1 / 43

Universal Scheduling for Networks with Arbitrary Traffic, Channels, and Mobility

This paper explores the design of "universal" scheduling algorithms that can work on general time-varying networks without knowledge of the future. It proposes a backpressure/max-weight algorithm that achieves utility close to an ideal algorithm with perfect future knowledge.

marcucci
Download Presentation

Universal Scheduling for Networks with Arbitrary Traffic, Channels, and Mobility

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Universal Scheduling for Networks with Arbitrary Traffic, Channels, and Mobility B Primary Path Alternate Paths Michael J. Neely, University of Southern California Proc. IEEE Conf. on Decision and Control (CDC), Atlanta, GA, Dec. 2010 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

  2. Want to optimally react to unexpected events. Example 1: Failure at Node B C A B D C A B D Primary Path Alternate Paths

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

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

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

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

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

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

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

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

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

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

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

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

  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). 4 Nodes: N = 8 5 8 1 2 3 7 6

  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). 4 Nodes: N = 8 Flows: M = 3 5 8 1 2 3 7 6

  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). 4 • Nodes: N = 8 • Flows: M = 3 • Flow 1: 13 5 1 8 1 2 3 7 6

  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). 4 • Nodes: N = 8 • Flows: M = 3 • Flow 1: 13 • Flow 2: 73 5 1 8 1 2 3 7 6 2

  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). 3 4 • Nodes: N = 8 • Flows: M = 3 • Flow 1: 13 • Flow 2: 73 • Flow 3: 56 5 1 8 1 2 3 7 6 2

  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). 3 4 • Nodes: N = 8 • Flows: M = 3 • Flow 1: 13 • Flow 2: 73 • Flow 3: 56 5 1 8 1 2 3 7 6 2

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

  25. State Information and Control Decisions: • A(t) = (A1(t), …, AM(t)) = New Arrivals. • X(t) = (X1(t), …, XM(t)) = Flow Control Decisions. • S(t) = “Topology State” observed on slot t. • (μij(c)(t)) = Transmission Decisions (in set Γ(S(t)) Node i Am(t)

  26. State Information and Control Decisions: • A(t) = (A1(t), …, AM(t)) = New Arrivals. • X(t) = (X1(t), …, XM(t)) = Flow Control Decisions. • S(t) = “Topology State” observed on slot t. • (μij(c)(t)) = Transmission Decisions (in set Γ(S(t)) Xm(t) Node i Am(t) Dropm(t)

  27. State Information and Control Decisions: • A(t) = (A1(t), …, AM(t)) = New Arrivals. • X(t) = (X1(t), …, XM(t)) = Flow Control Decisions. • S(t) = “Topology State” observed on slot t. • (μij(c)(t)) = Transmission Decisions (in set Γ(S(t)) Node j Xm(t) Node i Sij(t) Am(t) Dropm(t) Node k Sik(t)

  28. State Information and Control Decisions: • A(t) = (A1(t), …, AM(t)) = New Arrivals. • X(t) = (X1(t), …, XM(t)) = Flow Control Decisions. • S(t) = “Topology State” observed on slot t. • (μij(c)(t)) = Transmission Decisions (in set Γ(S(t)) Xm(t) Sij(t) Am(t) Dropm(t) Sik(t)

  29. Utility Maximization with T-Slot Lookahead: • φm(x) = concave utility function for flow m • Segment timeline into T-slot frames. • φopt[r] = optimal sum utility over frame r, • assuming future is known in frame! Frame 0 Frame 2 Frame 1 • Value of φopt[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 φopt[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) = ∑ [Qi(c)]2 • New sample path “T-slot” Lyapunov Drift: • ΔT(t) = L(Q(t+T)) – L(Q(t)) • Every slot “greedily” minimize drift-plus-penalty: • Δ1(t) + V xPenalty(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) Achieved Utility over RT slots ≥ (1/R)∑r=0φopt[r]– “Fudge Factor” R-1 BT + CV (i) “Fudge Factor” = V RT O(1/V), O(V) utility-backlog tradeoff when time horizon R infinity

  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 D1 S1 S2 Group 1 nodes: Random Walk on Upper Left Region

  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 D1 S1 S2 Group 2 nodes: Random Walk on Upper Right Region

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

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

  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 D1 S1 S2 Group 5 node: Periodically cycles about the clockwise orbit

  38. Example Mobile Network: Sim. 1– Change Social Contacts Backlog Bound for D1 in a sample RED node D1 S1 Backlog Bound for S1 in a sample RED node S2 • 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!

  39. Example Mobile Network: Sim. 1– Change Social Contacts Moving Average thruput:S2D1 D1 S1 Moving Average thruput:S2S1 S2 • 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!

  40. Example Mobile Network: Sim. 1– Change Social Contacts Moving Average thruput:S2D1 D1 S1 Moving Average thruput:S2S1 S2 • 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. Example Mobile Network: Sim. 2– Intermittent Jamming JAM! JAM! Time D1 S1 S2 • 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.

  42. Example Mobile Network: Sim. 2– Intermittent Jamming D1 JAM! S1 JAM! Time S2 • 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.

  43. Conclusion Slide: Backlog Bound for D1 in a sample RED node D1 S1 Backlog Bound for S1 in a sample RED node Moving Average Thruput of Source 2 S2 • 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)

More Related