11 After three months we set sail in a ship that had wintered in the island, a ship of Alexandria, with the twin gods  as a figurehead. 12 Putting in at Syracuse, we stayed there for three days. 13 And from there we made a circuit and arrived at Rhegium. And after one day a south wind sprang up, and on the second day we came to Puteoli. 14 There we found brothers  and were invited to stay with them for seven days. And so we came to Rome. 15 And the brothers there, when they heard about us, came as far as the Forum of Appius and Three Taverns to meet us. On seeing them, Paul thanked God and took courage. 16 And when we came into Rome, Paul was allowed to stay by himself, with the soldier that guarded him. (Acts 28:11-16 (ESV)
“On seeing them, Paul thanked God and took courage.” This implies that Paul was perhaps a bit apprehensive and unsure. He had written to the Romans three years prior to all of this from Corinth. Since then much had taken place, and though God had allowed Paul to live, a person can understand him being distraught. Sometimes it isn’t the living that you worry about, but what you are going to have to live through and endure. Sometimes living is harder than dying. Paul would have to be in Rome quite some time before he would be heard. During this time he would be a prisoner. Things would be perhaps quite difficult for him if the Christians of Rome had turned their backs on him, if indeed the Judiazers had gotten in among them to the point where they would contradict him. A prisoner under house arrest has a hard time making a living. At this time prisoners were dependent on family and Paul had none. No one to bring him food, or provide him shelter. He would have to rely on the Roman Christians for this sort of thing.
Now he is very relieved that the Christians have met him at Three Taverns. He doesn’t know them. He’s just relieved. If they have come it means his letter has found good soil as it were. They are willing to take him under their wing and support him, even as a prisoner. They had received his message with joy. This is something to take heart in, the gospel at work.