# What mathematical models can analyze and optimize such message passing system?

I look for a mathematical model that can accommodate, analyze and suggest optimizations for a system that can be humanly described as message passing black box programs to which where optimal message directions shall be suggested depending on their reactions to different messages.

## System description:

We have a graph. Its nodes can appear and disappear in time (we know only if node is alive at a discreet moment of time). We can assume that all nodes can be connected one to another via $N$ types of connections (message passing channels and patterns) any node to any node alike ZeroMQ.

Nodes send messages to one to another, messages are different, we know some hash function-based signature for each message and its size. We have f(size,t,c) that describes how fast a message can be passed from one node to another, it uses message size, current time, and c for size of all other messages being sent to this node concurrently.

Each node has a set $M$ of parameters describing their state given via monitoring utilities. We do not know lows of how parameters change, but we know that they change as time goes on and new messages arrive so we can try to approximate them for each node looking at incoming messages and time.