The doctor was exhausted because he'd been for duty at the hospital for 13 hours.
The doctor was exhausted because he'd been in duty at the hospital for 13 hours.
The doctor was exhausted because he'd been of duty at the hospital for 13 hours.
The doctor was exhausted because he'd been on duty at the hospital for 13 hours.
The doctor was exhausted because he'd been up duty at the hospital for 13 hours.