Joint Energy Management and Resource Allocation in Rechargable Sensor Networks

Transcription

1 Jont Energy Management and Resource Allocaton n Rechargable Sensor Networks Ren-Shou Lu, Prasun Snha and C. Emre Koksal Department of CSE and ECE The Oho State Unversty

2 Envronmental Energy Harvestng Many technologes avalable for harvestng energy n dfferent forms, etc.

3 Energy Management - Dfferent Paradgm Classcal data Wth replenshment data P n = (t) P out transcever P =ρ (t) n P out (t) transcever B(t) B(t) sensor nfo sensor nfo lfetme: < purpose: max R lfetme utlty(t) dt lm T max 1 T utlty(t) dt undesrable: empty battery empty or full battery challenge: extend lfetme perpetual operaton wth varable P n R T Q: Energy management a straghtforward extenson or fundamentally dfferent? A: Close to the latter.

4 Network Utlty Maxmzaton r k f j f j j s P n =ρ ( t) (t) B node P out (t) Σj f j Σ j transcever f j +r sensor r max r,f j P log r P subject to j f j P j f j + r, s flow balance P n X λ (tx) j f j + X λ (rx) j f j +λ (sn) r energy conservaton j j {z } f Π fxed xmt and recv power achevable rate regon But P n s nether a constant nor perfectly known Battery s fnte

5 Dynamc Problem τ ρ (t) π ( e) π long term tme Opton E n Issue (1) ρ (t) complexty/convergence overhead (2) π long-term fnte battery extended (3) ˆπ(e) = 1 τ P eτ t=(e 1)τ+1 ˆρ (t) perods of dscharge fndng optmal tradeoff between overhead and dscharge probablty

6 Overhead and Dscharge Rate -5-1 Computed utlty QuckFx Standard dual-based algorthm Iteratons Too slow a convergence n general networks. Need to choose τ 1 Hgh battery dscharge rate Need to sacrfce performance for perpetual operaton Convergence: Assume/generate DAGs Dscharge rate: SnapIt

7 Resource Allocaton over DAGs w j : fracton of node traffc over lnk j z k (w): fracton of node traffc over node k z k (w) = w j w jk w j z k j k s rewrte problem n terms of z and w The structure of the DAG enables effcent solutons QuckFx Algorthm Dual decomposton subgradent-based dstrbuted soluton Effcent jont updates explotng DAG structure

8 QuckFx - Dual Decomposton Approach Notes: MWM scheduler: weght s a combned battery/data queue state

9 QuckFx - Dual Decomposton Approach Notes: Two phases of QuckFx teratons: 1. Aggregate prces: parents chldren, update r 2. Aggregate traffc: chldren parents, update prces

10 QuckFx - Dual Decomposton Approach Notes: -5-1 Computed utlty QuckFx Standard dual-based algorthm Iteratons

11 SnapIt - Localzed Energy Management π (e+1) π (e+2) Cumulatve energy msmatch: P e π ( e) e τ ( e+1)τ ( e+2)τ h Peτ tme t=(e 1)τ+1 ρ (t) ˆπ (e) Issue - fnte battery sze causes: Unbased estmator battery drft hgh dscharge rate Based estmator very hgh dscharge rate or neffcent replenshment Soluton: Adaptvely control drft

12 SnapIt - Localzed Energy Management B(t) M/2 r δ B(t) > M/2 r + δ δ M M/2 B (t) δ u u u d utlty δ r* δ r Q1: What performance s lost due to r δ? Q2: How much s dscharge probablty reduced wth δ drft? Theorem: If the varance, σ 2 ρ var 1 Pτ Q τ Q t=1 ρ (t) s bounded and the utlty functon s the log functon, U( ) = log( ), then, gven any β 1, SnapIt acheves p SnapIt and Ū Ū SnapIt log M = Θ M wth the choce of δ = βσ2 ρ log M λ (sn) M. Optmal utlty & low dscharge rate possble smultaneously. (M ) = O(M β )

13 Smulatons - Parameters A 67-node testbed wth topology created based on an actual local testbed Rechargng profles based on real solar radaton measurements from NREL λ (sn) = 15µW, λ (tx) = 63µW, λ (rx) = 69µW, α =.1, δ =.1r τ = 1 hour and 1 teraton every 5 mnutes

14 Smulatons - Sum Rate and Network Utlty Sum rate Network utlty Cumulatve full/empty tme Intal battery - hgh Sum of data rates at snk [pkt/s] QuckFx w/o SnapIt QUckFx w/ SnapIt Instantaneous opt 6: 1: 14: 18: Tme Network utlty QuckFx w/o SnapIt QuckFx w/ SnapIt Instantaneous opt -3 6: 1: 14: 18: Tme Cumulatve battery full tme [s] Node 1 w/o SnapIt Node 1 w/ SnapIt Node 2 w/o SnapIt Node 2 w/ SnapIt 6: 1: 14: 18: Tme Intal battery - low Sum of data rates at snk [pkt/s] QuckFx w/o SnapIt QUckFx w/ SnapIt Instantaneous opt 6: 1: 14: 18: Tme Network utlty QuckFx w/o SnapIt QUckFx w/ SnapIt Instantaneous opt -3 6: 1: 14: 18: Tme Cumulatve down tme [s] Node 1 w/o SnapIt Node 1 w/ SnapIt Node 2 w/o SnapIt Node 2 w/ SnapIt 6: 1: 14: 18: Tme

15 Smulatons - Sunny/Cloudy Day vs. IFRC Sum rate Network utlty Sunny day Sum of data rates at snk QuckFx w/ SnapIt IFRC Network utlty QuckFx w/ SnapIt IFRC 6: 1: 14: 18: Tme -4 6: 1: 14: 18: Tme Cloudy day Sum of data rates at snk QuckFx w/ SnapIt IFRC Network utlty QuckFx w/ SnapIt IFRC 6: 1: 14: 18: Tme -4 6: 1: 14: 18: Tme

16 Summary and Future Work QuckFx + SnapIt to acheve optmal network utlty Addressed convergence ssue assocated wth varable replenshment Addressed (fnte) battery dscharge rate due to varable replenshment Can we mprove the convergence ssue wthout the DAG assumpton/constructon? Can we combne battery control wth data queue control to acheve low dscharge and data buffer overflow rates?