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ITMANET PI Meeting September 2009

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)

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ITMANET PI Meeting September 2009

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  1. ITMANET Nequ-IT Focus Talk (PI Neely): Reducing Delay in MANETS via Queue Engineering ITMANET PI Meeting September 2009

  2. Queueing Theory 101: • Slotted Queueing System • Random Packet Arrivals rateλ (packets/slot) • Random Service Opportunities rate μ (packets/slot) If:ε = μ – λ = proximity to boundary of capacity Then: Average Delay = O(1/ε) [Note: O(1/ε) tradeoff holds only for stochastic arrivals and/or channels] Example: Bernoulli Arrivals and Service μ λ E{Delay} ε μ 1- λ E{Delay} = = O(1/ε) λ μ - λ

  3. Stochastic Network Optimization Theory 101: T/R T/R T/R T/R T/R 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)} [ε = a positive parameter chosen as desired, Δ(Q(t)) = “Quadratic Lyapunov Drift”] E{Delay} ε max utility utility

  4. Stochastic Network Optimization Theory 101: T/R T/R T/R T/R T/R T/R T/R 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 E{Delay} ε max utility utility

  5. Stochastic Network Optimization Theory 101: T/R T/R T/R T/R T/R T/R T/R 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 Is this the optimal delay tradeoff??? E{Delay} ε max utility utility

  6. 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 optimaldelay 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)

  7. 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

  8. 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 Actual backlog under M1 M1 place-holder backlog M1

  9. 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

  10. 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) w/o place-holders Avg. Power Avg. Backlog with place-holders 1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

  11. 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) w/o place-holders Avg. Power Avg. Backlog with place-holders 1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

  12. 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) w/o place-holders Avg. Power Avg. Backlog with place-holders 1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

  13. 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) w/o place-holders Avg. Power Avg. Backlog with place-holders 1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

  14. 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) w/o place-holders Avg. Power Avg. Backlog with place-holders 1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

  15. 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) w/o place-holders Avg. Power Avg. Backlog with place-holders 1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

  16. 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) w/o place-holders Avg. Power Avg. Backlog with place-holders 1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

  17. 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) w/o place-holders Avg. Power Avg. Backlog with place-holders 1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

  18. 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) w/o place-holders Avg. Power Avg. Backlog with place-holders 1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

  19. 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) w/o place-holders Avg. Power Avg. Backlog with place-holders 1/ε (where 1/ε = V) 1/ε (where 1/ε = V)

  20. New Result 2: Magic Number M2 [Huang, Neely, WiOpt 2009] Lagrange Multiplier M2 Result of Huang-Neely WiOpt 09: • Steady state probability distribution for queue backlog decays exponentiallyabout 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)

  21. New Result 2: Magic Number M2 [Huang, Neely, WiOpt 2009] Lagrange Multiplier M2 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.

  22. 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

  23. 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!

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