Latency distributions model key factors relevant to performance distributed systems:

• computation cost
• network delay
• arrival of messages to different nodes at different times, when used as matrix elements.

We show basic algebra of latency distributions in a succinct way, which behave as random variables ranging over value of delay or being lost.

Then we go to generalize these operations to series and matrices of latency distributions. Operations on these series and matrices allow us to model message propagation (by iterated matrix multiplication), or voting (by generalizing n-over-k operator).

This approach allows for exact computation of long-tail latencies, which is unique given current problems with modeling long-tail latencies and “black swans” in general.

You may read more about the project in recently released article: Curious properties of latency distributions.