Equilibrium

1
Equilibrium Stability of TCP

• Steven Low
• CS/EE Caltech
• netlab.caltech.edu
• June 2002

2
Outline

• Equilibrium of TCP
• Stability of TCP
• FAST project overview

• Acknowledgments
• D. Choe (Postech/Caltech), J. Doyle (Caltech), C.
  Jin (Caltech), K. Kim (SNU/Caltech), F. Paganini
  (UCLA), J. Wang (Caltech)
• L. Peterson, L. Wang (Princeton)
• S. Athuraliya, D. Lapsley (UMelb)

3
Congestion Control

• Heavy tail ? Mice-elephants

4
TCP AQM
pl(t)
xi(t)

• Example congestion measure pl(t)
• Loss (Reno)
• Queueing delay (Vegas)

5
TCP/AQM

• Congestion control is a distributed asynchronous
  algorithm to share bandwidth among users
• It has two components
• TCP adapts sending rate (window) to congestion
• AQM adjusts feeds back congestion information
• They form a distributed feedback control system
• Equilibrium stability depends on both TCP and
  AQM
• And on delay, capacity, routing, connections

6
Understanding TCP/AQM

• Protocol (Reno, Vegas, RED, REM/PI)

7
Equilibrium duality model

• Flow control problem

• TCP/AQM
• Maximize aggregate source utility
• With different utility functions

8
Equilibrium of Vegas

• Network
• Link queueing delays pl
• Queue length clpl
• Sources
• Throughput xi
• E2E queueing delay qi
• Packets buffered
• Utility funtion Ui(x) ai di log x
• Proportional fairness

9
Stability of AIMD/RED

• Small effect on queue
• AIMD
• Mice traffic
• Heterogeneity
• Big effect on queue
• Stability!

10
Stable 20ms delay
Window
Ns-2 simulations, 50 identical FTP sources,
single link 9 pkts/ms, RED marking
11
Stable 20ms delay
Window
Ns-2 simulations, 50 identical FTP sources,
single link 9 pkts/ms, RED marking
12
Unstable 200ms delay
Window
Ns-2 simulations, 50 identical FTP sources,
single link 9 pkts/ms, RED marking
13
Unstable 200ms delay
Window
Ns-2 simulations, 50 identical FTP sources,
single link 9 pkts/ms, RED marking
14
Other effects on queue
20ms
200ms
15
Stability region

• Unstable for
• Large delay
• Large capacity
• Small load

16
Current protocols

• Current TCP/RED has equilibrium and stability
  problems
• Equilibrium problems
• Unfairness to connections with large delay
• At high bandwidth, equilibrium loss probability
  too small to be reliable
• Stability problems
• Unstable as delay, or more strikingly, as
  capacity scales up
• Instability causes large slow-timescale
  oscillations
• Long time to ramp up after packet losses
• Jitters in rate and delay
• Underutilization as queue jumps between empty
  high

17
FAST Fast AQM Scalable TCP

• FAST solves these equilibrium and stability
  problems
• Equilibrium properties
• Uses end-to-end delay rather than loss as
  congestion measure
• Achieves any desired fairness, expressed by
  utility function
• Very high utilization (99 in theory)
• Stability properties
• Maintains stability for arbitrary delay,
  capacity, routing load
• FAST rescales itself as these parameters change
• Non-oscillatory in equilibrium
• Need not re-tune as these parameters change
• Good performance
• Negligible queueing delay loss
• Fast response

18
Network upgrade 2001-06
19
Projected performance
04 5
05 10
Ns-2 capacity 155Mbps, 622Mbps, 2.5Gbps,
5Gbps, 10Gbps 100 sources, 100 ms round trip
propagation delay
J. Wang (Caltech)
20
Projected performance
TCP/RED
FAST
Ns-2 capacity 10Gbps 100 sources, 100 ms round
trip propagation delay
J. Wang (Caltech)
21
Coming together
Clear present Need
Resources
22
Coming together
Clear present Need
FAST Control
Resources
23
Papers
netlab.caltech.edu

• Optimization flow control, I basic algorithm
  convergence (ToN, 7(6), Dec 1999)
• A duality model of TCP flow controls (ITC, Sept
  2000)
• Understanding Vegas a duality model (J. ACM,
  2002)
• Scalable laws for stable network congestion
  control (CDC, 2001)
• Stabilized Vegas (Allerton Conf, 2002)