Measure the wait for a week, put people where the busy hours are, separate quick jobs from long ones, and tell every customer their place. Most of the gain comes from those four.
Step 1: measure before you change anything
For one week, write down four things: the usual wait, the longest wait, how many people leave before they are served, and the hours when the room is fullest. Without those you will fix the wrong thing. A queue system records them for you, but a notebook at the desk is enough to start.
Step 2: put your people where the busy hours are
Waits are rarely spread evenly. If the room is full between 11 and 1 and half empty at 3, moving a break or a shift is the cheapest fix there is. Look at your busiest hours, not your average.
Step 3: separate quick jobs from long ones
A one-minute pick-up stuck behind a twenty-minute fitting makes everyone angry. Give quick and long jobs their own line, or their own counter, so short jobs are not held hostage. Returns, repairs and collections at a shop desk are a typical case.
Step 4: take bookings for what you can predict
Anything with a known length can be booked. Keep walk-ins for the rest, and fill the gaps between bookings with them. The risk is two lists that disagree, so keep bookings and walk-ins in one line.
Step 5: let people leave and come back
A lot of the people who walk out do so because they cannot tell how long the wait will be, or are afraid of losing their place if they step away. If they can see their place on their phone and trust it, they can wait in the car, next door or in the aisles. The room is calmer and fewer people give up.
Step 6: find the slowest stop
In a visit with several stops, such as reception, then the doctor, then the pharmacy, the wait usually piles up at one of them. Time each stop separately. Often the fix is at the stop nobody was watching.
Step 7: say the wait honestly
Waits you cannot see feel longer than waits you can. Tell people their place and give a range, not a promise. “About 10 to 15 minutes” that turns out to be 12 builds trust. “Five minutes” that turns out to be 20 does the opposite.
Step 8: look after the person who has waited longest
A fair order has to protect against someone being pushed back again and again by newer arrivals. Pick a limit, such as 20 minutes, after which a long-waiting walk-in moves up. Say what the limit is on your sign, so people know the rule.
Step 9: look again every week
Compare this week's four numbers with last week's. Change one thing at a time. If the longest wait drops but more people leave, you have made the wrong trade.
In short
You cannot always shorten the wait, but you can almost always shorten the feeling of waiting. Measure it, spread it, and tell people where they stand.