Ever since the initial patch Private Matches on PS4 appear to be broken for many players.
Regardless of who initials the Private Match, the match either gets stuck at the Mission Start screen after the countdown reaches 00. If the match loads all except 1 player is booted to the main menu with the error, “Lost connection to host.”
I currently run a LAN connection with 1gb down/50mb up. My average connection, according to my router and my PSN network settings, are 800mb down/40mb up. My ping during private matches is always between 90-150ms, regardless of being a host or member, where my average ping during Quick Play is between 10-24ms.