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

2. 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 capacity Then: Average Delay = O(1/ε) Queueing Theory 101: Example: Bernoulli Arrivals and Service λ μ 1- λ μ - λ E{Delay} == O(1/ε) λ μ E{Delay} ε [Note: O(1/ε) tradeoff holds only for stochastic arrivals and/or channels]

3. ITMANET Nequ-IT –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 utility E{Delay} ε [ε = a positive parameter chosen as desired, Δ(Q(t)) = “Quadratic Lyapunov Drift”] utility –T/R

4. 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 utility E{Delay} ε utility –T/R

5. ITMANET Nequ-IT Stochastic Network Optimization Theory 101: max utility E{Delay} ε utility Is this the optimal delay 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

6. 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)

7. 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”:  M 2 : Hard to compute  M 1 : Easy to compute

8. 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”:  M 2 : Hard to compute  M 1 : Easy to compute M1M1 place-holder backlog M 1 Actual backlog under M 1

9. 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”:  M 2 : Hard to compute  M 1 : Easy to compute M2M2 place-holder backlog M 2

10. ITMANET Nequ-IT New Result 1: Magic Number M 1 [Neely, Asilomar, Dec. 08] Advantages of Magic Number M 1 :  Can be computed easily  Works for any MANET  Improves delay with no loss of utility!  30% Delay Savings in example Limitations:  Biggest M 1 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. Power Avg. Backlog w/o place-holders 1/ε (where 1/ε = V) with place-holders

11. ITMANET Nequ-IT New Result 1: Magic Number M 1 [Neely, Asilomar, Dec. 08] Advantages of Magic Number M 1 :  Can be computed easily  Works for any MANET  Improves delay with no loss of utility!  30% Delay Savings in example Limitations:  Biggest M 1 savings for min-penalty problems (e.g., energy minimization)  Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff Avg. Power Avg. Backlog w/o place-holders 1/ε (where 1/ε = V) with place-holders Example MANET: Uses diversity backpressure routing (DIVBAR)

12. ITMANET Nequ-IT New Result 1: Magic Number M 1 [Neely, Asilomar, Dec. 08] Advantages of Magic Number M 1 :  Can be computed easily  Works for any MANET  Improves delay with no loss of utility!  30% Delay Savings in example Limitations:  Biggest M 1 savings for min-penalty problems (e.g., energy minimization)  Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff Avg. Power Avg. Backlog w/o place-holders 1/ε (where 1/ε = V) with place-holders Example MANET: Uses diversity backpressure routing (DIVBAR)

13. ITMANET Nequ-IT New Result 1: Magic Number M 1 [Neely, Asilomar, Dec. 08] Advantages of Magic Number M 1 :  Can be computed easily  Works for any MANET  Improves delay with no loss of utility!  30% Delay Savings in example Limitations:  Biggest M 1 savings for min-penalty problems (e.g., energy minimization)  Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff Avg. Power Avg. Backlog w/o place-holders 1/ε (where 1/ε = V) with place-holders Example MANET: Uses diversity backpressure routing (DIVBAR)

14. ITMANET Nequ-IT New Result 1: Magic Number M 1 [Neely, Asilomar, Dec. 08] Advantages of Magic Number M 1 :  Can be computed easily  Works for any MANET  Improves delay with no loss of utility!  30% Delay Savings in example Limitations:  Biggest M 1 savings for min-penalty problems (e.g., energy minimization)  Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff Avg. Power Avg. Backlog w/o place-holders 1/ε (where 1/ε = V) with place-holders Example MANET: Uses diversity backpressure routing (DIVBAR)

15. ITMANET Nequ-IT New Result 1: Magic Number M 1 [Neely, Asilomar, Dec. 08] Advantages of Magic Number M 1 :  Can be computed easily  Works for any MANET  Improves delay with no loss of utility!  30% Delay Savings in example Limitations:  Biggest M 1 savings for min-penalty problems (e.g., energy minimization)  Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff Avg. Power Avg. Backlog w/o place-holders 1/ε (where 1/ε = V) with place-holders Example MANET: Uses diversity backpressure routing (DIVBAR)

16. ITMANET Nequ-IT New Result 1: Magic Number M 1 [Neely, Asilomar, Dec. 08] Advantages of Magic Number M 1 :  Can be computed easily  Works for any MANET  Improves delay with no loss of utility!  30% Delay Savings in example Limitations:  Biggest M 1 savings for min-penalty problems (e.g., energy minimization)  Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff Avg. Power Avg. Backlog w/o place-holders 1/ε (where 1/ε = V) with place-holders Example MANET: Uses diversity backpressure routing (DIVBAR)

17. ITMANET Nequ-IT New Result 1: Magic Number M 1 [Neely, Asilomar, Dec. 08] Advantages of Magic Number M 1 :  Can be computed easily  Works for any MANET  Improves delay with no loss of utility!  30% Delay Savings in example Limitations:  Biggest M 1 savings for min-penalty problems (e.g., energy minimization)  Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff Avg. Power Avg. Backlog w/o place-holders 1/ε (where 1/ε = V) with place-holders Example MANET: Uses diversity backpressure routing (DIVBAR)

18. ITMANET Nequ-IT New Result 1: Magic Number M 1 [Neely, Asilomar, Dec. 08] Advantages of Magic Number M 1 :  Can be computed easily  Works for any MANET  Improves delay with no loss of utility!  30% Delay Savings in example Limitations:  Biggest M 1 savings for min-penalty problems (e.g., energy minimization)  Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff Avg. Power Avg. Backlog w/o place-holders 1/ε (where 1/ε = V) with place-holders Example MANET: Uses diversity backpressure routing (DIVBAR)

19. ITMANET Nequ-IT New Result 1: Magic Number M 1 [Neely, Asilomar, Dec. 08] Advantages of Magic Number M 1 :  Can be computed easily  Works for any MANET  Improves delay with no loss of utility!  30% Delay Savings in example Limitations:  Biggest M 1 savings for min-penalty problems (e.g., energy minimization)  Only a constant factor delay reduction, still have [O(ε), Ο(1/ε)] tradeoff Avg. Power Avg. Backlog w/o place-holders 1/ε (where 1/ε = V) with place-holders Example MANET: Uses diversity backpressure routing (DIVBAR)

20. ITMANET Nequ-IT New Result 2: Magic Number M 2 [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) M2M2 Lagrange Multiplier

21. ITMANET Nequ-IT Advantages of Magic Number M 2 :  Dramatically improves delay. Backlog “rarely” falls below M 2  Achieves an improved delay tradeoff: [O(ε), O(log 2 [1/ε])] Within a log-factor of achieving the optimal log() delay tradeoff! Limitations:  Harder to compute M 2 (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 M 2. M2M2 New Result 2: Magic Number M 2 [Huang, Neely, WiOpt 2009] Lagrange Multiplier

22. 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

23. 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” M 2 algorithm without computing M 2 !! (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!