1. Fluid Modeling
Abstracting a discrete-valued system (e.g., packets, customers, users) into a continuous-valued model
Writing equations to model system (e.g., differential equations, PDEs)
Solving for steady-state
Determining optimal system config
Example: BitTorrent [Qiu/Srikant 2004]

2. BitTorrent System Model
Downloader
Seed
Downloader
Seed
Downloader
Torrent
(with x downloaders and y seeds)
Arrival rate = 
Departure rate =  y
Downloader
Residence Time 1/ 
Download Time T

3. Fluid Model Overview Arrivals x(t) Conversions Downloaders y(t) Seeds
Departures

4. Model: Rarest-First (1 of 2)
Conversion rate for downloaders becoming seeds is given by (x+y)UC.
Thus the change of swarm population obeys:
See [Parvez et al. 2008] dy

5. Model: Rarest-First (2 of 2)
Download latency:
Insights:
T does not depend on peer arrival rate!
Having more upload connections (U) helps
Having higher throughput (C) helps
Having seeds stay around longer is better
See [Parvez et al. 2008]