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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 - PowerPoint PPT Presentation
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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
6
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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
8
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.
11
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
13
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
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
– 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
20
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