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A TCP With Guaranteed Performance in Networks with Dynamic Congestion and Random Wireless Losses

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A TCP With Guaranteed Performance in Networks with Dynamic Congestion and Random Wireless Losses

Stefan Schmid, ETH Zurich

Roger Wattenhofer, ETH Zurich

DistributedComputing Group

2nd Annual International Wireless Internet Conference (WICON)

Boston, MA, USA, August 2006

ETH, Zurich

CERN, Geneva

Stefan Schmid, ETH Zurich @ WICON 2006

Lecture

E = mc2

ETH, Zurich

CERN, Geneva

TCP Connection

Stefan Schmid, ETH Zurich @ WICON 2006

Congestion

Losses

- Characteristics of transfer:
- Internet can be congested
- Available bandwidth changes over time
- Packets may be lost, especially on wireless link

Stefan Schmid, ETH Zurich @ WICON 2006

- TCP avoids congestion
- Congestion control lies at the heart of TCP
- Prevents congestion collapses of Internet (e.g., 1980)

How to prevent congestion?

- Senders reduce sending rate when Internet is congested
- senders maintain congestion window
- strategy: „additive-increase, multiplicative-decrease“ (AIMD)

Stefan Schmid, ETH Zurich @ WICON 2006

How does a sender know about congestion?

When packets are lost, TCP sender assumes that routers are overloaded!

For packets lost for other reasons than congestion,

throughput is reduced unnecessarily!

Stefan Schmid, ETH Zurich @ WICON 2006

Lecture

E = mc2

Wasted throughput: student may seek to increase her download bandwidth (selfishly)!

Stefan Schmid, ETH Zurich @ WICON 2006

- A model is presented which comprises both dynamic changes of the available bandwidth (dynamic congestion) and random packet losses (e.g., wireless links)
- Model allows for formal analysis of transfer protocol‘s performance!
- Thereby, a selfish perspective is assumed
- We look at protocols which aim at maximizing their throughput, regardless of consequences for other participants (no fairness).

Stefan Schmid, ETH Zurich @ WICON 2006

Basic Model

Extending the Model to Incorporate Bursts

TCP Wichita and Analysis

Simulation

Conclusion

Stefan Schmid, ETH Zurich @ WICON 2006

Basic Model

Extending the Model to Incorporate Bursts

TCP Wichita and Analysis

Simulation

Conclusion

Stefan Schmid, ETH Zurich @ WICON 2006

- Time is divided into synchronous rounds
- Framework of online algorithms:
- Adversary chooses available bandwidth ut
- Protocol chooses sending rate xt

- In addition, all packets are lost in a given round with probability p

Stefan Schmid, ETH Zurich @ WICON 2006

- Gain of transfer protocol ALG at time t:

- Gain of optimal (offline) transfer strategy OPT:

- We are interested in minimizing the (strict) competitive ratio, i.e., the gain of OPT divided by the gain of ALG.

Stefan Schmid, ETH Zurich @ WICON 2006

- Takes into account an opportunity cost
- Assumption: No packets are transmitted at all if rate too large
- Pessimistic, but losses engender overhead (e.g., time-outs)

Goal of ALG is to always send at (or slightly lower) rate

of currently available bandwidth. Thereby, ALG does

not know whether losses are due to

congestion or wireless links!

Stefan Schmid, ETH Zurich @ WICON 2006

- In practice, it can be assumed that congestion does not change too abruptly over time.
- Therefore, we bound the adversary ADV which chooses the available bandwidth as follows (multiplicative changes):
ut has to be chosen from [ut-1/μ, ut-1μ]

- A similar model but without random losses has been studied by Karp, Koutsoupias, Papadimitriou and Shenker (FOCS 2000)!

Stefan Schmid, ETH Zurich @ WICON 2006

- Transfer protocol achieving a provable performance:

- In order to compensate wireless losses, TCPW increases the bandwidth by a factor larger than μafter successful rounds (aggressive MIMD strategy).
- Strict competitive ratio: at most 4(μ2+ μ)

Stefan Schmid, ETH Zurich @ WICON 2006

Basic Model

Extending the Model to Incorporate Bursts

TCP Wichita and Analysis

Simulation

Conclusion

Stefan Schmid, ETH Zurich @ WICON 2006

Basic Model

Extending the Model to Incorporate Bursts

TCP Wichita and Analysis

Simulation

Conclusion

Stefan Schmid, ETH Zurich @ WICON 2006

- Network traffic is often bursty.
- Network calculus has introduced the notion of leaky-bucket arrival curves to study queuing theory from a worst-case perspective.
- Also a reasonable model for dynamics on transport layer!

leaky bucket arrival curve

Stefan Schmid, ETH Zurich @ WICON 2006

- Dynamics of ADV has to correspond to leaky-bucket constraints

- where

Adversary can accumulate power in some rounds to change available bandwidth more abruptly later!

Stefan Schmid, ETH Zurich @ WICON 2006

Basic Model

Extending the Model to Incorporate Bursts

TCP Wichita and Analysis

Simulation

Conclusion

Stefan Schmid, ETH Zurich @ WICON 2006

Basic Model

Extending the Model to Incorporate Bursts

TCP Wichita and Analysis

Simulation

Conclusion

Stefan Schmid, ETH Zurich @ WICON 2006

After successful transmissions, rate is increased by a factor of 2μ2.

Analysis: Look at cases x>u (fail) and x<u (pot. success) individually.

- xt>ut: Transmission rate compared to OPT can be described by Markov chain.
- Only in case of random errors, TCPW loses ground / reduces too much!

Stefan Schmid, ETH Zurich @ WICON 2006

- In rounds where xt>ut, TCPW has gain = 0!
- But: TCPW does not miss much gain!
- TCPW reduces its rate gemoetrically
- TCPW never overshoots much

The following result can be shown:

TCP Wichita is 4(μ+Bμ2)-competitive against a bursty adversary if μ<(1-p)/4Bp.

Stefan Schmid, ETH Zurich @ WICON 2006

Basic Model

Extending the Model to Incorporate Bursts

TCP Wichita and Analysis

Simulation

Conclusion

Stefan Schmid, ETH Zurich @ WICON 2006

Basic Model

Extending the Model to Incorporate Bursts

TCP Wichita and Analysis

Simulation

Conclusion

Stefan Schmid, ETH Zurich @ WICON 2006

- Random bandwidth changes with bursts
- Random changes smaller than μ, until enough is accumulated for burst

Stefan Schmid, ETH Zurich @ WICON 2006

Basic Model

Extending the Model to Incorporate Bursts

TCP Wichita and Analysis

Simulation

Conclusion

Stefan Schmid, ETH Zurich @ WICON 2006

Basic Model

Extending the Model to Incorporate Bursts

TCP Wichita and Analysis

Simulation

Conclusion

Stefan Schmid, ETH Zurich @ WICON 2006

- A framework which allows for formal protocol analysis and incorporates dynamic congestion and random losses
- We believe that there is still little algorithmic research on the transport layer!
- Network calculus may be a good model for dynamics in various settings!
- Selfish throughput maximization
- Really a threat? Experiences?
- Security: Routers often drop UDP packets first in case
of congestion! Cheating possible?

Stefan Schmid, ETH Zurich @ WICON 2006

- Open research questions:
- Better / tight bound for competitive ratio?
- Randomized online algorithms?
- Impact on stability in case of multiple flows?
- Model extensions: buffers, varying round trip times, etc.?
- Model verification & real implementation?

Stefan Schmid, ETH Zurich @ WICON 2006

Thank you for your attention!

Stefan Schmid

Distributed Computing Group

ETH Zurich, Switzerland

http://dcg.ethz.ch/members/stefan.html

Stefan Schmid, ETH Zurich @ WICON 2006