Although it is impossible for any DNS-based load balancing system to guarantee that any given user will remain mapped ("stick") to the same server indefinitely, there are some things that can be done to reduce the probability of a user being mapped away. One of these is the Persistent assignment handout mode. Normally, when GTM is computing the answer to return to a query, it maps the request to a data center, and then returns all of the IP addresses of servers in that data center that are considered live.
If the Persistent assignment handout mode is enabled for the property, GTM will instead return just one live IP from among all the live IPs. The IP is chosen based on a hash of the client nameserver's IP address, so that requests from different nameservers may get mapped to different server IPs (thus spreading the load across all of them), but all requests from the same nameserver IP will always get the same answer.
Persistent assignment has no effect if a data center has only one server IP address configured; the portal will issue a warning to that effect if you try to submit such a configuration.
Persistent assignment does not have any effect on which data center is chosen. It only controls which IPs in the data center are returned, once the data center choice has been made. A user could still be moved from one data center to another, if, for example, load feedback attributes for that data center suddenly go over target.