Happy Path:

Latency:

Latency is a critical metric that measures the time it takes for a transaction to be processed and committed in the network. There are two ways to define latency:

1. Transaction-to-Confirmation Latency: The time taken by a transaction from the moment it is sent by the client to the moment the client receives proof that the transaction is committed.
2. Leader-Proposal-to-Commitment Latency: The time is taken by a transaction to be proposed by a leader and subsequently committed in the network.

To showcase the protocol's scalability, latency should be measured for increasing network sizes. For instance, testing should be conducted with varying node counts, such as 100, 500, 1000, 5000, 10000, 50000, and 1000000 nodes.

Throughput:

Throughput is a crucial metric that indicates the number of transactions committed per second in the network. It is influenced by the block size and transaction size.

To demonstrate the protocol's scalability, throughput measurements should be taken for increasing network sizes, similar to the latency measurements. For example, testing with node counts of 100, 500, 1000, 5000, 10000, 50000, and 1000000 would be informative.

Additionally, it is essential to establish a relationship between throughput and latency for specific network sizes, such as 200, 1000, 5000, and 10000. By increasing the load (block size) until system failure occurs, the latency vs. throughput curve can be plotted, providing valuable insights into system performance under different conditions.

Unhappy Path:

For the "unhappy path" performance testing, latency measurements should be taken from the time nodes experience a timeout in the network to the first block that gets committed after the failure detection. The assumption should be made that the majority of nodes have timed out, and the protocol has initiated the "unhappy path" scenario.

It's important to note that the protocol's performance should remain consistent irrespective of the timeout period, making it unnecessary to consider the specific timeout duration during these measurements.

Authenticator/Signature Verification and Aggregation Cost (latency):

The cost of verification and aggregation of signatures is a critical bottleneck in consensus algorithms. Carnot aims to address this challenge by employing a committee-based approach, wherein a committee verifies the signatures of 2/3rd members of its child committees. Aggregation occurs only in the root committee and by the leader. As the total size of the network grows, the verification and aggregation cost of signatures are expected to grow logarithmically.