Hi,
I'm not aware that Payara Server can run 2 versions of the same application at the same time. It supports some related concepts, but none is as robust as what Tomcat probably provides.
With Payara server, you can get very close to the same behavior with
--keepstate argument to the redeploy command or alternatively
an element in a descriptor file. It won't keep the old version of the app running, but it will try to serialize all live session before the old version is deployed and deserialize them into the new version. The downside is that it's less robust because deserialization may fail in some cases and if anything fails, everything is thrown away. It's supported only on the default server instance, therefore it's mostly intended during development stage to keep sessions across frequent redeployments.
In production, it's worth to invest some time to set up the infrastructure for rolling upgrades, because most production environments run a cluster of servers with a load balancer anyway.
If you don't want to migrate old sessions to the new version of your application, you don't have to enable session replication with rolling upgrades. It's enough to create 2 different domains behind a load balancer with sticky sessions and instruct the load balancer to route new sessions only to the domain with the new version. After all old sessions are closed, get rid of the old domain. I know it's not automatic and requires manual steps during a potentially long period, but it's as close as you can get with Payara server if you really want to keep user sessions and you'd rather run 2 parallel versions of your application instead of migrating the session to the new application with --keppstate option.
Ondro