https://solarsystem.nasa.gov/moons/saturn-moons/titan/overvi...
According to this (at the time of reading) a one way trip at the speed of light is ~75 minutes, so you will have approximately two and a half hours of ping.
Ouch.
Still, it raises an interesting question: how would a hypothetical Earth-Titan network protocol work?
(Atleast this is my understanding from watching Apollo documentaries/movies etc.)