Prior to the restart, we have an operating system process (our edge server) accepting connections on a given port. When we restart, a new process starts accepting connections on the port (and the old process stops accepting connections). So connections are still accepted, but new connections are run with the new code, and the old process kills its connections over 15 minutes (the old code).
For 15 minutes, we have 2 edge server processes running, but only 1 actively accepts connections (the newest).