Explore the possibility of modelling more than timeliness with DeltaQ

[ghost]

Newly built tool allow us to easily explore relatively simple models of diffusion delay across an abstraction of the network.
However, Leios is primarily concerned about the usage of bandwidth and its possible saturation which has a consequence on timeliness of blocks diffusion and its reliability.

The goal of this work is to answer the following questions:

• Can DeltaQ "easily" incorporate models of bandwidth usage and the effect of saturation and backpressure?
• Can DeltaQ model the topology of the network, to represent possible bottlenecks?

We want to bound the amount of time spent on this to at most 1 week.

[ghost]

See https://github.com/input-output-hk/ouroboros-leios/blob/main/Logbook.md#2024-10-15

[rkuhn]

Update: last week I developed enough of a sketch of the math behind the problem to get something that I want to try out in code. The main ideas are:

• enrich the current CDF atom with a second distribution that models ephemeral (meaning non-accumulated) load
• enrich the syntax with a multiplier that models that some part of the expression will be performed multiple times in parallel; this factor is only considered for computing the resulting load, it does not influence the timeliness CDF

These two changes should allow using the same ΔQ model for timeliness and load. In addition I’m considering adding an exponentiation or fix point operator specifically designed to model gossip-like activities in a network graph (assuming logarithmic maximal path length and allowing for small-world if desired). If this works out, then it could replace the empirically (or magically) obtained N-hop-distribution ladder with something more malleable. This fix point will make use of the same multiplication factor as the load analysis for modelling information diffusion.