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On Optimal Throughput-Energy Curve for Multi-hop Wireless Networks

On Optimal Throughput-Energy Curve for Multi-hop Wireless Networks. Yi Shi Virginia Tech, Dept. of ECE (with Canming Jiang, Thomas Hou , and Sastry Kompella ). IEEE INFOCOM 2011 – Shanghai, China. Throughput & Energy Consumption. Minimizing energy consumption!

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On Optimal Throughput-Energy Curve for Multi-hop Wireless Networks

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  1. On Optimal Throughput-Energy Curve forMulti-hop Wireless Networks Yi Shi Virginia Tech, Dept. of ECE (with CanmingJiang, Thomas Hou, and SastryKompella) IEEE INFOCOM 2011 – Shanghai, China

  2. Throughput & Energy Consumption Minimizing energy consumption! • Battery capacity is limited! • Limited improvement over the years Maximizing throughput! IEEE INFOCOM 2011 2

  3. A Dilemma • How to maximize the throughput and minimize the energy consumption simultaneously? • A multi-criteria optimization problem IEEE INFOCOM 2011 3

  4. Network Model Multi-hop wirelessnetworks with active user sessions Employing orthogonal channels Energy consumed at both the transmitter and receiver To save energy, a link may be on and off IEEE INFOCOM 2011 4

  5. Constraints Flow balance at each node Source node Relay node Destination node Achievable rate on link l: Flow rate constraint: IEEE INFOCOM 2011 5

  6. Our Objectives IEEE INFOCOM 2011 6 The network throughput utility U: The network energy consumption rate P: Conflicting Objectives: Maximizing U & Minimizing P

  7. Multi-criteria Formulation IEEE INFOCOM 2011 7

  8. Pareto Optimality • No single solution can optimize both objectives • So what solutions are we looking for? • Pareto-optimal points IEEE INFOCOM 2011 8

  9. How to Obtain Pareto-optimal Points? Each optimal solution to OPT(P) corresponds one Pareto-optimal point of MOPT. Each Pareto-optimal point of MOPT can be obtained by solving OPT(P) for a particular P. IEEE INFOCOM 2011 9

  10. Optimal Throughput-Energy Curve IEEE INFOCOM 2011 10 • Solve OPT(P) gives us U=f(P) for each P ∈ [0, Pmax] • Obtain an optimal throughput-energy curve U = f(P)

  11. Optimal Throughput-Energy Curve- Some Properties - • U = f(P) is a non-decreasing function • U = f(P) is a concave function • A saturation point on the optimal throughput-energy curve • U = f(P) is a strictly increasing function when P ≤ Ps • U = f(P) is flat when P > Ps IEEE INFOCOM 2011 11

  12. Case 1: Linear Throughput Function • Impractical to solve LP(P) for each P ∈ [0, Pmax] • Need to solve infinite number of LPs! • Parametric analysis on P • Only need to solve finite number of LPs IEEE INFOCOM 2011 12

  13. Parametric Analysis (PA) • PA: A technique to analyze the impact of a parameter on objective value • For LP(P), U = f(P) is piece-wise linear function • For any P, PA can determine the slop and length of the current segment IEEE INFOCOM 2011 13

  14. Obtain The Optimal Curve U . . . P • Starting from (0,0), find the next endpoint of each linear segment • Using PA to determine the slop and length of the current segment • Connecting the endpoints gives us the entire curve IEEE INFOCOM 2011 14

  15. Numerical Results Network topology IEEE INFOCOM 2011 15

  16. The Obtained Curve by PA Consider two scenarios: Equal weights and random weights IEEE INFOCOM 2011 16

  17. Case 2: Nonlinear Throughput Function • We consider the throughput function as h[r(m)] = ln[r(m)] • No method to compute the exact optimal throughput-energy curve efficiently • Propose a piece-wise linear approximation for this curve • Guaranteed to be (1 − )-optimal for each P IEEE INFOCOM 2011 17

  18. Piece-wise Linear Approximation U c a b P Connectpoints (P0,U0) and (Ps,Us) as the initial approximation Compute an error bound of this approximation If not good enough, identify a point (P*, U*) to improve the approximation Continue until the error bound is small enough on each segment IEEE INFOCOM 2011 18

  19. Determining Error Bound and Finding (P∗,U∗) This is a convex problem! IEEE INFOCOM 2011 19

  20. Numerical Results Network Topology A (1 − )-optimal throughput-energy curve. = 1%.

  21. Summary • Explored the relationship between two key performance metrics:network throughput and energy consumption • Casting the problem into a multi-criteria optimization • The solution to this problem: Optimal throughput-energy curve • Solved both linear and nonlinear throughput functions • Linear: Designed an exact algorithm based on PA • Nonlinear: Designed a (1 − 𝜖)-optimal approximation algorithm IEEE INFOCOM 2011 21

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