1. Multi-Hop Networking with Hard Delay Constraints Michael J. Neely, University of Southern California DARPA IT-MANET Presentation, January 2011 PDF of paper at: http://PDF of paper at: http://www-bcf.usc.edu/~mjneely/ B B Primary PathAlternate Paths

2. Non-Equilibrium Networking for MANETS Delay Guarantees Optimization of Throughput-Utility M. J. Neely, “Opportunistic Scheduling with Worst Case Delay Guarantees in Single and Multi-Hop Networks,” Proc. IEEE INFOCOM 2011. This work builds on: i) “Universal Scheduling” (Neely, Proc. IEEE CDC 2010) ARL CTA Task. Social Networks extensions: M. J. Neely, L. Golubchik, “Utility Optimization for Dynamic Peer-to-Peer Networks with Tit-for-Tat Constraints,” Proc. IEEE INFOCOM 2011. ii) “Hop Count Limited Networking” (IT-MANET, PI Shakkottai) L. Ying, S. Shakkottai, A. Reddy, “On Combining Shortest Path And Back-pressure Routing over Multihop Wireless Networks,” Proc. IEEE INFOCOM 2009. IT-MANET Topics:

3. A A B B D D C C A A B B D D C C Primary PathAlternate Paths Want to optimally react to unexpected events. Example 1: Failure at Node B

4. A A B B D D C C Primary Path Example 2: Opportunity via Mobility mobile node

5. A A B B D D C C Primary Path Example 2: Opportunity via Mobility mobile node

6. A A B B D D C C Primary Path Example 2: Opportunity via Mobility mobile node

7. A A B B D D C C Primary Path Example 2: Opportunity via Mobility mobile node

8. A A B B D D C C Primary Path Example 2: Opportunity via Mobility mobile node

9. A A B B D D C C Primary Path Example 2: Opportunity via Mobility mobile node

10. A A B B D D C C Primary Path Example 2: Opportunity via Mobility mobile node

11. A A B B D D C C Primary Path Example 2: Opportunity via Mobility mobile node

12. A A B B D D C C Primary Path Example 2: Opportunity via Mobility mobile node

13. A A B B D D C C Primary Path Example 2: Opportunity via Mobility mobile node

14. A A B B D D C C Primary Path Example 2: Opportunity via Mobility mobile node

15. A A B B D D C C Primary Path Example 2: Opportunity via Mobility mobile node

16. Assumptions and Main Questions: Assumptions: Arbitrary mobility, traffic, channels. Little or no probability models known in advance. Any sample path is possible (non-ergodic). Future is unknown. Questions: Can we develop math for non-equilibrium networks? Can we optimize without knowing the future? Can we make worst-case delay guarantees?

17. Main Results: We use a backpressure/max-weight algorithm that does not know future. Design a novel “ε-persistent service” virtual queue for delay guarantees. Use “T-Slot Lookahead Utility” defined by an “ideal” alg. that has perfect knowledge of the future up to T slots. For any T, our algorithm can achieve utility that is arbitrarily close to the T-slot Lookahead utility, with tradeoff in worst case delay.

18. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N node MANET. M data flows (each with source-destination). No pre-specified routes (we learn them).

19. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N node MANET. M data flows (each with source-destination). No pre-specified routes (we learn them). 1 1 4 4 5 5 6 6 7 7 2 2 3 3 8 8 Nodes: N = 8

20. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N node MANET. M data flows (each with source-destination). No pre-specified routes (we learn them). 1 1 4 4 5 5 6 6 7 7 2 2 3 3 8 8 Nodes: N = 8 Flows: M = 3

21. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N node MANET. M data flows (each with source-destination). No pre-specified routes (we learn them). 1 1 4 4 5 5 6 6 7 7 2 2 3 3 8 8 1 Nodes: N = 8 Flows: M = 3 Flow 1: 1  3

22. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N node MANET. M data flows (each with source-destination). No pre-specified routes (we learn them). 1 1 4 4 5 5 6 6 7 7 2 2 3 3 8 8 1 2 Nodes: N = 8 Flows: M = 3 Flow 1: 1  3 Flow 2: 7  3

23. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N node MANET. M data flows (each with source-destination). No pre-specified routes (we learn them). 1 1 4 4 5 5 6 6 7 7 2 2 3 3 8 8 1 2 3 Nodes: N = 8 Flows: M = 3 Flow 1: 1  3 Flow 2: 7  3 Flow 3: 5  6

24. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N node MANET. M data flows (each with source-destination). No pre-specified routes (we learn them). 1 1 4 4 5 5 6 6 7 7 2 2 3 3 8 8 1 2 3 Nodes: N = 8 Flows: M = 3 Flow 1: 1  3 Flow 2: 7  3 Flow 3: 5  6

25. S(t) = “Topology State” observed on slot t. (μ ij (c) (t)) = Transmission Decisions (in set Γ(S(t)) State Information and Network Decisions: S ij (t) S ik (t)

26. How to enforce delay guarantees? (1) Allow Packet Dropping at Source Flow Control: (2) Allow Packet Dropping at in-Network Queues: arrivals j (t) D j (t) μ j (t) Source node m Q j (t) A m (t) R m (t) Maximize: ∑ g m (r m – d m ) Subject to: Net. Stability Maximize: ∑ [g m (r m ) – ν m d m ] Subject to: Net. Stability r m = time avg admission rate of flow m d m = time avg packet drops of flow m This transformation separates out the variables, and is useful for distributed implementation.

27. How to enforce delay guarantees? (1) Allow Packet Dropping at Source Flow Control: (2) Allow Packet Dropping at in-Network Queues: arrivals j (t) D j (t) μ j (t) Source node m Q j (t) A m (t) R m (t) Maximize: ∑ g m (r m – d m ) Subject to: Net. Stability Maximize: ∑ [g m (γ m ) – ν m d m ] Subject to: r m ≥ γ m Net. Stability r m = time avg admission rate of flow m d m = time avg packet drops of flow m This transformation turns a maximization of a function of a time average into a maximization of a pure time average.

28. How to enforce delay guarantees? (3) Use New Virtual Queue for ε-Persistent Service: Theorem: If Q j (t) ≤ Q max, Z j (t) ≤ Z max, then: Worst Case Delay in Node j ≤ (Q max + Z max )/ε a(t) t Q(t) ≤ Q max t+MaxDelay arrivals j (t)μ j (t)+D j (t) Q j (t) Actual Queue: Virtual Queue: Z j (t) μ j (t)+D j (t)ε 1{Q j (t)>0}

29. Segment timeline into T-slot frames. φ opt [r] = optimal sum utility over frame r, assuming future is known in frame! Utility Maximization with T-Slot Lookahead: Frame 0 Frame 1 Frame 2 Value of φ opt [r] can be written as a non-linear program (assuming future arrivals, channels, and topology states are known)…

30. Analytical Approach: Lyapunov Function for queues: L(Q(t)) = ∑ [Q i (t) 2 +Z i (t) 2 + Y i (t) 2 ] New sample path “T-slot” Lyapunov Drift: Δ T (t) = L(Q(t+T)) – L(Q(t)) Every slot “greedily” minimize 1-slot drift-plus-penalty: Δ 1 (t) + V x Penalty(t), Penalty(t) = -φ(γ(t))+ν m D m (t) Results in a joint backpressure, flow control, packet dropping alg with modified backpressure weights: Q j (t) + Z j (t)1{Q j (t)>0}

31. Performance Result Theorem: Arbitrary Traffic, Mobility. For any R>0, T>0: (ii) Worst Case Queue Delay = B 3 V/ε B 1, Β 2, Β 3 are known constants. V = “knob” to turn to affect the tradeoff R = Running Time (number of T-slot frames) V RT (i) “Fudge Factor” = B 1 T + B 2 V O(1/V), O(V) utility-backlog tradeoff when time horizon R  infinity Achieved Utility over RT slots ≥ (1/R) ∑ r=0 φ opt [r] – “ Fudge Factor ” R-1

32. Conclusions: Arbitrary Traffic, Mobility (can be “non-ergodic”). New Math for “Non-Equilibrium” Networking. O(V), O(1/V) tradeoff between worst case queue delay and network utility. Easily extends to worst-case end-to-end delay via: (i) Restrict routing paths to H hops. (ii) Use PI Shakkottai result on H-hop limited Queueing. New Book Advertisement: M. J. Neely, Stochastic Network Optimization with Application to Communication and Queueing Systems. Morgan & Claypool, 2010. PDF available from “Synthesis Lecture Series” (on digital library), link on Neely homepage (for PDF and/or order form for hardcopy)

33. Extra Detail Slides: Network Transmission Model Some Simulations for “Universal Scheduling” in the presence of non-ergodic traffic and jamming.

34. Network Queueing: ab a Each node keeps queues for each separate commodity (“commodity” = “destination”). For commodity c (say, green commodity): Q a (c) (t+1) = Q a (c) (t) – Transmit out + Endogenous Arrivals + Exogenous Arrivals

35. Example Mobile Network: Five Mobility Groups: 10 nodes Group 1 (upper left) 10 nodes Group 2 (upper right) 10 nodes Group 3 (lower right) 10 nodes Group 4 (lower left) 1 node Group 5 Group 1 nodes: Random Walk on Upper Left Region S1 S2 D1

36. Example Mobile Network: Five Mobility Groups: 10 nodes Group 1 (upper left) 10 nodes Group 2 (upper right) 10 nodes Group 3 (lower right) 10 nodes Group 4 (lower left) 1 node Group 5 Group 2 nodes: Random Walk on Upper Right Region S1 S2 D1

37. Example Mobile Network: Five Mobility Groups: 10 nodes Group 1 (upper left) 10 nodes Group 2 (upper right) 10 nodes Group 3 (lower right) 10 nodes Group 4 (lower left) 1 node Group 5 Group 3 nodes: Random Walk on Lower Right Region S1 S2 D1

38. Example Mobile Network: Five Mobility Groups: 10 nodes Group 1 (upper left) 10 nodes Group 2 (upper right) 10 nodes Group 3 (lower right) 10 nodes Group 4 (lower left) 1 node Group 5 Group 4 nodes: Random Walk on Lower Left Region S1 S2 D1

39. Example Mobile Network: S1 S2 D1 Five Mobility Groups: 10 nodes Group 1 (upper left) 10 nodes Group 2 (upper right) 10 nodes Group 3 (lower right) 10 nodes Group 4 (lower left) 1 node Group 5 Group 5 node: Periodically cycles about the clockwise orbit

40. Social Contacts: Source 1: S1  D1 (constant rate = 0.07 packets/slot) Source 2: S2  S1 (for first half of simulation) S2  D1 (for second half of simulation) Goal: Maximize Throughput of Source 2 subject to stability Use V=10, so guarantee no more that 11 source 2 packets in any queue! S1 S2 D1 Backlog Bound for D1 in a sample RED node Backlog Bound for S1 in a sample RED node Example Mobile Network: Sim. 1– Change Social Contacts

41. Social Contacts: Source 1: S1  D1 (constant rate = 0.07 packets/slot) Source 2: S2  S1 (for first half of simulation) S2  D1 (for second half of simulation) Goal: Maximize Throughput of Source 2 subject to stability Use V=10, so guarantee no more that 11 source 2 packets in any queue! S1 S2 D1 Example Mobile Network: Sim. 1– Change Social Contacts Moving Average thruput:S2  D1 Moving Average thruput:S2  S1

42. S1 S2 D1 Example Mobile Network: Sim. 1– Change Social Contacts Moving Average thruput:S2  D1 Moving Average thruput:S2  S1 Overall Performance is Seamless: Backlog no more than 11 packets in any queue for Source 1 data Backlog no more than 15 packets in any queue for Source 2 data Overall Thruput of Source 2 is maintained at near-optimal over the change, even though the routes must fundamentally change!

43. S1 S2 D1 Example Mobile Network: Sim. 2– Intermittent Jamming Social Contacts: Source 1: S1  D1 (constant rate = 0.07 packets/slot) Source 2: S2  S1 (Goal to maximize its throughput) Intermittent Interference during 2 intervals of the simulation That completely cut interaction between the groups 1-4. Can only use the cyclic mobile node at these times! Max Thruput of Source 2 during interference ~= 0.03. Time JAM!

44. S1 S2 D1 Example Mobile Network: Sim. 2– Intermittent Jamming Social Contacts: Source 1: S1  D1 (constant rate = 0.07 packets/slot) Source 2: S2  S1 (Goal to maximize its throughput) Intermittent Interference during 2 intervals of the simulation That completely cut interaction between the groups 1-4. Can only use the cyclic mobile node at these times! Max Thruput of Source 2 during interference ~= 0.03. Time JAM!

45. S1 S2 D1 Conclusion Slide: Backlog Bound for D1 in a sample RED node Backlog Bound for S1 in a sample RED node Moving Average Thruput of Source 2 Overall Seamless Operation Throughput During Jamming goes down, but is close to optimal value of 0.03. Fudge Factor = BT/V + CV/RT Worst Case Queue Backlog = O(V) Framework useful for stock market trading! ( Thursday @ 10:20am )