====================
0. LOGISTICS, REVIEW, OUTLINE
====================
* Review: last class
  * Sliding window protocol
  * Throughput of sliding window
  * Animation of sliding window throughput on the course web site.
* This class: congestion collapse
  * What happens if everyone sets their own large window?
  * Three examples of congestion collapse
* Next class: how do we fix congestion collapse?

====================
1. CONDITIONS FOR CONGESTION COLLAPSE
====================
* Sliding window protocol throughput is W/RTT
* What is the right value of W?: C*RTT
* What happens if W exceeds this: queueing delay of W/C - RTT Why?
* Why this can happen:
   * Don't know C,
   * Don't know RTT
   * Can vary over a flow's lifetime
* What happens if the window is not right
   * Delays go up for everyone. Interactive apps are frustrated
   * Duplicate packets can degrade throughput
* Further compounded when there are multiple senders, setting their W independently 
   * Don't know effective C (depends on other flows)
   * Effective window is sum of individual windows
* General term for all these bad conditions: congestion collapse
   * Formally, after a nw has collapsed, offered load (demand) for the nw is going up, but utility (useful work) is going down.
   (Draw out a cartoon figure of congestion collapse).
   * Similar to too many people talking in a room.
   * Similar concepts elsewhere:
     ** Economics: tragedy of the commons. Connections to game theory.
     ** OS: Thrashing

====================
2. CONGESTION COLLAPSE EXAMPLE
==================
* Several assumptions for our network:
  * n flows, each runs sliding window
  * window size is W
  * each flow has the same RTT
  * All flows share their bottleneck link of capacity C
  * Link has infinite buffers, never drops a packet
  * No retransmissions
  * Utility = throughput/latency. Aggregate utility = sum (utilities)
  * Offered load is n
* 2 regimes:
  * nW < CRTT
  * nW > CRTT
* First regime
  * Throughput increases linearly
  * Queueing delay is zero. RTT is constant
  * Aggregate utility increases linearly
* Second regime
  * Throughput constant at C
  * Queueing delay increases linearly
  * Aggregate utility decreases as 1/x
* Network is still 100% utilized, but not all its work is useful.
  * Late packets are not as useful as early ones.

=========================
3. A MORE LATENCY-ORIENTED UTILITY FUNCTION
=========================
* What if the user decides utility = 0 once the latency crosses a threshold?
  * Many web browser users are like this.
* Then the congestion collapse is more severe.

========================
4. ANOTHER EXAMPLE
=======================
* Similar conditions as previous example, except
  * Assume all packets are retransmitted after a fixed timeout T
  * Utility only measures number of unique in order packets received at the receiver
  * No latency in utility
* Three regimes:
  * nW < CRTT, utility (and throughput) increase linearly
  * CRTT < nW < T, utility remains constant at C
  * nW > T, retransmissions start, soon overwhelm the network, utility falls to 0
* Regime three is hard to reason about using pen and paper
  * Run a simulation
  * Show them simulation results

========================
5. HISTORICAL NOTES IN LECTURE NOTES (where to look for more information)
========================