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
Dynamic Internet
Internet
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Dynamic Internet
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Dynamic Internet
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Dynamic Internet
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TCP Congestion Control
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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
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Selfish Behavior (1)
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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!
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In this Paper…
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Introduction of models for dynamic changes of congestion.
•
Study of selfish (online) algorithms which maximize
throughput.
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Talk Overview
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Model
•
Multiplicative Dynamics
•
„Bursty Dynamics“
•
Open Research Questions and Conclusion
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Talk Overview
•
Model
•
Multiplicative Dynamics
•
„Bursty Dynamics“
•
Open Research Questions and Conclusion
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Model (1)
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We divide time into rounds t, for t = 1, 2, ….!
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The available bandwidth at time t is ut
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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!
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Model (2)
•
•
The optimization problem can be
formalized as follows!
rate
Sending rate too large,
no transmission at all!
Gain of optimal (offline algorithm) OPT:
ut
xt
•
t
Gain of online algorithm ALG:
Packets come through,
but opportunity costs!
Maybe harsh, but retransmissions,
timeouts, etc. is overhead!
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Model (3)
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Goal of the online algorithm is to send always at the rate of the available
bandwidth, or slightly lower!
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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!
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Talk Overview
•
Model
•
Multiplicative Dynamics
•
„Bursty Dynamics“
•
Open Research Questions and Conclusion
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Talk Overview
•
Model
•
Multiplicative Dynamics
•
„Bursty Dynamics“
•
Open Research Questions and Conclusion
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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
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Multiplicative Dynamics (2)
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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
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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,
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Talk Overview
•
Model
•
Multiplicative Dynamics
•
„Bursty Dynamics“
•
Open Research Questions and Conclusion
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Talk Overview
•
Model
•
Multiplicative Dynamics
•
„Bursty Dynamics“
•
Open Research Questions and Conclusion
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Bursty Dynamics (1)
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So far: Adversary can change congestion by at most a
constant factor in each round.
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There are many additional models for congestion dynamics,
waiting for efficient online algorithms!
•
One dynamics model studied on the network layer is
network calculus!
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Bursty Dynamics (2)
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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!
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Network Calculus (1)
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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!
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Network Calculus (2)
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Leaky-bucket arrival curve allows for bursts in the traffic, as
long as they are only temporal.
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After quite times with low rates, power can be accumulated
for another traffic burst.
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Dynamic Network Calculus Congestion
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We adopt these properties and allow our congestion
adversary to change the available bandwidth with bursts!
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The adversary can choose the new bandwidth as follows:
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Thereby,
Change in round t
Arrival curve: accumulate
during quiet times with few changes,
but at most factor B
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Results
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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
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Lower Bound: No online algorithm can achieve a
competitive ratio better than
against a Network Calculus adversary.
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Talk Overview
•
Model
•
Multiplicative Dynamics
•
„Bursty Dynamics“
•
Open Research Questions and Conclusion
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Talk Overview
•
Model
•
Multiplicative Dynamics
•
„Bursty Dynamics“
•
Open Research Questions and Conclusion
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Open Research Questions
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Selfish TCP: A real threat?
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Verification of model in practice!
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Fill gap between our upper and lower bound!
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Randomized algorithms (also for multiplicative adversary)
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Other arrival curves, study of different dynamics
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More generally: Adaption and analysis of network calculus
for other dynamic models! Limitations?
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Discussion
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Selfishness in congestion control
- Devise throughput maximizing protocols
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Network Calculus: An interesting model for dynamics!
- Lots of future research!
- However, challenging analysis!
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Transport layer: Algorithmically less understood than other
layers!
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Questions and Comments?
Thank you for your attention!
Stefan Schmid
Distributed Computing Group
schmiste@ethz.ch
http://dcg.ethz.ch/members/stefan.html
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