Steady and Fair Rate Allocation for Rechargeable Sensors in Perpetual Sensor Networks

Steady and Fair Rate Allocation for Rechargeable Sensorsin Perpetual Sensor Networks

Zizhan ZhengAuthors: Kai-Wei Fan, Zizhan Zheng and Prasun

Sinha

Department of Computer Science & EngineeringThe 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

D

C

B

A SINK

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 = {x1, x2, …, xn} is lexicographically optimal if xi can not be increased any further without reducing xj <= xi

• 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

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LexRateAssignment Algorithm

• Given a network G=(V, E). Let A = V1. Find the maximum common rate C for A2. Find the maximum single rate of each node in

A assuming other nodes’ rates are C3. Ac, = set of nodes whose maximum single rate

is C4. Remove Ac from A

5. Repeat step 1 until A is empty

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C

A

B

D

LexRateAssignment Algorithm

• Parameters

– Πi : Battery Capacity

– Wi : Battery Level

– : Recharging Rate Vector

• Constraints:– Flow Constraints– Energy Constraints

DDD W ,,

BBB W ,,

CCC W ,,

AAA W ,,

i

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– <14, 14, 9, 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

r=6

r=6

rr=14r=6

r

r=6

r=9

r

r

r

r

r=14

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Optimality of LexRateAssignment

• Lemma: The optimal lexicographic rate assignment is unique

• Theorem: LexRateAssignment computes the optimal lexicographic rate assignment.

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C

A

B

D

Distributed Algorithm

• Assumptions:– Fixed Routes– Unsplittable Flows

• Parameters

– Πi : Battery Capacity

– Wi : Battery Level

– : Recharging Rate Vector

• Constraints:– Flow Constraints– Energy Constraints

DDD W ,,

BBB W ,,

CCC W ,,

AAA W ,,i

12

DLEX Algorithm

• For each node i :– Initialization:

1. Compute maximum achievable rate locally2. Send the maximum achievable rate to its

parent node p– When Receiving a Rate:

1. Compute and update rates2. Send updated rates to parent node p

• Sink notifies received rates to source nodes

• Theorem: DLEX converges and computes the optimal lexicographic rate assignment

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A

B

C

D

Distributed Algorithm

id rmax rA 30 15

B 16 15

id rmax rD 6 6

id rmax rB 16 16

id rCmax r

C 15 9

D 6 6

id rmax rC 15 15

id rmax rA 30 8

B 16 8

C 9 8

D 6 6

id rmax rA 30 30

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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

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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.

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Experiment Results

• Key Observations– Bottlenecks are 1-hop

nodes– Balanced tree performs

better

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Experiment Results - Overhead

• Nodes closer to root have higher overhead

• Running time varies from 50 to 244 seconds (depending on quality of selected links)

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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

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DLEX Algorithm

• Each node i maintains following

– rjmax : Maximum feasible rate for flow j at node i

– rj : Assigned rate for flow j at node i

– R : The set contains flow j if rjmax < r

– U : The set contains flow j if rjmax > r

• Parameters

– Ei: Available energy for node i

– es: Energy consumption for sensing and transmitting

– ef: Energy consumption for receiving and transmitting

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DLEX Algorithm

• For each node i :1. Compute maximum achievable rate locally2. Send the maximum achievable rate to its parent node p

3. Update ri as when node i

receives rate updates from children nodes4. Update rate for each flow j:

rj = rjmax if j R

rj = ri if j U

5. Send updated rates ris to parent node p

• Sink notifies received rates to source nodes

sf

Rj jfi

i eRne

reEr

|)|(

max

21

Rate Computation

B C D

9

15

30

6

15

id rmax rA 30

B 16

C 9

D 6

A

8

6

8

8

8

Computation at node A