Greedy strategy: Serve people in order of increasing service time. Shortest first.
Intuition: A person with short service time adds little to everyone behind them. Putting them first minimizes the cumulative delay.
Claim: Sorting by service time (ascending) minimizes total waiting time. I will prove this using exchange argument. If you swap a long and short person where the long person comes first, you reduce total waiting. The person who takes less time should go earlier to minimize the delay for others.