I think the worst case scenario is us getting hit by a hurricane at the same time our local nuclear plant has a major meltdown, there's widespread cellular network outages, our dispatch center catches fire and we have to evacuate to our backup center, and there's also a mass shooting incident going on while someone's trying to deliver a baby over the phone with someone in a moving car speeding down the highway refusing to pull over and also fighting with their husband and causing multiple accidents.

Serious answer- my agency is lucky, even with handling basically every emergency and non emergency call in our county, our staffing and call volume are good enough that even a long wait for us to answer the phone is usually only like 2 or 3 rings. My coworkers are good at what we do, our training is better than what some other centers get, we can keep the calls moving, there's about 20-30 of us on at any given time depending on the shift and staffing and such, and there have been major incidents where we've handled something like 1000 calls in the space of an hour or two and no one had any significant delay in getting their call answered. As a general rule, we don't even put callers on hold regardless of how minor the incident is, or if they called 911 or 10-digit, we just handle the call and move on.

Non emergency calls, and honestly even a lot of actual emergency calls are a lot more simple than you might think. The majority of my calls have maybe a dozen or so words in the notes, many are just one or two words. I'm not taking a full report, I'm getting a location, a brief description of what's happening, and some general safety information, giving them some brief instructions if necessary, then the callers name (if they'll give it to me) and phone number and I'm off to answer the next call. I'm not taking a full report, I'm not an officer I'm not taking a full report that's the cops' job, I'm sending responders to go handle the emergency.

Every situation is different, sometimes I've had to stay on longer, I've had a couple calls I've been on for over an hour because the situation kept evolving and we needed constant updates from the caller, but that's an extreme outlier. Most of the time my calls are well less than 5 minutes, often less than 2 or even less than 1 minute and between all of us we move through the queue quickly.

If we're not busy, I can take my time, go full customer service, and help people with all of their stupid problems that are in no way a police issue. If we get busy, I can cut right to the chase, get what I need, and hang up.

Some agencies have higher call volumes, major staffing issues, and frankly are sometimes just bad at what they do, and that can cause delays. Some places it is a real issue, but I've had to transfer calls all over the country and most of the time it's a non-issue. Overall, dispatchers know how to keep the queue moving, when they can slow down and take their time, and when they need to power through.

Also it's a somewhat self-correcting problem. If there's a long non-emergency queue, there's probably a long 911 queue as well, and someone who doesn't really have an emergency is probably going to hang up pretty quickly instead of waiting 2, 3, 5, 10, 20+ minutes for an answer for someone to answer. They'll hang up and try the non emergency line, or try back later, or drive themselves to the station or hospital, or maybe just decide it's not a big enough deal to worry about.

There are always weird exceptions and edge cases in our job, there's very little we can say that will apply to all situations in all dispatch centers across the country. To some extent, you just kind of have to try being aware of what things are like where you are. If you're not sure what to do, that's what's 911 is for, just try to keep things to-the-point, and listen to what we're asking/telling you.