What you described is almost exactly like my university - about 2800 total users, managing around 900-1000 computers. Lots of servers. This is what we have:
4 "systems support" (desktop, laptop, user stuff)
4 network/server/that kind of thing
3 or 4 help desk
2 or 3 for telecom
about 6 for remaining tasks: web, software, management, etc.
Now, we also have about 16 part time student workers for systems support, 4 for network/server, and 8 for help desk. I can attest that at times the 16 is overkill, but most of the time they are fixing small problems.
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What you described is almost exactly like my university - about 2800 total users, managing around 900-1000 computers. Lots of servers. This is what we have: 4 "systems support" (desktop, laptop, user stuff) 4 network/server/that kind of thing 3 or 4 help desk 2 or 3 for telecom about 6 for remaining tasks: web, software, management, etc. Now, we also have about 16 part time student workers for systems support, 4 for network/server, and 8 for help desk. I can attest that at times the 16 is overkill, but most of the time they are fixing small problems.