1. Actively or fully engaged or occupied Adjective
2. Overcrowded or cluttered with detail Adjective Satellite
3. Intrusive in a meddling or offensive manner Adjective Satellite
4. Crowded with or characterized by much activity Adjective Satellite
5. (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) Adjective Satellite