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Sucha's Presentation at ECTI-CON 09

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The presentation was displayed at ECTI international conference 2009. The title is "Joint Flow Control, Routing, and Medium Access Control in Random Access Multi-Hop Wireless Networks with Time …

The presentation was displayed at ECTI international conference 2009. The title is "Joint Flow Control, Routing, and Medium Access Control in Random Access Multi-Hop Wireless Networks with Time Varying Link Capacities." http://tinyurl.com/q54bmc

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  • 1. Joint Flow Control, Routing and MAC in Random Access Multi-Hop Wireless Networks with Time Varying Link Capacities Sucha Supittayapornpong Poompat Saengudomlert International Conference on Electrical Engineering/Electronics, Computer, Telecommunications, and Information Technology (ECTI-CON) May 7, 2009 Telecommunications Field of Study Asian Institute of Technology, Thailand
  • 2. Introduction Traditional design and control multi-hop wireless networks: The decision is based on experiment and practice. Current research works toward cross-layer protocol design. There exists theoritcal research on cross-layer protocol design. Joint flow control and MAC in multi-hop wireless networks[Wang, 06] Joint flow control, routing and MAC in multi-hop wireless networks [Supittayapornpong, 08] Motivation: Theoretical approach to the protocol design for multi-hop wireless networks Distributive algorithm Achieve optimal performance (according to the model) More realistic with link capacity variation A step closer from theory to practice 2/15
  • 3. Outline Methods System model Network formulation Decomposition technique Distributive algorithm Simulation results Conclusion and contribution 3/15
  • 4. Methods 1. Create a considered network model as an optimization problem. Rigorous system and objective goal are defined. The best performance is known. (optimal solution and cost from centralized solver) 2. Decompose the optimization problem. The problem is devided by functionality to sub problems. Each sub problem is distributively solved. 3. Derive a distributive algorithm - To obtain mechnisms for control the network 4/15
  • 5. Model: Link Rate Network is a graph with sets, N and L, of active nodes and links. Varying link capacity (ideal) Cl (ωl , t) ∈ {11, 5.5, 2, 1} Mbps. All link capacities are independent. Slotted ALOHA Random acces MAC [Bertsekas, 95; Fang, 04] pl is transmission probability of link l. P (n) is transmission probability of node n. Successful transmission probability of link l is “ ” φl (p) = pl k∈I(l) 1 − P (k) where p = (pl : l ∈ L) Q where I(l) is a set of nodes interfering to link l. Link rate is Φl (Cl (ωl , t), p) = Cl (ωl , t)φl (p). 5/15
  • 6. Model: Networks A network has a set of source-destination (S-D) pairs S. Each S-D pair s ∈ S has predefined paths, F(s). Each path f ∈ F(s) has flow rate yf . S-D pair’s utility is its harmonic rate. [Supittayapornpong, 08] 2 |F(s)| , ys = (yf : f ∈ F(s)) χ(ys ) = −1 yf f ∈F (s) Fairness on S-D pair’s utility is proportional fairness. [Kelly, 98] Us = log [χ(ys )] Network utility (objective function) is Us s∈S 6/15
  • 7. Optimization Formulation Direct formulation is non-convex. - Transformed to a convex problem. [Supittayapornpong, 08] System is considered in long term (LT) [O’Neill, 08] - LT average link rate is T 1 limT →∞ T t=1 Φl (Cl (ωl , t), p) (System can’t wait.) Under stationary and ergodic assumptions - LT average link rate is Φl (E [Cl (ωl )] , p) - System does not have to wait but must know ensemble average. The resulting (convex) formulation: ˘ e−zf − log F : Maximize f ∈F (s) s∈S ez f ≤ log Φl (E [Cl (ωl )] , p) ∀l ∈ L Subject to log f ∈R(l) p ∈ P, zf ∈ R ∀f ∈ F - where P is the feasible set of p and F is a set of all flows. 7/15
  • 8. Vertical Decomposition The centralized problem is solved distributively. [Chiang, 07] Separable problem is considered. Vertical decomposition devides the problem to flow distribution (FD) and MAC problems. 8/15
  • 9. Horizontal Decomposition and Stochastic Approximation Each problem is solved distributively by horizontal decomposition. MAC problem: iP t(l) h [i] (p[i] ∂Q[i] (p[i] ) [i+1] [i] = pl + β [i] ∂Q ∂pl ) pl , where contains E [Cl (ωl )] ∂pl FD problem: «–+ » „ [j] [j+1] [j] zf ˆ = λl − γ [j] Φl (E [Cl (ωl )], p) − P λl e f ∈R(l) From stochastic approximation [Borkar, 00], E [Cl (ωl )] is obtained by sampling of channel in each iteration. 9/15
  • 10. Iterative Mechanisms MAC problem: P t(l) [i] [i] [i+1] [i] = pl + β [i] ∂Q ∂pl ) (p pl - Each update requires at most two-hop local information. 10/15
  • 11. Iterative Mechanisms MAC problem: P t(l) [i] [i] [i+1] [i] = pl + β [i] ∂Q ∂pl ) (p pl - Each update requires at most two-hop local information. 10/15
  • 12. Iterative Mechanisms MAC problem: P t(l) [i] [i] [i+1] [i] = pl + β [i] ∂Q ∂pl ) (p pl - Each update requires at most two-hop local information. 10/15
  • 13. Iterative Mechanisms MAC problem: P t(l) [i] [i] [i+1] [i] = pl + β [i] ∂Q ∂pl ) (p pl - Each update requires at most two-hop local information. 10/15
  • 14. Iterative Mechanisms MAC problem: P t(l) [i] [i] [i+1] [i] = pl + β [i] ∂Q ∂pl ) (p pl - Each update requires at most two-hop local information. FD problem: + [j] [j+1] [j] [j] ez f ˆ = λl − γ [j] Φl Cl (ωl ), p − λl f ∈R(l) - Each update requires local flow information (source’s flows). 10/15
  • 15. Iterative Mechanisms MAC problem: P t(l) [i] [i] [i+1] [i] = pl + β [i] ∂Q ∂pl ) (p pl - Each update requires at most two-hop local information. FD problem: + [j] [j+1] [j] [j] ez f ˆ = λl − γ [j] Φl Cl (ωl ), p − λl f ∈R(l) - Each update requires local flow information (source’s flows). 10/15
  • 16. Iterative Mechanisms MAC problem: P t(l) [i] [i] [i+1] [i] = pl + β [i] ∂Q ∂pl ) (p pl - Each update requires at most two-hop local information. FD problem: + [j] [j+1] [j] [j] ez f ˆ = λl − γ [j] Φl Cl (ωl ), p − λl f ∈R(l) - Each update requires local flow information (source’s flows). 10/15
  • 17. Iterative Mechanisms MAC problem: P t(l) [i] [i] [i+1] [i] = pl + β [i] ∂Q ∂pl ) (p pl - Each update requires at most two-hop local information. FD problem: + [j] [j+1] [j] [j] ez f ˆ = λl − γ [j] Φl Cl (ωl ), p − λl f ∈R(l) - Each update requires local flow information (source’s flows). 10/15
  • 18. Iterative Mechanisms MAC problem: P t(l) [i] [i] [i+1] [i] = pl + β [i] ∂Q ∂pl ) (p pl - Each update requires at most two-hop local information. FD problem: + [j] [j+1] [j] [j] ez f ˆ = λl − γ [j] Φl Cl (ωl ), p − λl f ∈R(l) - Each update requires local flow information (source’s flows). 10/15
  • 19. Iterative Mechanisms MAC problem: P t(l) [i] [i] [i+1] [i] = pl + β [i] ∂Q ∂pl ) (p pl - Each update requires at most two-hop local information. FD problem: + [j] [j+1] [j] [j] ez f ˆ = λl − γ [j] Φl Cl (ωl ), p − λl f ∈R(l) - Each update requires local flow information (source’s flows). 10/15
  • 20. Distributive Algorithm Joint Flow Control, Routing and MAC Algorithm Each link l ∈ L sets its initial values of pl and λl . 1: 2: MAC-loop (iteration index i) 3: Flow distribution-loop (iteration index j) Each s ∈ S computes new z[j] (s). ˆ 4: [j] Each l ∈ L samples current link capacity Cl . 5: [j+1] Each l ∈ L computes new price λl 6: . 7: Repeat 3 to 6 until λ converges. [i] Each l ∈ L samples current link capacity Cl . 8: [i+1] Each l ∈ L computes new pl 9: . 10: Repeat 2 to 9 until p converges. 11/15
  • 21. Distributive Algorithm Joint Flow Control, Routing and MAC Algorithm Each link l ∈ L sets its initial values of pl and λl . 1: 2: MAC-loop (iteration index i) 3: Flow distribution-loop (iteration index j) Each s ∈ S computes new z[j] (s). ˆ 4: [j] Each l ∈ L samples current link capacity Cl . 5: [j+1] Each l ∈ L computes new price λl 6: . 7: Repeat 3 to 6 until λ converges. [i] Each l ∈ L samples current link capacity Cl . 8: [i+1] Each l ∈ L computes new pl 9: . 10: Repeat 2 to 9 until p converges. 11/15
  • 22. Distributive Algorithm Joint Flow Control, Routing and MAC Algorithm Each link l ∈ L sets its initial values of pl and λl . 1: 2: MAC-loop (iteration index i) 3: Flow distribution-loop (iteration index j) Each s ∈ S computes new z[j] (s). ˆ 4: [j] Each l ∈ L samples current link capacity Cl . 5: [j+1] Each l ∈ L computes new price λl 6: . 7: Repeat 3 to 6 until λ converges. [i] Each l ∈ L samples current link capacity Cl . 8: [i+1] Each l ∈ L computes new pl 9: . 10: Repeat 2 to 9 until p converges. 11/15
  • 23. Distributive Algorithm Joint Flow Control, Routing and MAC Algorithm Each link l ∈ L sets its initial values of pl and λl . 1: 2: MAC-loop (iteration index i) 3: Flow distribution-loop (iteration index j) Each s ∈ S computes new z[j] (s). ˆ 4: [j] Each l ∈ L samples current link capacity Cl . 5: [j+1] Each l ∈ L computes new price λl 6: . 7: Repeat 3 to 6 until λ converges. [i] Each l ∈ L samples current link capacity Cl . 8: [i+1] Each l ∈ L computes new pl 9: . 10: Repeat 2 to 9 until p converges. 11/15
  • 24. Distributive Algorithm Joint Flow Control, Routing and MAC Algorithm Each link l ∈ L sets its initial values of pl and λl . 1: 2: MAC-loop (iteration index i) 3: Flow distribution-loop (iteration index j) Each s ∈ S computes new z[j] (s). ˆ 4: [j] Each l ∈ L samples current link capacity Cl . 5: [j+1] Each l ∈ L computes new price λl 6: . 7: Repeat 3 to 6 until λ converges. [i] Each l ∈ L samples current link capacity Cl . 8: [i+1] Each l ∈ L computes new pl 9: . 10: Repeat 2 to 9 until p converges. 11/15
  • 25. Distributive Algorithm Joint Flow Control, Routing and MAC Algorithm Each link l ∈ L sets its initial values of pl and λl . 1: 2: MAC-loop (iteration index i) 3: Flow distribution-loop (iteration index j) Each s ∈ S computes new z[j] (s). ˆ 4: [j] Each l ∈ L samples current link capacity Cl . 5: [j+1] Each l ∈ L computes new price λl 6: . 7: Repeat 3 to 6 until λ converges. [i] Each l ∈ L samples current link capacity Cl . 8: [i+1] Each l ∈ L computes new pl 9: . 10: Repeat 2 to 9 until p converges. 11/15
  • 26. Distributive Algorithm Joint Flow Control, Routing and MAC Algorithm Each link l ∈ L sets its initial values of pl and λl . 1: 2: MAC-loop (iteration index i) 3: Flow distribution-loop (iteration index j) Each s ∈ S computes new z[j] (s). ˆ 4: [j] Each l ∈ L samples current link capacity Cl . 5: [j+1] Each l ∈ L computes new price λl 6: . 7: Repeat 3 to 6 until λ converges. [i] Each l ∈ L samples current link capacity Cl . 8: [i+1] Each l ∈ L computes new pl 9: . 10: Repeat 2 to 9 until p converges. 11/15
  • 27. Distributive Algorithm Joint Flow Control, Routing and MAC Algorithm Each link l ∈ L sets its initial values of pl and λl . 1: 2: MAC-loop (iteration index i) 3: Flow distribution-loop (iteration index j) Each s ∈ S computes new z[j] (s). ˆ 4: [j] Each l ∈ L samples current link capacity Cl . 5: [j+1] Each l ∈ L computes new price λl 6: . 7: Repeat 3 to 6 until λ converges. [i] Each l ∈ L samples current link capacity Cl . 8: [i+1] Each l ∈ L computes new pl 9: . 10: Repeat 2 to 9 until p converges. 11/15
  • 28. Distributive Algorithm Joint Flow Control, Routing and MAC Algorithm Each link l ∈ L sets its initial values of pl and λl . 1: 2: MAC-loop (iteration index i) 3: Flow distribution-loop (iteration index j) Each s ∈ S computes new z[j] (s). ˆ 4: [j] Each l ∈ L samples current link capacity Cl . 5: [j+1] Each l ∈ L computes new price λl 6: . 7: Repeat 3 to 6 until λ converges. [i] Each l ∈ L samples current link capacity Cl . 8: [i+1] Each l ∈ L computes new pl 9: . 10: Repeat 2 to 9 until p converges. 11/15
  • 29. Distributive Algorithm Joint Flow Control, Routing and MAC Algorithm Each link l ∈ L sets its initial values of pl and λl . 1: 2: MAC-loop (iteration index i) 3: Flow distribution-loop (iteration index j) Each s ∈ S computes new z[j] (s). ˆ 4: [j] Each l ∈ L samples current link capacity Cl . 5: [j+1] Each l ∈ L computes new price λl 6: . 7: Repeat 3 to 6 until λ converges. [i] Each l ∈ L samples current link capacity Cl . 8: [i+1] Each l ∈ L computes new pl 9: . 10: Repeat 2 to 9 until p converges. 11/15
  • 30. Simulation Setup ˘ The convex problem, F, is solved by a centralized Octave solver. The simulation is impremented by Python. A four-state Markov chain is used to generate link capacity variation. Cl ∈ {11, 5.5, 2, 1} l∈L for all   0.85 0.05 0.05 0.05 0.25 0.25 0.25 0.25 [T ] =   0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 12/15
  • 31. Simulation Results: [1] Static link capacity Link transmission probabilities Flow rates 0.30 1.0 0.25 0.8 Rate (Mbps) Probability 0.20 0.6 0.15 (1, 2) 0.4 (2, 3) 0.10 [2, 3, 4] (1, 3) [2, 4] 0.2 (3, 4) 0.05 [1, 2, 4] (2, 4) [1, 3, 4] 0.000 0.00 500 1000 1500 2000 500 1000 1500 2000 MAC iteration index (i) MAC iteration index (i) S-D pair (N 1 : N 4) [N 1, N 2, N 4] → 0.74 Dynamic link capacity [N 1, N 3, N 4] → 0.67 Link transmission probabilities Moving average flow rates S-D pair (N 2 : N 4) [N 2, N 3, N 4] → 0.53 0.30 1.0 Moving average rate (Mbps) 0.25 [N 2, N 4] → 0.97 0.8 Probability 0.20 0.6 0.15 (1, 2) 0.4 (2, 3) 0.10 (2, 3, 4) (1, 3) (2, 4) 0.2 (3, 4) 0.05 (1, 2, 4) (2, 4) (1, 3, 4) 0.000 0.00 500 1000 1500 2000 500 1000 1500 2000 MAC iteration index (i) MAC iteration index (i) The network sustains an optimal solution regardless of the variation. 13/15
  • 32. Simulation Results: [2] Static link capacity (1, 2) Link transmission probabilities Flow rates 0.8 (6, 4) (3, 2) 0.7 0.20 (1, 3) 0.6 (6, 7) 0.15 (4, 5) 0.5 Rate (Mbps) Probability (3, 1) 0.4 (2, 1) [3, 2, 1] 0.10 (7, 5) [6, 7, 5, 3] 0.3 (4, 3) [3, 1] 0.2 (5, 3) [1, 3, 5] 0.05 (2, 4) [6, 4, 3] 0.1 (3, 5) [1, 2, 4, 5] S-D pair (N 1 : N 5) 0.000 0.00 2000 4000 6000 8000 10000 2000 4000 6000 8000 10000 MAC iteration index (i) MAC iteration index (i) [N 1, N 2, N 4, N 5] [N 1, N 3, N 5] Dynamic link capacity S-D pair (N 3 : N 1) (1, 2) Link transmission probabilities Moving average flow rates [N 3, N 1] 0.8 (6, 4) (3, 2) 0.7 0.20 [N 3, N 2, N 1] (1, 3) Moving average rate (Mbps) 0.6 (6, 7) 0.15 (4, 5) 0.5 S-D pair (N 6 : N 3) Probability (3, 1) 0.4 (2, 1) (3, 2, 1) [N 6, N 4, N 3] 0.10 (7, 5) (6, 7, 5, 3) 0.3 (4, 3) (3, 1) [N 6, N 7, N 5, N 3] 0.2 (3, 5) (1, 3, 5) 0.05 (2, 4) (6, 4, 3) 0.1 (5, 3) (1, 2, 4, 5) 0.000 0.00 2000 4000 6000 8000 10000 2000 4000 6000 8000 10000 MAC iteration index (i) MAC iteration index (i) The network sustains an optimal solution regardless of the variation. 14/15
  • 33. Conclusions and Contribution Conclusions We have theoretically designed the protocol for cross-layer flow control, routing and MAC networks - Link capacity variation - ALOHA random access MAC - Predefined routes - Flow control under harmonic rate function We have purposed the distributive algorithm for the system. - The algorithm works under the stationary and ergodic assumptions. - The network’s operation sustain an optimal solution regardless of the variation. Contribution We, first time, cooperate link capacity variation into the optimization decompostion framework. 15/15

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