dynamic internet congestion with bursts

Dynamic Internet Congestion with Bursts

Stefan Schmid

Roger Wattenhofer

Distributed Computing Group, ETH Zurich

13th International Conference On High Performance Computing (HiPC)

Bangalore, India, December 2006

Stefan Schmid, ETH Zurich @ HiPC 2006 2

Dynamic Internet

Internet


Dynamic Internet


TCP Congestion Control

• The available bandwidth changes dynamically over time depending on the demands of other computers.

• In order to prevent collapses, hosts in the

Internet collaboratively reduce load in busy

times of high congestion!

• Successful strategy: TCP congestion control - Additive Increase, Muliplicative Decrease (AIMD)

- Indications for congestion: e.g., packet loss


Selfish Behavior (1)


Selfish Behavior (2)

• Some participants may not care about stability of Internet, but selfishly aim at maximizing own throughput!

• Given the dynamics of the available bandwidth, selfish throughput maximization constitutes an optimization problem!


In this Paper…

• Introduction of models for dynamic changes of congestion.

• Study of selfish (online) algorithms which maximize throughput.


Talk Overview

• Model

• Multiplicative Dynamics

• „Bursty Dynamics“

• Open Research Questions and Conclusion


Talk Overview

• Model





Model (1)

• We divide time into rounds t, for t = 1, 2, ….!

• The available bandwidth at time t is ut

• The selfish sender uses a sending rate xt at time t

• Selfish player does not know ut: All a sender knows is whether her sending in the last round was larger than the available bandwidth (i.e., xt>ut, hence congestion!), or not (binary feedback).

- If xt>ut packets are dropped by routers.

- Consequently, a selfish transfer protocol has to decide xt without knowing the present or future available bandwidth: framework for online algorithms!


Model (2)

• The optimization problem can be formalized as follows!

• Gain of optimal (offline algorithm) OPT:

• Gain of online algorithm ALG:

Maybe harsh, but retransmissions, timeouts, etc. is overhead!

t

rate

ut

xt

Packets come through,

but opportunity costs!

Sending rate too large,

no transmission at all!


Model (3)

• Goal of the online algorithm is to send always at the rate of the available bandwidth, or slightly lower!

• We are interested in minimizing the strict competitive ratio (worst-case!):

That is, the gain of ALG should be almost as large as the one of the optimal offline algorithm OPT!


Talk Overview

• Model





Multiplicative Dynamics (1)

• If ut can change arbitrarily over time, there is no competitive algorithm: ut can always be chosen slightly smaller than xt!

• However, assuming arbitrary changes may also be too pessimistic!

• Consequently, we want to restrict the dynamics.

• Model 1: Multiplicative dynamics changes max by a constant factor μ, i.e., an adversary (worst-case!) can choose the available bandwidth from the interval


Multiplicative Dynamics (2)

• Online Algorithm: After a round with sending rate lower or equal the available bandwidth, increase rate by a factor of μ, otherwise reduce sending rate by a factor μ3

• Analysis: - After a „bad“ round, there will always be a „good“ round due to the sharp cut of the sending rate.

- Good rounds are at most μ4-competitive.

- The gain of OPT in bad round is at most a factor μ larger than the gain of ALG in the preceding good round.

- Consequently,


Talk Overview

• Model





Bursty Dynamics (1)

• So far: Adversary can change congestion by at most a constant factor in each round.

• There are many additional models for congestion dynamics, waiting for efficient online algorithms!

• One dynamics model studied on the network layer is network calculus!


Bursty Dynamics (2)

• Network Calculus is used to analyse queuing strategies in networks from a worst-case perspective (worst-case queuing)!

• Network Caculus are not only interesting on the network layer, but may serve as a good dynamics model on the transport layer as well!

• In our paper, we propose to study Network Calculus models for congestion control!


Network Calculus (1)

• Traditional Network Calculus- Defines arrival curves (e.g., leaky-bucket arrival curve)- Traffic coming out of a router is assumed to adhere to arrival curve.- If this is the case, bounds for queue lengths and delays can be computed (with min-plus algebra).

Arrival curve:

max burst b and rate r

Total number of bits coming out of

router should never exceed arrival

curve attached at all points!


Network Calculus (2)

• Leaky-bucket arrival curve allows for bursts in the traffic, as long as they are only temporal.

• After quite times with low rates, power can be accumulated for another traffic burst.


Dynamic Network Calculus Congestion

• We adopt these properties and allow our congestion adversary to change the available bandwidth with bursts!

• The adversary can choose the new bandwidth as follows:

• Thereby,

Arrival curve: accumulate

during quiet times with few changes,

but at most factor B

Change in round t


Results

• Upper Bound: Online algorithm which cuts sending rate by half after bad rounds, and increases the rate by μ B1/3 yields a competitive ratio of

• Lower Bound: No online algorithm can achieve a competitive ratio better than

against a Network Calculus adversary.


Talk Overview

• Model





Open Research Questions

• Selfish TCP: A real threat?

• Verification of model in practice!

• Fill gap between our upper and lower bound!

• Randomized algorithms (also for multiplicative adversary)

• Other arrival curves, study of different dynamics

• More generally: Adaption and analysis of network calculus for other dynamic models! Limitations?


Discussion

• Selfishness in congestion control

- Devise throughput maximizing protocols

• Network Calculus: An interesting model for dynamics! - Lots of future research! - However, challenging analysis!

• Transport layer: Algorithmically less understood than other layers!


Questions and Comments?

Stefan SchmidDistributed Computing Group

[email protected]

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

Thank you for your attention!

dynamic internet congestion with bursts

Documents

future available bandwidth

dynamic changes of congestion

sending rate xt

dynamic internet congestion

gain of online algorithm

competitive algorithm

rate lower

optimal offline algorithm