Steady and Fair Rate Allocation for Rechargeable Sensors in Perpetual Sensor Networks Zizhan Zheng Authors: Kai-Wei Fan, Zizhan Zheng and Prasun Sinha Department of Computer Science & Engineering The Ohio State University

Agenda Motivation Centralized algorithm Distributed algorithm Evaluation Conclusion and future work 2

3 Perpetual Sensor Networks Renewable Energy Source –Solar, wind, vibration, etc. –Replenish rechargeable batteries Planning for renewable energy –Increase network lifetime –Optimize system performance Goals –Perpetual Data Collection Service –Steady and Fair Data Collection

4 Rate Assignment L={8.6, 8.6, 6.4, 6.4} L={5, 5, 5, 5} L={10, 10, 10, 10} Recharging Profiles

5 Lexicographic Rate Assignment Definition –A rate assignment L = {x 1, x 2, …, x n } is lexicographically optimal if x i can not be increased any further without reducing x j <= x i Approaches –Centralized Iteratively solving a maximization problem –Distributed Fixed, unsplittable flows Two-phase rate assignment

Given a network G=(V, E) : a recharging cycle is divided into slots : amount of energy collected by node i in time slot t : battery capacity of node i : initial battery level of node i : sensing, transmission, receiving energy consumption per packet Formulation - LP-Lex 6

7 LexRateAssignment Algorithm Given a network G=(V, E). Let A = V 1.Find the maximum common rate C for A 2.Find the maximum single rate of each node in A assuming other nodes’ rates are C 3.A c, = set of nodes whose maximum single rate is C 4.Remove A c from A 5.Repeat step 1 until A is empty

8 C A B D LexRateAssignment Algorithm Parameters –Π i : Battery Capacity –W i : Battery Level – : Recharging Rate Vector Constraints: –Flow Constraints –Energy Constraints

9 A B C D LexRateAssignment Algorithm Find Maximum Common Rate r Find Maximum Rate for each node assuming the rates of other nodes are 6 – Fix the rate of nodes whose rates are 6 Repeat the process for remaining nodes until rates of all nodes are fixed r=6 rr=14r=6 r r=9 r r r r r=14

10 Optimality of LexRateAssignment Lemma: The optimal lexicographic rate assignment is unique Theorem: LexRateAssignment computes the optimal lexicographic rate assignment.

11 C A B D Distributed Algorithm Assumptions: –Fixed Routes –Unsplittable Flows Parameters –Π i : Battery Capacity –W i : Battery Level – : Recharging Rate Vector Constraints: –Flow Constraints –Energy Constraints

12 DLEX Algorithm For each node i : –Initialization: 1.Compute maximum achievable rate locally 2.Send the maximum achievable rate to its parent node p –When Receiving a Rate: 1.Compute and update rates 2.Send updated rates to parent node p Sink notifies received rates to source nodes Theorem: DLEX converges and computes the optimal lexicographic rate assignment

13 A B C D Distributed Algorithm idr max r A3015 B1615 idr max r D66 idr max r B16 idr C max r C159 D66 idr max r C15 idr max r A308 B168 C98 D66 idr max r A30

14 Experiment Results Motelab: A network of 155 nodes Random topology Solar Energy Profiles –Field Experiments with Solar Panels –National Climatic Data Center Evaluated Algorithm –DLEX: Distributed algorithm –DLEX-A: Distributed algorithm without considering initial battery level –NAVG: Average recharging rate

15 Emulation Results In NAVG, over 30% of nodes run out of energy for over 50% of the time; throughput is close to zero for about 2.5 hours.

16 Experiment Results Key Observations –Bottlenecks are 1-hop nodes –Balanced tree performs better

17 Experiment Results - Overhead Nodes closer to root have higher overhead Running time varies from 50 to 244 seconds (depending on quality of selected links)

18 Conclusion and Future work Centralized Algorithm –Uniqueness of the optimal solution –Iteratively solving a maximization problem –Jointly solving routing and rate assignment problem Distributed Algorithm –Two-phase rate assignment –Asynchronous computation –Only for fixed route, unsplittable flows Future Work –Distributed algorithm for joint rate assignment and routing –Model link quality in the formulation

19 DLEX Algorithm Each node i maintains following –r j max : Maximum feasible rate for flow j at node i –r j : Assigned rate for flow j at node i –R : The set contains flow j if r j max < r –U : The set contains flow j if r j max > r Parameters –E i : Available energy for node i –e s : Energy consumption for sensing and transmitting –e f : Energy consumption for receiving and transmitting

20 DLEX Algorithm For each node i : 1.Compute maximum achievable rate locally 2.Send the maximum achievable rate to its parent node p 3.Update r i as when node i receives rate updates from children nodes 4.Update rate for each flow j: r j = r j max if j R r j = r i if j U 5.Send updated rates r i s to parent node p Sink notifies received rates to source nodes

21 Rate Computation BCD idr max r A30 B16 C9 D6 A Computation at node A