One line or many?

The supermarket gives every cashier a queue; the airport runs one snake line feeding every desk. Same staff, same arrivals, same load — wildly different waits. Separate lines waste capacity: a server stands idle while the queue next door is five deep, and the line you've joined can't borrow anyone else's slack. One shared line never lets a server idle while anyone waits, and the math says how much that's worth — at the defaults below, about 5× less time in line, most of what a mythical cashier four times as fast would buy, with no mythical hardware.

workers, each takingper customer, running% busy.
99× the service time0.1×10×
0%20%40%60%80%85% busy100%
4 separate linesone snake lineone 4×-fast server
4 separate lines: 22m 40s in line. One shared line: 4m 36s — same staff, same load, 4.9× faster.
WorkersSeparate linesOne snake lineAdvantage
2
22m 40s
10m 25s
2.2×
3
22m 40s
6m 30s
3.5×
4you
22m 40s
4m 36s
4.9×
6
22m 40s
2m 46s
8.2×
8
22m 40s
1m 55s
12×
12
22m 40s
1m 6s
21×

The separate-lines column never moves: splitting the arrivals across more lines splits the capacity to match, so at the same per-server load twelve queues of one wait exactly as long as one queue of one — adding tellers each with their own line never shortens the wait. All the gain sits in the shared column, and it grows with both team size and load: big, busy teams have the most to win by merging. The dashed fast server still wins door-to-door, since it also serves each customer in a fraction of the time — but on time spent waiting the snake edges past even it. The snake's honest costs: nobody gets to pick the fast cashier or the short line, and the one queue everyone shares looks dauntingly long even when it's moving quickly.