I need to model data access for a storage system where I have:
- $S = $ Number of Server Nodes (that hand out data to clients and store data)
- $D = $ Number of Data Nodes (that do not hand out data to clients and only store data)
- $F = $ Number of Frontend Nodes (that hand out data to clients and do not store data)
- $R = $ Replication factor (copies of the data, no more than one copy per node)
For my purposes, either $D$ or $F$ will be $0$ (not sure if that affects the formula but it makes thinking about it easier). What I am trying to model is the probability that on any given I/O operation (read or write), the $S$ or $F$ node being accessed by a client will have NO local copy of the data.