ITMANET PI MeetingSeptember 2009

ITMANET Nequ-ITFocus Talk (PI Neely):

Reducing Delay in MANETS via Queue Engineering

ITMANET Nequ-IT

Slotted Queueing System Random Packet Arrivals rate λ (packets/slot) Random Service Opportunities rate μ (packets/slot)

If: ε = μ – λ = proximity to boundary of capacityThen: Average Delay = O(1/ε)

Queueing Theory 101:

Example: Bernoulli Arrivals and Service

λ μ

1- λμ - λE{Delay} = = O(1/ε)

λμE

{Del

ay}

ε

[Note: O(1/ε) tradeoff holds only for stochastic arrivals and/or channels]

ITMANET Nequ-IT

– T/R

– T/R

Random Packet Arrivals, Random Channels, MANET Unknown Traffic, Channel Probabilities, Mobility Model “Backpressure + Max-Weight + Flow Control” result from

greedy action to minimize “drift-plus-penalty” *[Neely 03, 06]:

*Minimize: Δ(Q(t)) + (1/ε)Ε{Penalty(t)|Q(t)}

Stochastic Network Optimization Theory 101:

max utilityE{D

elay

}

ε

[ε = a positive parameter chosen as desired, Δ(Q(t)) = “Quadratic Lyapunov Drift”]

utility– T/R– T/R

– T/R

– T/R– T/R

ITMANET Nequ-IT

Theorem [PI Neely: MIT thesis 2003, F&T text 2006]:Under the drift-plus-penalty algorithm with any desired ε>0:

Distance to Optimal Utility < O(ε)

Average end-to-end delay < O(1/ε)Holds for: General Performance Objectives (thruput, thruput-utility, energy) General Multi-Hop MANETS, Any size, General ergodic mobility

Stochastic Network Optimization Theory 101:

max utilityE{D

elay

}

ε

utility– T/R

– T/R

– T/R– T/R

– T/R

– T/R– T/R

ITMANET Nequ-IT

Stochastic Network Optimization Theory 101:

max utilityE{D

elay

}

ε

utility

Is this the optimaldelay tradeoff???

Theorem [PI Neely: MIT thesis 2003, F&T text 2006]:Under the drift-plus-penalty algorithm with any desired ε>0:

Distance to Optimal Utility < O(ε)

Average end-to-end delay < O(1/ε)Holds for: General Performance Objectives (thruput, thruput-utility, energy) General Multi-Hop MANETS, Any size, General ergodic mobility

– T/R– T/R

– T/R

– T/R

– T/R

– T/R– T/R

ITMANET Nequ-IT

Optimal Network Delay Tradeoff Theory:

O(1/ε) is NOT the optimal delay tradeoff!

Depending on the network situation, for single-hop nets, we know the optimal delay tradeoff is either: Square Root Law: Average Delay > Ω(sqrt[1/ε]) Logarithm Law: Average Delay > Ω(log[1/ε])

These Results were proven by Nequ-IT PIs: PI Berry [Information Theory 2002]

• Single Queue System with Energy Optimization• Known Traffic and Channel Statistics

PI Neely [JSAC 2006, Information Theory 2007]• Multi-Queue System with Energy or Thruput-Utility Optimization• Unknown Traffic and Channel Statistics• Different control technique. Holds in single-hop, limited multi-hop

(not as general as drift-plus-penalty)

ITMANET Nequ-IT

Re-Visit the Drift-Plus-Penalty Algorithm:

Drift-Plus-Penalty (Quadratic Lyapunov Algorithm): Disadvantages: Only gives the (sub-optimal) [O(ε), Ο(1/ε)] tradeoff Advantages: Works in more extensive (multi-hop, mobile) networks

Observations: Algorithm uses Queue Backlog to inform the stochastic optimization Queue Backlogs must go high to get good utility performance Information in Relative Magnitudes of Backlogs, and in the Oscillations

Idea: Use “Fake Backlog” to trick the optimizer!

Two “Magic Numbers”:

M2: Hard to compute

M1: Easy to compute

ITMANET Nequ-IT

Re-Visit the Drift-Plus-Penalty Algorithm:

Drift-Plus-Penalty (Quadratic Lyapunov Algorithm): Disadvantages: Only gives the (sub-optimal) [O(ε), Ο(1/ε)] tradeoff Advantages: Works in more extensive (multi-hop, mobile) networks

Observations: Algorithm uses Queue Backlog to inform the stochastic optimization Queue Backlogs must go high to get good utility performance Information in Relative Magnitudes of Backlogs, and in the Oscillations

Idea: Use “Fake Backlog” to trick the optimizer!

Two “Magic Numbers”:

M2: Hard to compute

M1: Easy to compute

M1 place-holder backlog M1

Actual backlog under M1

ITMANET Nequ-IT

Re-Visit the Drift-Plus-Penalty Algorithm:

Drift-Plus-Penalty (Quadratic Lyapunov Algorithm): Disadvantages: Only gives the (sub-optimal) [O(ε), Ο(1/ε)] tradeoff Advantages: Works in more extensive (multi-hop, mobile) networks

Observations: Algorithm uses Queue Backlog to inform the stochastic optimization Queue Backlogs must go high to get good utility performance Information in Relative Magnitudes of Backlogs, and in the Oscillations

Idea: Use “Fake Backlog” to trick the optimizer!

Two “Magic Numbers”:

M2: Hard to compute

M1: Easy to compute

M2

place-holder backlog M2

ITMANET Nequ-IT

New Result 1: Magic Number M1 [Neely, Asilomar, Dec. 08]

Advantages of Magic Number M1: Can be computed easily Works for any MANET Improves delay with no loss of utility! 30% Delay Savings in example

Limitations: Biggest M1 savings for min-penalty problems (e.g., energy minimization) Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff

Example MANET:

Uses diversity backpressure routing (DIVBAR)

Avg

. Pow

er

Avg

. Bac

klog

w/o place-holders

1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

with place-holders

ITMANET Nequ-IT

New Result 1: Magic Number M1 [Neely, Asilomar, Dec. 08]

Advantages of Magic Number M1: Can be computed easily Works for any MANET Improves delay with no loss of utility! 30% Delay Savings in example

Limitations: Biggest M1 savings for min-penalty problems (e.g., energy minimization) Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff

Avg

. Pow

er

Avg

. Bac

klog

w/o place-holders

1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

with place-holders

Example MANET:

Uses diversity backpressure routing (DIVBAR)

ITMANET Nequ-IT

New Result 1: Magic Number M1 [Neely, Asilomar, Dec. 08]

Advantages of Magic Number M1: Can be computed easily Works for any MANET Improves delay with no loss of utility! 30% Delay Savings in example

Limitations: Biggest M1 savings for min-penalty problems (e.g., energy minimization) Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff

Avg

. Pow

er

Avg

. Bac

klog

w/o place-holders

1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

with place-holders

Example MANET:

Uses diversity backpressure routing (DIVBAR)

ITMANET Nequ-IT

New Result 1: Magic Number M1 [Neely, Asilomar, Dec. 08]

Advantages of Magic Number M1: Can be computed easily Works for any MANET Improves delay with no loss of utility! 30% Delay Savings in example

Limitations: Biggest M1 savings for min-penalty problems (e.g., energy minimization) Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff

Avg

. Pow

er

Avg

. Bac

klog

w/o place-holders

1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

with place-holders

Example MANET:

Uses diversity backpressure routing (DIVBAR)

ITMANET Nequ-IT

New Result 1: Magic Number M1 [Neely, Asilomar, Dec. 08]

Advantages of Magic Number M1: Can be computed easily Works for any MANET Improves delay with no loss of utility! 30% Delay Savings in example

Limitations: Biggest M1 savings for min-penalty problems (e.g., energy minimization) Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff

Avg

. Pow

er

Avg

. Bac

klog

w/o place-holders

1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

with place-holders

Example MANET:

Uses diversity backpressure routing (DIVBAR)

ITMANET Nequ-IT

New Result 1: Magic Number M1 [Neely, Asilomar, Dec. 08]

Advantages of Magic Number M1: Can be computed easily Works for any MANET Improves delay with no loss of utility! 30% Delay Savings in example

Limitations: Biggest M1 savings for min-penalty problems (e.g., energy minimization) Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff

Avg

. Pow

er

Avg

. Bac

klog

w/o place-holders

1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

with place-holders

Example MANET:

Uses diversity backpressure routing (DIVBAR)

ITMANET Nequ-IT

New Result 1: Magic Number M1 [Neely, Asilomar, Dec. 08]

Advantages of Magic Number M1: Can be computed easily Works for any MANET Improves delay with no loss of utility! 30% Delay Savings in example

Limitations: Biggest M1 savings for min-penalty problems (e.g., energy minimization) Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff

Avg

. Pow

er

Avg

. Bac

klog

w/o place-holders

1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

with place-holders

Example MANET:

Uses diversity backpressure routing (DIVBAR)

ITMANET Nequ-IT

New Result 1: Magic Number M1 [Neely, Asilomar, Dec. 08]

Advantages of Magic Number M1: Can be computed easily Works for any MANET Improves delay with no loss of utility! 30% Delay Savings in example

Limitations: Biggest M1 savings for min-penalty problems (e.g., energy minimization) Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff

Avg

. Pow

er

Avg

. Bac

klog

w/o place-holders

1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

with place-holders

Example MANET:

Uses diversity backpressure routing (DIVBAR)

ITMANET Nequ-IT

New Result 1: Magic Number M1 [Neely, Asilomar, Dec. 08]

Advantages of Magic Number M1: Can be computed easily Works for any MANET Improves delay with no loss of utility! 30% Delay Savings in example

Limitations: Biggest M1 savings for min-penalty problems (e.g., energy minimization) Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff

Avg

. Pow

er

Avg

. Bac

klog

w/o place-holders

1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

with place-holders

Example MANET:

Uses diversity backpressure routing (DIVBAR)

ITMANET Nequ-IT

New Result 1: Magic Number M1 [Neely, Asilomar, Dec. 08]

Advantages of Magic Number M1: Can be computed easily Works for any MANET Improves delay with no loss of utility! 30% Delay Savings in example

Limitations: Biggest M1 savings for min-penalty problems (e.g., energy minimization) Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff

Avg

. Pow

er

Avg

. Bac

klog

w/o place-holders

1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

with place-holders

Example MANET:

Uses diversity backpressure routing (DIVBAR)

ITMANET Nequ-IT

New Result 2: Magic Number M2 [Huang, Neely, WiOpt 2009]

Result of Huang-Neely WiOpt 09: Steady state probability distribution for queue backlog decays

exponentially about a suitably defined “Lagrange Multiplier” of a corresponding non-stochastic problem.

Works for the drift-plus-penalty algorithm [Neely 2003, 2006] Significantly tightens the prior result on proximity to Lagrange

multiplier by Eryilmaz-Srikant 06 (they used a “fluid-limit” argument)

M2

Lagrange Multiplier

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Advantages of Magic Number M2: Dramatically improves delay. Backlog “rarely” falls below M2

Achieves an improved delay tradeoff: [O(ε), O(log2[1/ε])] Within a log-factor of achieving the optimal log() delay tradeoff!Limitations: Harder to compute M2 (ideally should know the “Lagrange Multiplier”) Works for single-hop and limited classes of multi-hop Must drop a small fraction of packets (O(ε)) to compensate when cross M2.

M2

New Result 2: Magic Number M2 [Huang, Neely, WiOpt 2009]

Lagrange Multiplier

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Concluding Remarks: Experimental Work at USC

This analysis also motivates and fundamentally explains recent USC experimental results showing dramatic delay improvement for backpressure by:

Moeller, Sridharan, Krishnamachari, Gnawali, “Backpressure Routing Made Practical,”

Submitted to Hotnets 09. See also tech report at: http://anrg.usc.edu/www/index.phpPublications_by_Year#techreport2009

Experimental Results next slide

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Concluding Remarks: Experimental Work at USC

• 40 Node Tiny OS2.x Multi-Hop Sensor Network

• Moeller et. al. develop 2 simplified implementations of “effective” M2 algorithm without computing M2!! (one answer: “Use Last-In-First-Out” )

• Dramatic Backpressure Delay Improvement (75-98%), for all but 1% of packets!

• 50% improvement in throughput compared to conventional shortest path algs!