity

a very busy week

a busy life

actively or fully engaged or occupied

busy with her work

a busy man

intrusive in a meddling or offensive manner

an interfering old woman

bustling about self-importantly making an officious nuisance of himself

(of facilities such as telephones or lavatories) unavailable for use by anyone else or indicating unavailability; (`engaged' is a British term for a busy telephone line)

her line is busy

receptionists' telephones are always engaged

overcrowded or cluttered with detail

a busy painting

a fussy design

keep busy with

She busies herself with her butterfly collection