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ITMANET Nequ-IT. Focus Talk (PI Neely): Reducing Delay in MANETS via Queue Engineering. ITMANET PI Meeting September 2009. Queueing Theory 101:. Slotted Queueing System Random Packet Arrivals rate λ ( packets/slot ) Random Service Opportunities rate μ (packets/slot) - PowerPoint PPT Presentation
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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
ITMANET Nequ-IT
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
ITMANET Nequ-IT
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
ITMANET Nequ-IT
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!