I want to create a fairly simple mathematical model that describes usage patterns and performance trade-offs in a system.
The system behaves as follows:
- clients periodically issue multi-cast packets to a network of hosts
- any host that receives the packet, responds with a unicast answer directly
- the initiating host caches the responses for some given time period, then discards them
- if the cache is full the next time a request is required, data is pulled from the cache not the network
- packets are of a fixed size and always contain the same information
- hosts are symmetic - any host can issue a request and respond to requests
I want to produce some simple mathematical models (and plotted X/Y graphs) that describe the trade-offs available given some changes to the above system:
- What happens where you vary the amount of time a host caches responses? How much data does this save? How many calls to the network do you avoid? (clearly depends on activity)
- Suppose responses are also multi-cast, and any host that overhears another client's request can cache all the responses it hears - thereby saving itself potentially making a network request - how would this affect the overall state of the system?
- Now, this one gets a bit more complicated - each request-response cycle alters the state of one other host in the network, so the more activity the quicker caches become invalid. How do I model the trade off between the number of hosts, the rate of activity, the "dirtyness" of the caches (assuming hosts listen in to other's responses) and how this changes with cache validity period? Not sure where to begin.
I don't really know what sort of mathematical model I need, or how I construct it. Clearly it's easier to just vary two parameters, but particularly with the last one, I've got maybe four variables changing that I want to explore.
Help and advice appreciated.