Implement a mechanism that holds session information whilst the user is interacting with the system and makes this information available to the duplicate servers in the system.
Architecture introduces a session persistence mechanism in the form of a session backup server. The session state is saved whenever it is changed in response to a request. We introduce request-based failover so that the system software tries to load session state from the session backup server whenever it receives a request that forms part of a session that it doesn't recognize.
This pattern applies essentially to software. The state is maintained in the context of a software component, and the session backup server is usually implemented in software. Hardware is only required to host the backup server--sometimes this hosting is provided by a dedicated hardware server, sometimes the backup servers live on the same hardware server as the system software.