generic name for deli counter machine

Facial tissues are the generic term for Kleenex; cola is the generic term for Coca-Cola and Pepsi.

Is there a generic term for a deli-counter numbering machine?

Good question!

When I ran a Google search just now, I obtained the following results at my time and location:

"ticket dispenser" — 224,000 hits
"take a number dispenser" — 17,600 hits
"number dispenser" — 12,000 hits
"number ticket dispenser" — 93 hits
"ticket number dispenser" — 38 hits
"take a ticket dispenser" — 17 hits.

Some of those totals will be inflated by spurious matches because the context is different to what the questioner has in mind. To pluck an example out of the air, a string like "random number dispenser" (which gets 14 hits) would logically also have been counted in the search for "number dispenser".

So bear that caveat in mind: these totals are just a rough guide, not a scientifically validated result.

Edit

The crudeness of the "Google total" method is demonstrated by the paradoxical results for "take a number dispenser" (17,600 hits) versus "number dispenser" (12,000 hits).

The search for the string "number dispenser" is less restrictive than the one for "take a number dispenser", yet it achieves 5600 less hits. This makes no logical sense.

I'd love to know why the Google search algorithm produces anomalous results like this.

Probably a number dispenser:

• Provide fair, organized, and efficient customer service with a number dispenser! A ticket dispenser machine is a great way to organize a line of customers as they wait to be served at your grocery store, market, deli, or sandwich shop.