I work for a county sheriff's dept. There's close to 2 million population wise in the county, but our jurisdiction covers only about 500,000 people. The incorporated municipalities within the county cover the other 1.5 million or so. My center dispatches police only. We're what's known as a Primary PSAP. We receive the initial 911 call from the public. From there, we determine whether the emergency is police, fire or medical in nature and triage the call accordingly. If it's fire or medical, we transfer it to the proper fire/ems Secondary PSAP. Almost all of our employees at the center are cross trained to do dispatch and call taking, though we don't do both at the same time as what happens in smaller centers. All of our call takers are also responsible for answering non-emergency lines, internal communications lines (dedicated lines for the officers to call in), hot lines (or ring downs, depending on what term you use) from other agencies, in addition to the 911 lines.
All that said, we receive over 1000 calls per day from the public, which translates to somewhere around 300-350 calls for service daily. Of course, this number varies based on many different things. Day of the week, time of the year, holidays, etc. For example, Monday mornings are usually very busy because people who put off calling over the weekend, are going to try on their way to work, or before work. Friday and Saturday nights are usually pretty busy as well. At any given time, we'll have anywhere from 1-7 dedicated call takers on shift. This number varies based on time of day, day of the week, whether breaks are being given, etc. Our center is very lucky in that we have nearly 90% of our optimal work force. Most centers are operating near 70% due to the high turnover and difficulty and time needed to train new dispatchers (my training, including classroom and on the job took 22 weeks from start to finish, and less than half that started with me made it through).
Calls per hours is difficult to calculate. We could just take 1000/24 to get about 42 calls per hour, but that really doesn't fit what the actual experience is. I still haven't figured out why, but calls come in in waves for some reason. It could be dead for 30 minutes, with only 4 or 5 calls coming in, then all of a sudden the phone blows up and you have 5 call takers answering lines constantly for an hour, and having to put some lines on hold to deal with the volume. Staffing is set up to deal with the spikes. And we know basically when the spikes typically happen. We do have a decent amount of downtime, but when the calls come in, you need enough bodies to answer them.
Having said all that, there are some centers that are literally 1 person, they answer phones and dispatch. Then you get others that look like the call center in "The Call" (terribly inaccurate movie, btw) that service big cities, like LA or NY. I'd imagine most centers are more like the one I work in. Not huge, but not small. Anyway, hope that answered some of your questions. Got a bit long winded. Anything else you're curious about? Ask away.