What do you define as a large network? And what would efficient mean for a network that size?
100,000+ nodes
efficient would mean close to optimal redundancy
still need to work out what sort of probability distribution there will be so I am not sure what "optimal" is yet
How many public/private nodes?
this depends on the users. I am counting each computer as a node and most will probably have a loopback privacy server along with the private node, then the 100+ public privacyservers, so that is 1000 clients for the 100+ privacyservers. sounds like a lot, but UDP processing will be fast and network packets are so slow compared to CPU, I dont think it will be an issue. RAM will probably be the limiting factor, but even if things have to swap to HDD it could be fast enough
I'm a little lost now

I was originally thinking there would be ~100,000 'ordinary' users, then a much smaller number of public privacyservers (100); a user sends a packet, which bounces around between the 100 privacyservers for a while (1-3 onion skins), then 'exits' the privacyserver subset of the network to another user. This may be an oversimplification, or just plain wrong, especially as I'm not sure what a loopback privacyserver is.
Assuming I have understood properly, then although there are a LOT of users, there aren't many privacyservers in comparison - 1000:1. And the optimisation needs to occur only within those 100?
I guess I was just wondering whether there was some kind of shortcut, as 100 isn't that big a number, but that depends on what acceptable traffic is, and what sort of fanout is considered acceptable.
Just trying to understand better. This is what happens when you ask 'anyone' for feedback.
every ordinary user will have to use a privacy server
i assume most will use their own computer as the privacy server
so each user will have a private node and a loopback privacy server
this means 100,000 private nodes, 100,000 loopback servers
to have a reference set of public IP addresses that are always there, there will be 100+ community run public IP privacy servers
so 100,000 private nodes, 100,000 loopback privacyservers, 100 public IP privacyservers
onion packets will bounce around all the privacyservers loopback or public IP