Back in the old days, they'd provision trunks into the voicemail system between the Class-5 switch and the voicemail system. They'd have to know how many trunks to provision to let all the subscribers both receive voicemails, and call in to check the voicemails.
I don't have any good answers here. But I did a quick study using data from logs on a couple of service providers.
These are new-fangled VoIP service providers. So for them, a media/application server supports:
However, the server can email voicemails somewhere else. So when people check their voicemail, they may not be checking over the phone. This is different than the old-school voicemail systems of 2001, and affects the utilization.
Just as an example, one service provider I checked had a 48:1 oversubscription ratio: i.e., for each 48 subscribers, there's one RTP stream at peak. They also had about 0.0001 calls-per-second-per-subscriber.
(I say "at peak" because I'm interested in building a network that supports the peak, "busy-hour" load. If I design for the average, I'll have problems when the load goes above that average.)
Does this ratio apply to you? All of these things could affect it:
As another note, it appears that the average duration of voicemail is in the 25-30 second range. This is true at two service providers, both in NFL cities.
Update -- A residential service provider reports around a 160:1 oversubscription ratio just for basic voicemail. (I.e., One concurrent call for every 160 subscribers.) A few of them do get voicemail via email.
Someone familiar with voicemail software development told me they expect over 200 subscribers per concurrent call for traditional voicemail.