Nimbostratus
If i understand this correctly:
1) you have a server in each data center.
2) you have a BIGIP LTM in each data center and they each have a corresponding VIP.
3) Users now connect to their local VIP.
You need to think about hostnames, not IP addresses:
globalApp.company.com will translate, via DNS, to three different IP addresses in three different datacenters. You DNS servers pass all three IP addresses to the browser in a round robing fashion. The browser will try first, then second, then third.
Having said that; that would be poor-man's GSLB.
The better and more flexible way of dealing with this is to use the F5 GTM. It will give you a lot of capabilities. Get in touch with your F5 Field Sales Engineer and he/she will draw out a complete solution.
What do you mean by , all users are on the same subnet? What about when they are traveling?
John
