engaged

having ones attention or mind or energy engaged; "she keeps herself fully occupied with volunteer activities"; "deeply engaged in conversation"

involved in military hostilities; "the desperately engaged ships continued the fight"

reserved in advance

(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"; "the lavatory is in use"; "kept getting a busy signal"

(used of toothed parts or gears) interlocked and interacting; "the gears are engaged"; "meshed gears"; "intermeshed twin rotors"

having services contracted for; "the carpenter engaged (or employed) for the job is sick"

built against or attached to a wall; "engaged columns"