1. Universal Scheduling for Networks with Arbitrary Traffic, Channels, and Mobility Michael J. Neely, University of Southern California Proc. IEEE Conf. on Decision and Control (CDC), Atlanta, GA, Dec. 2010 PDF of paper at: http://PDF of paper at: http://www-bcf.usc.edu/~mjneely/ Sponsored in part by the NSF Career CCF-0747525, ARL Network Science Collaborative Tech. Alliance B B Primary PathAlternate Paths

2. 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

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

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. 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 design “universal” scheduling algorithms that work on general time-varying networks? Can we optimize without knowing the future?

16. Main Results: We use a backpressure/max-weight algorithm that does not know future. Define a “T-Slot Lookahead” Utility as that obtained by an “ideal” algorithm 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 utility of the ideal T-slot Lookahead algorithm, with tradeoff in convergence time and queue backlog.

17. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N network nodes (possibly mobile). M Data Flows (each with source-destination). No pre-specified routes (we learn them).

18. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N network nodes (possibly mobile). 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

19. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N network nodes (possibly mobile). 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

20. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N network nodes (possibly mobile). 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

21. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N network nodes (possibly mobile). 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

22. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N network nodes (possibly mobile). 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

23. Problem Formulation: Timeslotted system, slots t = {0, 1, 2, …}. N network nodes (possibly mobile). 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. 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

25. A(t) = (A 1 (t), …, A M (t)) = New Arrivals. X(t) = (X 1 (t), …, X M (t)) = Flow Control Decisions. S(t) = “Topology State” observed on slot t. (μ ij (c) (t)) = Transmission Decisions (in set Γ(S(t)) State Information and Control Decisions: Node i A m (t)

26. A(t) = (A 1 (t), …, A M (t)) = New Arrivals. X(t) = (X 1 (t), …, X M (t)) = Flow Control Decisions. S(t) = “Topology State” observed on slot t. (μ ij (c) (t)) = Transmission Decisions (in set Γ(S(t)) State Information and Control Decisions: Node i A m (t) X m (t) Drop m (t)

27. A(t) = (A 1 (t), …, A M (t)) = New Arrivals. X(t) = (X 1 (t), …, X M (t)) = Flow Control Decisions. S(t) = “Topology State” observed on slot t. (μ ij (c) (t)) = Transmission Decisions (in set Γ(S(t)) State Information and Control Decisions: Node i A m (t) X m (t) Drop m (t) Node j Node k S ij (t) S ik (t)

28. A(t) = (A 1 (t), …, A M (t)) = New Arrivals. X(t) = (X 1 (t), …, X M (t)) = Flow Control Decisions. S(t) = “Topology State” observed on slot t. (μ ij (c) (t)) = Transmission Decisions (in set Γ(S(t)) State Information and Control Decisions: A m (t) X m (t) Drop m (t) S ij (t) S ik (t)

29. φ m (x) = concave utility function for flow m 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 A(t), S(t) known)…

30. Utility Maximization with T-Slot Lookahead: Frame r Value of φ opt [r] can be written as a non-linear program (assuming future A(t), S(t) known): Ω(t) = set of rates possible under S(t)

31. Analytical Approach: Lyapunov Function for queues: L(Q) = ∑ [Q i (c) ] 2 New sample path “T-slot” Lyapunov Drift: Δ T (t) = L(Q(t+T)) – L(Q(t)) Every slot “greedily” minimize drift-plus-penalty: Δ 1 (t) + V x Penalty(t), Penalty(t) = -φ(γ(t)) Results in a joint backpressure and flow control alg similar to those defined for ergodic systems in: [Neely, Modiano, Li -- INFOCOM 2005] [Georgiadis, Neely, Tassiulas -- F&T 2006]

32. Performance Result: Theorem: For any R>0, T>0: (ii) Worst Case Queue Backlog = O(V). B, C are known constants. V = “knob” to turn to affect the tradeoff R = Running Time (number of T-slot frames) V RT (i) “Fudge Factor” = BT + CV 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

33. 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

34. 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

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 3 nodes: Random Walk on Lower Right 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 4 nodes: Random Walk on Lower Left Region S1 S2 D1

37. 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

38. 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

39. 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

40. 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!

41. 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!

42. 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!

43. 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 )