A Measurement-Based Algorithm to Maximize the Utility of Wireless - - PowerPoint PPT Presentation

A Measurement-Based Algorithm to Maximize the Utility of Wireless Networks

Julien Herzen

joint work with

Adel Aziz, Ruben Merz, Seva Shneer and Patrick Thiran September 19th, 2011

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Context

Inefficient situations in wireless LANs

• Example, performance anomaly:

GW 1 Mb/s 11 Mb/s UDP

1000 2000 3000 200 400 600 800 Time [s] Throughput [Kb/s] Flow at 1Mb/s Flow at 11Mb/s

TCP

1000 2000 3000 200 400 600 800 Time [s] Throughput [Kb/s] Flow at 1Mb/s Flow at 11Mb/s

• Intuition: Send slightly fewer packets at 1 Mb/s, so that the flow at

11 Mb/s can send many more

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Approach

GW 1 Mb/s 11 Mb/s

• Formalization: Capture the efficiency and the fairness of the network

using a utility function U =

• i

ui(xi), xi: throughput of flow i Examples Umax =

• i

xi Uprop =

• i

log xi

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Network Stack

• Backward compatibility → runs on top of IEEE 802.11
• Congestion control → throttle each flow
• One limiter per IP source in the network

GW i j k MAC Round Robin ρi

1

ρi

2

ρi

3

... ρi

F

queue 1 queue 2 queue 3 ... queue F IP

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How to throttle the flows?

• Find the rate allocation ρ that maximizes the utility U
• Problem: We do not know the feasible rate region!

◮ hard to predict or measure

rate of flow 1 rate of flow 2 U = µ1 U∗ U = µ2

• ptimum

?

U = log xi

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Decide at the gateway

The gateway knows

• The throughput achieved by the flows: x
• The current utility of the network: U(x) = ui(xi)
• If x = ρ, then ρ belongs to the rate region

Measure and Decide loop

• Measure each flow

GW i j k xi xj xk

• Decide

?

• Broadcast decision

GW i j k ρi ρj ρk

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Model

At time slot n:

• Measured throughput: x[n] ∈ RF

+

• Rate allocation vector: ρ[n] ∈ RF

+

• Last stable rate allocation: r[n] ∈ RF

+

• Utility function: U(x) =

i ui(xi)

rate of flow 1 rate of flow 2

L(µ)

• Level set: L(µ[n]) = {x[n] : U(x[n]) = µ[n], x[n] ∈ RF

+}

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Step 1 - Start from IEEE 802.11 allocation

• ρ[0] ← x[0]
• Current level set: L(U(x[0]))
• Remember allocation r[0] ← x[0]

rate of flow 1 rate of flow 2

L(µ[0])

• ptimum

x[0] = ρ[0] U = log xi

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Step 2 - Enhance phase

Time step n:

• If x[n − 1] = ρ[n − 1]:

◮ Obtain a new target utility µ[n] by

a full size gradient ascent

• Else:

◮ Obtain a new target utility µ[n] by

halving the size of the gradient ascent

• Go to Explore phase (next slide)

rate of flow 1 rate of flow 2

L(µ[n − 1]) L(µ[n])

• ptimum

attempt U = log xi

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Step 3 - Explore phase

• If x[n − 1] = ρ[n − 1]:

◮ Remember r[n] = ρ[n − 1] ◮ Go to Enhance phase

• Else:

◮ Keep target utility:

µ[n] = µ[n − 1]

◮ Pick ρ[n] randomly in L(µ[n]) ◮ Repeat explore phase at most N

times, then move to Enhance phase (and reduce the size of the gradient ascent)

rate of flow 1 rate of flow 2

L(µ[n])

• ptimum

attempt U = log xi

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Step 3 - Explore phase

• If x[n − 1] = ρ[n − 1]:

◮ Remember r[n] = ρ[n − 1] ◮ Go to Enhance phase

• Else:

◮ Keep target utility:

µ[n] = µ[n − 1]

◮ Pick ρ[n] randomly in L(µ[n]) ◮ Repeat explore phase at most N

times, then move to Enhance phase (and reduce the size of the gradient ascent)

rate of flow 1 rate of flow 2

L(µ[n]) L(µ[n − 1])

• ptimum

attempt U = log xi

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Step 3 - Explore phase

• If x[n − 1] = ρ[n − 1]:

◮ Remember r[n] = ρ[n − 1] ◮ Go to Enhance phase

• Else:

◮ Keep target utility:

µ[n] = µ[n − 1]

◮ Pick ρ[n] randomly in L(µ[n]) ◮ Repeat explore phase at most N

times, then move to Enhance phase (and reduce the size of the gradient ascent)

rate of flow 1 rate of flow 2

L(µ[n])

• ptimum

attempt U = log xi

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Step 3 - Explore phase

• If x[n − 1] = ρ[n − 1]:

◮ Remember r[n] = ρ[n − 1] ◮ Go to Enhance phase

• Else:

◮ Keep target utility:

µ[n] = µ[n − 1]

◮ Pick ρ[n] randomly in L(µ[n]) ◮ Repeat explore phase at most N

times, then move to Enhance phase (and reduce the size of the gradient ascent)

rate of flow 1 rate of flow 2

L(µ[n])

• ptimum

attempt

truncated Gaussian PDF for picking ρ1: u−1

1

(µ[n]) attempt

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Optimality result

Assumptions

• Fixed rate region Λ[n] = Λ
• Coordinate-convex rate region

◮ Much weaker than convexity!

Theorem The Enhance & Explore algorithm guarantees that, for any initial rate allocation r[0], the utility of the last stable rate allocation r[n] converges to the maximal utility for n → ∞.

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Practical implementation

• Based on Click[1] with MultiflowDispatcher[2]
• Creation of 4 new Click

elements

◮ MFQueue ◮ MFLeakyBucket ◮ EEadapter ◮ EEscheduler

• Evaluation with

◮ Asus routers ◮ ns-3

MAC Round Robin ρi

1

ρi

2

ρi

3

...

ρi

F

queue 1 queue 2 queue 3

...

queue F IP

GW

[1] Kohler et al., Transactions on Computer Systems, 2000 [2] Schi¨

• berg et al., SyClick, 2009

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Experimental results

• Deployment map:
• Without E&E:

UDP traffic

1000 2000 3000 200 400 600 800 Time [s] Throughput [Kb/s] Flow at 1Mb/s Flow at 11Mb/s

TCP traffic

1000 2000 3000 200 400 600 800 Time [s] Throughput [Kb/s] Flow at 1Mb/s Flow at 11Mb/s

• With E&E (Uprop):

1000 2000 3000 1 2 3 4 Time [s] Throughput [Mb/s] Flow at 1Mb/s Flow at 11Mb/s 1000 2000 3000 1 2 3 4 Time [s] Throughput [Mb/s] Flow at 1Mb/s Flow at 11Mb/s

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Experimental results

• Deployment map:
• Without E&E:

1000 2000 3000 0.5 1 1.5 2 Time [s] Throughput [Mb/s] Flow at 2Mb/s Flow at 5.5Mb/s Flow at 11Mb/s

• With E&E (Uprop):

1000 2000 3000 0.5 1 1.5 2 Time [s] Throughput [Mb/s] Flow at 2Mb/s Flow at 5.5Mb/s Flow at 11Mb/s

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Simulation results

ns-3 simulator

• Re-use of the same Click elements
• More controlled environment
• Possible estimation of the rate region
• Computation of optima

GW 1 Mb/s 11 Mb/s

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Simulation results

• Adaptivity to time-varying traffic
• Cyclic validation of last stable allocation r[n]

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Conclusion

Problem

• Inefficient and/or unfair situations in WLANs
• Capture efficiency and fairness using a utilility function

◮ The feasible rate region is unknown!

Solution

• Successive decisions and measurements by the GW
• Optimal for a fixed rate region
• When rate region changes, keeps adapting
• More details in [1], with an extension to multi-hop networks

Future work:

• Downlink traffic
• Rate adaptation

[1] Aziz et al., Mobicom 2011

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