Arrivato alla stazione degli autobus raggiungo a piedi in tre minuti quella ferroviaria, e mi guardo in giro per capire dove comprare il biglietto.
also: Dopo essere arrivato alla stazione degli autobus...
also: Essendo arrivato alla stazione....
After having arrived at the bus station I went to the train station and looked around in order to find out where the tickets are sold.
Risolto questo problema me ne si presenta un altro.
possible as well: Dopo avere risolto questo problema....
possible as well: Avendo risolto questo problema...
This problem resolved I found myself confronted with another one.
Una volta finito il lavoro vi dirò com' è andato.
possible as well: Dopo aver finito il lavoro....
possible as well: Avendo finito il lavoro....
When the work is finished I will tell you how things went.
It is quite obvious that the past participle / participio passato is mostly used to substitute a relative clause. A relative clause is nothing else than an attribute of a noun, matches with that noun through the relative pronoun in gender and number.
The car bought yesterday is yellow. La macchina comprata ieri è gialla. The car that we bought yesterday is yellow. La macchina che abbiamo comprato ieri è gialla.
It is obvious as well that a gerund and an infinitive can substitute a lot of subordinate clauses, but never a relative clause because the gerundio and the infinitivo are really infinite can't therefore match in gender and number with a noun. A relative clause is an attribute and must match in gender and number with the noun it refers to.
Besides a relative clause the past participle can be a temporal clause. We have the same phenomenon we already knew from the gerund. The relationship between the subordinate clause and the main clause is not revealed because there is no conjunction.
a) Riparata la macchina, sono partiti.
b) La macchina riparata ieri, si è guastata di nuovo oggi.
In case a) we have a temporal clause (After the car had been repaired, they left), in case b) a relative clause (The car that has been repaired yesterday, has got broken once again today) but this relationship has to be deduced from the context, because there is either a conjunction (after) nor a relativ pronoun (that) revealing the relationship.