1 Time-scale Decomposition and Equivalent Rate Based Marking Yung Yi, Sanjay Shakkottai ECE Dept.,...
Transcript of 1 Time-scale Decomposition and Equivalent Rate Based Marking Yung Yi, Sanjay Shakkottai ECE Dept.,...
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Time-scale Decomposition and Equivalent Rate Based
Marking
Yung Yi, Sanjay Shakkottai
ECE Dept., UT Austin
{yi,shakkott}@ece.utexas.edu
Supratim Deb
LIDS, MIT
2Contents
Introduction Marking Based Congestion Control, Motivation
System Model and Problem Definition Source Update Model: Congestion Control Algorithm
Intuition and Results
Simulation Results
Summary
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Marking Based Congestion Control
Router reacts to the aggregate flow passing through it
Marks packets during congestion control Explicit Congestion Notification (ECN) [Floyd 94]
Active Queue Management (AQM) [Kelly 98, Kunniyur 01, Low 99, Towsley 00]
Users adapt their transmission rate
Congestion Control System Marking function at routers
Rate Adaptation algorithm at sources
marked packet unmarked packet
Source decreases rateSource increases rate
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How Do Routers Mark Packets?
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0total arrival rate
queue length
Rate Based Marking
Queue Based Marking
Markingprobability
Adjust its transmission rate depending on volume of marks received
marked packet unmarked packet
Source decreases rateSource increases rate
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How Can We Simulate the Internet? Pure Packet Model: Discrete Event
Simulation [ns2, pdns, parsec, ssfnet] Accurate transient behavior, but high complexity
State changes at discrete events (message generated, packet arrival, packet departure, etc.)
Computation: a sequence of event computations, processed in time stamp order
Most of complexity: Queueing Dynamics
Pure Fluid Model [Danzig 96, Towsley 00, 04, Hou 04, others] Fast and low complexity, but only steady state and
approximate results
Time-stepped evolution of system states
Good in parallel processing
slow,accurate,off-line
fast,approximate,
on-line
6Motivation
In reality, A significant number of uncontrolled flows (e.g. multimedia and web
mice)
Queue based marking (e.g., REM and RED) is popular in the real implementation cf) REM: Random Exponential Marking, RED: Random Early Detection
Question 1: Can queue dynamics be decoupled from user dynamics?
Question 2: What is the implication on the marking function? Is there an equivalent marking function which depends only on “instanta
neous” data transmission rate?
7Contents
Introduction Marking Based Congestion Control, Motivation
System Model and Problem Definition Source Update Model: Congestion Control Algorithm
Intuition and Results
Simulation Results
Summary
8System Model
n controlled flows, n uncontrolled flows
Controlled flows Differential equation based controller with queue based marking
Link Bandwidth: n c Capacity proportional to the number of flows
Small Buffer Regime
9Small Buffer Regime
Modeling of Buffer Size: nB or B ? Queue buffer scale linearly with the # of flows or not ?
Small Buffer Regime High Link speeds need high-speed buffer with high cost
Buffers need not scale with the link speed in order to achieve significant multiplexing gain [Cao & Ramanan 02] [Mandjes & Kim 01] [Mckeown 04]
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What Kind of Source Controller Model? [kelly 98, et el] Rate based Marking
Queue Based Marking
Uncontrolled rate
Controlled rate
: Utility function of i-th controlled flow
: TCP controller
: Proportional Fair Controller
Problem in this research: Finding given
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Optimization Framework [Kelly et el.]
c1 c2
x1
x2x3
Differential Equation Based
Distributed Congestion Control Algorithm
Resource Constraints in Wired Networks
12Contents
Introduction Marking Based Congestion Control, Motivation
System Model and Problem Definition Source Update Model: Congestion Control Algorithm
Intuition and Results
Simulation Results
Summary
13Intuition
large number of uncontrolled flows
(e.g., multimedia or web mice)
large amount of randomness
…….
Q length
1 round trip time
Controlled flows(e.g., TCP flows)
End-system controller influenced only through the (statistical) stationary queueing dynamics
Queue
Feedback (Ack)
large number of cycles,where queue becomes empty
Underlying Theory: Law of large numbers and Ergodic theorem
14Large System Limit
Unscaled system: n flows
Uncontrolled flows: Stationary point process aggregate arrival rate:
not necessarily a Poisson process
Limiting system M/D/1 queue with service rate:
n uncontrolled flows
(aggregate arrival rate = )
n
suitable scaling
Poisson( )
n controlled flows
(aggregate arrival rate = )
15Implications
Low complexity model for large system dynamics No queueing dynamics in the model
Simpler analysis and simulation
Asynchronous event simulation Synchronous time-stepped evolving simulation
n
suitable scaling
Queue BasedMarking Function
Rate BasedMarking Function
M/D/1 Queue
Cf) Discrete Time DomainS. Deb and R. Srikant. Rate-based versus Queue-based models of congestion control. ACM Sigmetrics, June 2004.
16Equivalent Rate Based Marking Equivalent Rate Based Marking Function
x: arrival rate of controlled flows
Lambda: arrival rate of uncontrolled flows
Depends only on the stationary distribution of an M/D/1 queue
17Sketch of Proof
18Example : REM [Low 99]
REM’s queue based marking function
Equivalent Marking Function (from P-K formula)
19Contents
Introduction Marking Based Congestion Control, Motivation
System Model and Problem Definition Source Update Model: Congestion Control Algorithm
Intuition and Results
Simulation Results
Summary
20Simulation Results (1)
Bottleneck bw: 100 x n pkts n = 100 ( n: # of controlled and uncontrolled flows )
TCP Sack, Proportional Fair Controller
REM, RED Queue based marking scheme
21Simulation Results (2)
Throughput
Distributionof CWND
22Summary In the Internet
Significant number of uncontrolled (short and unresponsive) flows
Queue based marking is popular
Randomness due to short and unresponsive flows in the Internet
sufficient to decouple the dynamics of the router queues from those of end controllers
We can find an equivalent rate based marking function given the queue based marking function
Easier analysis and simulation
We can apply nice mathematical tools to the analysis
Asynchronous event-driven simulation Synchronous fluid model based time-stepped evolving simulation leading to low simulation complexity
23References
Y. Yi, S. Deb, and S. Shakkottai, “Short Queue Behavior and Rate Based Marking,” Proceedings of the 38th CISS, Princeton University, NJ, March, 2004. A longer version has been submitted to IEEE/ACM Transactions on Networking
Cao and Ramanan, “A Poisson Limit for Buffer Overflow Probabilities,” Proc. IEEE Infocom, June, 2002.
Daley and Vere-Jones, “An Introduction to the Theory of Point Processes,” Springer-Verlag, 1988.
R. Srikant. "The Mathematics of Internet Congestion Control." Birkhauser, 2004.