That's the same load shedding as grocery stores use - if everything gets too crowded people start leaving (not queueing).
Now that may actually be suboptimal for the business (if they can only let 10 people in they'd rather let the 10 who will spend the most, say) which is why things like reservations, etc come into play. I wonder if restaurants that do both reservations and a queue see one group pay more on average ...
That's the same load shedding as grocery stores use - if everything gets too crowded people start leaving (not queueing).
Yes. That's called the "rejection rate".
Unless, some of the time, queue length is zero, you will have a nonzero rejection rate. This is worth bringing up with store managers who want to run understaffed checkouts. One of the things retail consultants do is point out how sales are being lost that way, both in customers who leave and customers who never come back.
Much of my early work on network congestion was based on that. In the early days of networking, everyone was thinking Poisson arrivals, where arrivals are unaffected by queue lengths. This is partly because the original analysis for the ARPANET, by Leonard Klienrock, was done that way. It was done that way because his PhD thesis was based on analyzing Western Union Plan 55-A, which handled telegrams. (Think of Plan 55-A as a network of Sendmail servers, but with queues made from paper tape punches feeding paper tape readers. The queue was a bin between punch and reader.)[1], at 7:00. Queue length was invisible to people sending telegrams, so senders did behave like Poisson arrivals. That's still true of email today.
The IP layer is open loop with rejection. Transport protocols such as TCP are closed loop systems. The two have to be considered together. Everybody gets this now, but it was a radical idea in 1985.[2]
This is a big part of self checkout - it reduces rejection rate.
And that can be done with queues in general, if alternate paths are available at some point intelligent operators will change path (this can be problematic also, when the option to change isn’t available - I’d normally like to connect to a server near me but if it is overloaded give me the option to take a further away one).
I've never managed a restaurant, but thinking about my own habits I'd bet that a restaurant that takes reservations but also some walk-ins almost surely makes more on the reservation guests. The meal is the main attraction for them, often a special occasion, while walk-ins are more likely to spread their money over other businesses (shopping before, drinks elsewhere after, etc.). I bet group size is also higher for reservations; most people know a reservation is all-but-required for larger groups.
Now that may actually be suboptimal for the business (if they can only let 10 people in they'd rather let the 10 who will spend the most, say) which is why things like reservations, etc come into play. I wonder if restaurants that do both reservations and a queue see one group pay more on average ...