Finite-Horizon Energy Allocation and Routing
Scheme in Rechargeable Sensor Networks
Shengbo Chen, Prasun Sinha, Ness Shroff,
Changhee Joo
Electrical and Computer Engineering & Computer
Science and Engineering
Introduction
[Rechargeable sensor network]

Environment monitoring


Unattended Operability for long periods


Earthquake, structural, soil, glacial
Battery with renewable energy (like solar or wind)
Challenge: energy allocation


Sensor Network without replenishment: full battery is
desirable feature
Sensor Network with replenishment: no opportunity to
harvest energy
2
Introduction(cont’)
[Rechargeable sensor network]
r(t)
B(t)
B(t+1) e(t)
M
M: Battery size
B(t): Battery level at time slot t
e(t): allocated energy at time slot t
r(t): harvested energy at time slot t
B(t  1)  min max B(t )  e(t ),0  r (t ), M 
3
Motivation

Rate-power function  (e)



 (e)
Nondecreasing and strictly concave
Data transmission with spending units of energy
e
e
How to design e* (t )
T
max e
  (e(t ))
t 1
4
Motivation(cont’)

Example 1:


r(2)
r(1)=4, r(2)=2, r(3)=0
e*(1)=2, e*(2)=2, e*(3)=2
r(1)
Average replenishment rate is the
best because of Jensen’s inequality
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Motivation(cont’)

Example 2:

r(3)
r(1)=2, r(2)=0, r(3)=4
r(2)
r(1)
Average replenishment rate is infeasible
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Problem Statement


Sensor Network with renewal energy
Assumption


No interference from other nodes
Problem: throughput maximization
T
max  x s (t )
s
s.t.
t 1
Energy constraints
Routing constraints
s
x
where, (t ) is the amount of data from
source to the destination at time slot t
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Problem Statement (cont’)

Convex optimization problem


Joint energy allocation and routing
Complex due to the “time coupling property”

Concave rate-power function
8
Related Literatures

Finite horizon

A. Fu, E. Modiano and J. Tsitsiklis, 2003.


Dynamic programming
Infinite horizon

L. Lin, N. B. Shroff, and R. Srikant, 2007


M. Gatzianas, L. Georgiadis, and L. Tassiulas, 2010.


Asymptotically optimal competitive ratio
Maximize a function of the long-term rate per link
L. Huang, Neely

Asymptotically optimal
9
Three-step Approach



One node with full knowledge of replenishment
profile
One node with estimation of replenishment profile
Multiple-node network
10
Three-step Approach



One node with full knowledge of replenishment
profile
One node with estimation of replenishment profile
Multiple-node network
11
One node with full knowledge of
replenishment profile


Finite time horizon: T time slots
Assumption: replenishment profile is known
T
max e

  (e(t ))
t 1
Constraints:

Cumulative used no greater than cumulative harvested
E (t )  R (t )

Residual no greater than the battery size
R(t )  E (t )  M
12
Result 1
Shortest path S(t):
curve that connects
two points (0, 0) and
(T,K) in the domain D
with least Euclidean
length
K
Cumulative
Energy
R(t)
D
R(t)-M
T
time

Theorem 1: The energy allocation scheme s, satisfying
s(t) = S(t) − S(t − 1), is the optimal energy allocation
scheme
13
Three-step Approach



One node with full knowledge of replenishment
profile
One node with estimation of replenishment profile
Multiple-node network
14
One node with estimation of
replenishment profile

Assumption relaxed



Replenishment profile is unknown
Estimation replenishment rate rˆ(t )
Actual replenishment rate r (t )
(1  1 )rˆ(t )  r (t )  (1   2 )rˆ(t )
15
Online algorithm
1.
K
Cumulative
Energy
(1+β2)R(t)R(t)
2.
(1-β1)R(t)
time

Calculate e(t) from the
lower-bound of the
estimated replenishment
profile by the shortestpath solution
The allocated energy is
determined as e(t) = e(t)
+ r(t) − r(t)
T
Theorem 2: The throughput U of the online algorithm,
1 
achieves 1   fraction of the optimal throughput
1
2
16
Three-step Approach



One node with full knowledge of replenishment
profile
One node with estimation of replenishment profile
Multiple-node network
17
Heuristic scheme: NetOnline

Throughput maximization
T
max  x s (t )
s
s.t.
t 1
Energy constraints
Routing constraints

Decouple energy allocation and routing：


Energy allocation of each node follows the online
algorithm
Routing:
max  x s (t )
s
s.t.
Routing constraints
18
Result 3

Theorem 3: The heuristic scheme is optimal if all
nodes have the same replenishment profile and
perfect estimation.
19
Simulations
20
Simulations (cont’)
21
Simulations (cont’)

NRABP: Infinite-horizon based scheme in Gatzianas’s
paper
22
Future work



Considering interference in the model
Replenishment rate is known with some distribution,
what is the best strategy?
Infinite horizon but only finite period of estimation
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