Multi-Paxos
A typical deployment of Paxos requires a continuous stream of agreed values acting as commands to a distributed state machine. If each command is the result of a single instance of the Basic Paxos protocol, a significant amount of overhead would result.
If the leader is relatively stable, phase 1 becomes unnecessary. Thus, it is possible to skip phase 1 for future instances of the protocol with the same leader.
To achieve this, the instance number I is included along with each value. Multi-Paxos reduces the failure-free message delay (proposal to learning) from 4 delays to 2 delays.
Read more about this topic: Paxos (computer Science)