Current — PoS only

Global PoS components:

• $f_c$ — cover message frequency
• $f_p$ — proposal message frequency
• $e$ — encapsulation replication factor
• $r_c$ — cover message redundancy factor
• $r_p$ — proposal message redundancy factor
• $\omega$ — observation window
• $\delta$ — minimal divergence controller
• $\Delta$ — maximal divergence controller

We assume $f_p \le f_c$.

Expected message relay frequency (per connection):

$f_{PoS} = (f_c \cdot r_c + f_p \cdot r_p) \cdot e$

Expected number of messages relayed during the observation window (per connection):

$M_{PoS} = f_{PoS} \cdot \omega$

Minimum

Minimum expected number of relayed messages (per connection):

$\lfloor M_{PoS} \rfloor = M_{PoS} \cdot \delta$

Setting a safe minimum for the expected number of relayed messages is difficult, because the value depends on both the network topology and each node's position within it. Consider the following edge case: a healthy node receives the same message from all of its peers simultaneously and stays silent, because every peer has already forwarded that message to it. By chance, the node may remain silent for an extended period, since messages are emitted at random times by random nodes. The probability of such an event decreases as the observation window grows. For this reason, detecting an unhealthy node is better expressed not as a minimum expected number of relayed messages, but as a sufficiently long period during which no messages are received.

Maximum