SLIDE 1 Optimal Utility-Lifetime Trade-off in Self-regulating Wireless Sensor Networks: A Distributed Approach
Hithesh Nama, WINLAB, Rutgers University
- Dr. Narayan Mandayam, WINLAB, Rutgers University
Joint work with
- Dr. Mung Chiang, Princeton University
WINLAB RESEARCH REVIEW May 15, 2006
IAB Meeting: May 15, 2006 – p. 1
SLIDE 2
Overview
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SLIDE 3
Motivation: Sensors over Information Fields
Energy-limited sensors collect data and deliver to a sink
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SLIDE 4
Motivation: Routing and Power control
Route with many short hops Low transmit power per hop
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SLIDE 5
Motivation: Routing and Power control
Route with fewer but longer hops Higher transmit power per hop
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SLIDE 6
Motivation: Application Performance
Less data from sensors ⇒ Coarse resolution
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SLIDE 7
Motivation: Application Performance
More data from sensors ⇒ Fine resolution But more data ⇒ more energy dissipation in sensors
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SLIDE 8 In short ...
- Energy-efficient designs should address all layers of
protocol stack
- Application performance or Network Utility increases with
amount of gathered data
- Network Lifetime decreases with amount of gathered data
- Network Utility vs. Network Lifetime: An inherent trade-off
IAB Meeting: May 15, 2006 – p. 8
SLIDE 9
Objective #1:
Characterize optimal Utility vs Lifetime trade-off through efficient cross-layer design
50 100 150 200 10 11 12 13 14 15 16 17 18 19 Network Lifetime (in s) Network Utility in bps (log10 scale)
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SLIDE 10
Objective #2:
Design distributed algorithms to achieve any desired trade-off
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SLIDE 11 System Model: The Network - I
- Network modeled as a directed graph G(V, L)
- V = N D; N - Set of sources; D - Set of
sinks/destinations
- L - Set of arcs/links
- O(n) - Set of outgoing links of node n
O(n2) = l2, l3
- I(n) - Set of incoming links of node n
I(n2) = l1, l4
- Nn - Set of one-hop neighbors of node n
IAB Meeting: May 15, 2006 – p. 11
SLIDE 12 System Model: The Network - II
- Self-regulating network ⇒ source rates are adaptive
- Sources route data to sinks possibly over multiple hops
- Any two links with a common node cannot be
simultaneously scheduled E.g., {l1, l4} - NO but {l1, l6} - YES
- Link-transmissions are orthogonal i.e., no interference
E.g., DSSS/FHSS systems with orthogonal sequences
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SLIDE 13 System Model: Routing and Source Rate Control
- Multi-commodity flow model
- Non-negative source rates {rd
n} and flows {fd l }
- Flow conservation constraint:
- l∈O(n)
fd
l −
fd
l = rd n, d ∈ D, n ∈ N
- Total flow through link l
fl =
fd
l
IAB Meeting: May 15, 2006 – p. 13
SLIDE 14 System Model: Radio Resource Allocation - I
- Feasible mode of operation consists of independent set of
links E.g., {}, {l1}, ..., {l6}, {l1, l5}, {l1, l6}, {l2, l5}, {l2, l6}
- A feasible schedule corresponds to time-fractions τm of
each feasible mode m
- m τm = 1
- Average Tx power of link l in mode m - P m
l
- Link Tx power constraint: P m
l
≤ P max
l
IAB Meeting: May 15, 2006 – p. 14
SLIDE 15 System Model: Radio Resource Allocation - II
- We assume schedule is fixed ⇒ {τm} are constants
- τl - Total fraction of time link l is in operation
- Capacity of link l with power Pl
Cl(Pl) = W log2(1 + PlKd−α
l
N0W )
- Link capacity constraint:
fl ≤ τlCl(Pl, W), l ∈ L
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SLIDE 16 Network Utility Maximization - I
- Application performance depends on the amount of data
gathered
n(rd n) - Increasing and strictly concave function of rd n, e.g.,
log(rd
n)
- Network utility is sum of node utilities
- Network utility maximization:
max
{rd
n,f d l ,Pl}≥0
Ud
n(rd n)
subject to Flow conservation constraint, Link capacity constraint, & Link Tx power constraint.
IAB Meeting: May 15, 2006 – p. 16
SLIDE 17 Network Utility Maximization - II
- Convex optimization problem with a unique set of source
rates
- Useful formulation in broadband ad hoc wireless networks
- But sensors are energy-constrained
- Network utility maximization does not factor in power
dissipation at nodes
- Can lead to widely varying power dissipation levels
- Potentially results in a disconnected network
IAB Meeting: May 15, 2006 – p. 17
SLIDE 18 Power Dissipation Model
- Etx - Energy dissipated per bit in transmitter electronics
- Erx - Energy dissipated per bit in receiver electronics
- Es - Energy dissipated per bit in sensing
- Average power dissipated in a node n
P avg
n
=
{τlPl + flEtx} +
flErx +
rd
nEs
- fl - Total flow through link l
- Pl - Average Tx power of link l
- rd
n - Source rate of node n towards destination d
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SLIDE 19 Network Lifetime Maximization
- En - Initial energy of node n
- Lifetime of node n, tn = En/P avg
n
- Network lifetime, tnwk = minn∈N tn, i.e., time until death of
first node
- Node power dissipation constraint:
P avg
n
= En/tn ≤ En/tnwk = Ens, n ∈ N
- Network lifetime maximization:
min
{s,rd
n,f d l ,Pl}≥0 s
subject to Flow conservation constraint, Link capacity constraint, Link Tx power constraint, & Node power dissipation constraint.
IAB Meeting: May 15, 2006 – p. 19
SLIDE 20 Utility-Lifetime Trade-off - I
- Vector objective function in 2D - [utility, inverse-lifetime]
0.5 1 1.5 2 2 4 6 8 10 12 14 16 18 20 Inverse Network Lifetime (in s−1) Network Utility in bps (log10 scale)
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SLIDE 21 Utility-Lifetime Trade-off - II
- Choose γ ∈ (0, 1) and ‘scalarize’ to obtain Pareto-optimal
points max
{s,rd
n,f d l ,Pl}≥0 γ
Ud
n(rd n) − (1 − γ)s
subject to
fd
l −
fd
l = rd n, d ∈ D, n ∈ N
fd
l ≤ τlCl(Pl, W), l ∈ L
Pl ≤ P max
l
, l ∈ L
τlPl +
flEtx +
flErx +
rd
nEs ≤ Ens, n ∈ N
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SLIDE 22
Numerical Illustration - Utility vs. Lifetime
50 100 150 200 10 11 12 13 14 15 16 17 18 19 Network Lifetime (in s) Network Utility in bps (log10 scale)
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SLIDE 23
Numerical Illustration - Source rate vs. Lifetime
50 100 150 200 3 3.5 4 4.5 5 5.5 6 6.5 Network Lifetime (in s) Node source rate in bps (log10 scale) node n1 node n2 node n3
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SLIDE 24 Towards a distributed implementation
- “Layering” as “optimization decomposition” approach:
Network protocols as distributed solutions to some global optimization problems Each protocol layer corresponds to a separate sub-problem Distributed implementation of each sub-problem
- Alternate formulation of the joint optimization problem
Enables recovery of primal solutions Alternate formulation of the lifetime maximization problem Add a regularization term involving flows in the
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SLIDE 25 Joint Utility-Lifetime Maximization: Primal Problem
max
{sn,rd
n,f d l ,Pl}≥0 γ
Ud
n(rd n)−(1−γ)
Fn(sn)−ǫ
(fd
l )2
subject to
fd
l −
fd
l = rd n, d ∈ D, n ∈ N
fd
l ≤ τlCl(Pl), l ∈ L
Pl ≤ P max
l
, l ∈ L P avg
n
≤ Ensn, n ∈ N sn ≤ sm, m ∈ Nn, n ∈ N
IAB Meeting: May 15, 2006 – p. 25
SLIDE 26 Lagrange Dual Function and Dual Problem
D(λ, µ, ν, δ) = max
{sn,rd
n,f d l ,P m l }≥0 γ
Ud
n(rd n) − (1 − γ)
Fn(sn) −ǫ
(fd
l )2 −
λl
fd
l − τlCl(Pl)
µn
n
− Ensn
δd
n
rd
n −
fd
l +
fd
l
−
νm
n
- sn − sm
- subject to Pl ≤ P max
l
, l ∈ L Dual problem: min
λ0,µ0,ν0,δ D(λ, µ, ν, δ)
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SLIDE 27
Dual-based Solution of Primal Problem
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SLIDE 28 Dual Decomposition
Application/Transport Layer: D1(λ, µ, ν, δ) = max
{rd
n}≥0
n(rd n) − µnrd nEs−δd nrd n
D2(λ, µ, ν, δ) = min
{f d
l }≥0
l )2+fd l {λl + µnEtx + µpErx − δd n + δd p}
D3(λ, µ, ν, δ) = max
{0≤Pl≤P max
l
}
- n∈N
- l∈O(n)
- λl τl Cl(Pl, W)−µnτlPl
- Energy-Management Layer:
D4(λ, µ, ν, δ) = min
{sn}≥0
- n∈N
- (1 − γ)Fn(sn)−µnEnsn + sn
- m∈Nn
(νm
n − νn m)
- IAB Meeting: May 15, 2006 – p. 28
SLIDE 29
Vertical and Horizontal Decomposition
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SLIDE 30 Conclusions and Future Work
- Characterized the optimal utility-lifetime trade-off in sensor
networks
- Proposed distributed solutions that result in near-optimal
performance
Asynchronous implementations Variable scheduling but with fixed powers Joint scheduling and power control Extensions to networks with interference
IAB Meeting: May 15, 2006 – p. 30
