1. Queue Dynamics with Window Flow Control
Karl Henrik Johansson
Håkan Hjalmarsson
Steven Low
Kevin Tang
Lachlan Andrew
Krister Jacobsson –
Queue Dynamics with Window Flow Control
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2. Introduction Window = Outstanding Packets 1001 1001 0101 0101 1101
BASIC PROBLEM
Transfer data over a communication network
PACKET SWITCHED NETWORK
File divided into chunks---packets.
Packets transmitted to the receiver.
Data ACKed.
FEEDBACK MECHANISM
CONTROL PROBLEM
In what pace should packets be transmitted
Network operates at a favorable region of the state space
Stable (TCP/RED)
Decentralized
Etc.
CONGESTION WINDOW
ROUND TRIP TIME
ACK
ACK

3. Background TCP is window based
TCP carries >80% of the Internet traffic
TCP limitations
Bandwidth scalability issues
Wireless links
Delay dependent resource allocation
New designs needed! Window based?
Tractable flow-level models valuable

4. Fluid Flow Modeling Packet-level Internet is extremely complex
Abstract away packet level detail
Model flows of packets as fluids
Feedback mechanism
ODEs
Powerful analysis frameworks
Used to reverse engineer TCP
PROBLEMS WITH QUEUEING MODELS
FEEDBACK SYSTEM

5. Motivation

6. WindoW Based Congestion Control
Window = Outstanding Packets
1101
ACK
1101
SHOPPING CART ANALOGY
INPUT ONE WINDOW AMOUNT OF PACKETS PER RTT
DEFINE ROUND TRIP TIME

7. WindoW Based Congestion Control
Round Trip Time (RTT)
SHOPPING CART ANALOGY
INPUT ONE WINDOW AMOUNT OF PACKETS PER RTT
DEFINE ROUND TRIP TIME

8. WindoW Based Congestion Control
Sending rate is dependent on the network state!
Sending rate per RTT = Window
1101
1101
SHOPPING CART ANALOGY
INPUT ONE WINDOW AMOUNT OF PACKETS PER RTT
DEFINE ROUND TRIP TIME

9. Window Based Congestion Control
Routers operate buffers
Queuing delay
RTT = Propagation delay Queuing delay
Control system
ACK-Clocking
Load increase
Larger delay
Lower rate
Load decrease
Smaller delay
Higher rate

10. Window Based Congestion Control
EXPLAIN
KEY OBSERVATION:
Two loops
FOCUS ON THE OUTER LOOP
Design of window update mechanism

11. Modeling Input: Window size Output: Queue size Assumptions No loss
FIFO buffering
Single link
No forward propagation delay
Operate far from static nonlinearities

12. Modeling a queue Integrates the link excess rate Rate of change: 

13. Modeling the Instantaneous Rate
What is xn(t)???
Common approximation: xn(t)¼ wn(t)/¿n(t)
Does not consider ACK-clocking!
NO CROSS TRAFFIC
Single window based source, single bottleneck
Capacity 50 Mbit/s
Window control disabled
Step of size 10 packets in window at t=20 s
CROSS TRAFFIC
40 Mbit/s UDP traffic present

14. Modeling the Instantaneous Rate
1101 t0

15. Model Summary Queue integration: Instantaneous rates:
Round trip time = Prop. Delay + Queuing Delay:

16. Model Validation Step response, single source, single bottleneck
UDP cross traffic!

17. Analyzing the effect of cross traffic
LINEAR DISCRETE SYSTEM
POLE IN x_c/c
No cross traffic: Proportional response
Cross traffic: Smooth response

18. Analyzing the stepwise convergence

19. More Model Validation

20. Equilibrium Unique equilibrium Rates xn(t) non-unique
By solving a convex problem

21. Stability Single bottleneck locally stable from windows to queue
Rate (FFT)
Queue (FFT)
Single bottleneck locally stable from windows to queue
Not stable from windows to rates when flows’ RTT ratios are rational
Marginally stable from windows to rates when flows’ RTTs are multiples of each other
FFT of rate x_1 and queue
Upper: rational RTT ratios.
Lower non-rational RTT rations.
Captures burstiness rate phenomenon, sub-RTT dynamics.

22. Stability
Multilink networks may be unstable from windows to the queues!
RTT = 400 ms
Forward RTT = RTT/4 ms
Poles at j2/RTT -> frequency = 2/RTT=5 Hz

23. Approximations and Previous Work
Previous models appears as approximations of the integral
Numerical quadrature
Taylor approximations, Padé approximations
Low order models valid for small RTTs

24. Closing the Loop
FAST TCP
Queuing
Delay

25. Case study: FAST TcP Previous models: locally asymptotically stable
Proposed model: system destabilizes for
Heterogeneous RTTs
Rational RTT ratios
NS simulations and testbed experiments confirms predictions

26. Some remarks FAST TCP designed to be stable for all delays
Scale down gain inversely proportional to RTT
Feedback on the scale of other flows’ RTT
Need to scale down gain inversely proportional to other flows’ RTTs
Alternatively: attenuate the large delay feedback
Gain is dependent on sending rate
Punish large delay flows
TCP Reno: RTT biased resource allocation!!!
It exists stabilizing controllers using locally available information only (cancel the ACK-clocking)

27. Conclusions New accurate model of the ACK-clocking mechanism
Unstable for certain configurations!!!
Dynamics more complex than previously known
May have impact on existing (stability) results
Model validation is crucial
Equally fair window based congestion control problematic
Window based or rate based congestion control?

28. WindoW Based Congestion Control
Window size = 2
Window size = 1
1101
1101
SHOPPING CART ANALOGY
INPUT ONE WINDOW AMOUNT OF PACKETS PER RTT
DEFINE ROUND TRIP TIME

29. Outline Window Based Congestion Control Modeling Model Properties
Model Application
Conclusions