Session persistence is the saving (persisting) to disk of HTTP sessions when the server is shut down and the corresponding reloading when the server is restarted. Without session persistence, a server restart will result in all active user sessions being lost. To users this means they will be asked to log in again (if you're using container-managed security), and they may lose the web page they were on, along with any shopping cart information or other web page state information that was stored in the session. Persisting that information helps to ensure that it won't be lost.
Persistent sessions implementation will allow saving the status of any transaction so in the event of a TomcatCrash the status and session information can be restored avoiding any disruption of user transactions.
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