Mobility to Improve the Lifetime of Wireless Sensor Networks: Theory and Practice

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Mobility to Improve the Lifetime of Wireless
Sensor Networks Theory and Practice

• Jun Luo
• In collaboration with Prof. Jean-Pierre Hubaux
• Laboratory of Computer Communications and
  Applications (LCA)
• EPFL (Swiss Federal Institute of Technology
  Lausanne), Switzerland

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Longevity is Important
Preamble
An example of sensor networks environmental
monitoring
Many-to-one traffic pattern
Sink
Longevity is very important for many reasons
deployment costs, environmental disturbance, ...
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Our Treatment of the Problem
Outline
Massively Dense Network (Continuum Model)
II
Sparse Networks(Graph Model)
Routing Protocol(Implementation)
III
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Section 1 Joint Sink Mobility and Routing

• Improving Lifetime of Wireless Sensor Networks
• Using Sink Mobility
• Analysis under a Graph model

• Background and motivations
• Network model and problem formulation
• Problem tractability
• Approximation algorithm
• Simulation results

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Traditional Solutions
Section 1 Joint SMR Background and motivations

• Basic principle flow scheduling to balance the
  load among forwarding nodes
• Example Chang Tassiulas CT00 solving
  maximum multi-commodity flow problem.
• Problem only the load among nodes that are at
  the same distance from the sink is balanced.
• Consequence the closer a node is from the sink,
  the higher its load is.

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Mobile Relay Approach
Section 1 Joint SMR Background and motivations

• Basic principle picking up data from nodes with
  a mobile sink
• Examples
• Shah et al. SRJB03 Data MULE
  unpredictable mobility
• Chakrabarti et al. CSA03 Predictable observer
  mobility
• Kansal et al. KSJ04 Controllable mobilityIt
  is a compromise between the mobile relay
  approach and a later defined mobilesink
  approach.
• Problem the latency of data delivery is large.
• Consequence these approaches are limited to
  certain applications that do not have a stringent
  latency requirement.

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Mobile Sink Approach
Section 1 Joint SMR Background and motivations

• Move the sink to distribute the role of hot
  spots (i.e., the nodes around the sink) over
  time a complement to the traditional flow
  scheduling solution GDPV03, WBMP05, PG05
• The data collection continues through multi-hop
  routing wherever the sink is, so the solution
  does not sacrifice latency in contrast to the
  mobile relay approach
• Problem involving an optimization with higher
  complexity.
• Consequence a real optimal solution was never
  found in the literature.

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Network Model
Section 1 Joint SMR Network model and problem
formulation

• Static nodes and mobile sinks sinks change
  their locations at the end of an epoch and sink
  locations always coincide those of the nodes
  (i.e., mobility does not change network
  topology).
• Data traffic flows from all nodes (sources) to
  one of the sinks control traffic is neglected.

• For node i
• Energy reserve Ei
• Tx and Rx energies eit and er
• Information generation rate li

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Problem Formulation
Section 1 Joint SMR Network model and problem
formulation
k th epoch
k1th epoch
i
i
? Flow conservation
Energy conservation ?
Lifetime the time until the first node dies
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Problem Formulation
Section 1 Joint SMR Problem tractability
Where p refers to a certain path and f(p) is the
flow that follows the path. Pik stands for the
set of paths between a node i and one of the
sinks in the kth sink layouts and Pik represents
the set of paths that go through node i.
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The problem is NP-hard
Section 1 Joint SMR Problem tractability
Dual
Primal

• The primal problem is solvable in polynomial
  time iff the dual problem has a polynomial
  complexity.
• The dual problem is solvable in polynomial time
  iff its separation problem has a polynomial
  complexity NW88.
• The separation problem ?i ?i?w(j)(etier) 1 is
  equivalent to the p-median problem GJ79, which
  is known to be NP-complete.

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Tractable Sub-problem Pre-Defined Flow
Section 1 Joint SMR Problem tractability
In reality, given a specified routing protocol,
the flow for each sink layout is pre-defined by
the protocol WBMP05, LPPGH06.
Where pik refers to the power consumption of
node i for the kth sink layouts (and for the
corresponding flow).
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Tractable Sub-problem Single Mobile Sink
Section 1 Joint SMR Problem tractability
Dual
Primal
Where p refers to a certain path and f(p) is the
flow that follows the path. Pik stands for the
set of paths between a node i and the kth sink
location (at node k for simplicity) and Pik
represents the set of paths that go through node
i.

• The separation problem is solvable by, e.g.,
  Floyd-Warshall Q(n3), so this problem is
  tractable.
• However, directly solving the linear program is
  practically ineffective on all but very small
  scale problems.

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Duality Theory
Section 1 Joint SMR Approximation algorithm
Max-flow Min-distance ratio GK97 The optimal
lifetime achieved by a static sink at node k is
such that Where and dik is the distance
(given the weight w ) from node i to k.
Max-lifetime Min-potential ratio The optimal
lifetime achieved by a mobile sink is such
that Where and We term the
potential of sink location k.
Observation T gt T. In other words, mobility
always helps!
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The Problem with a Static Sink
Section 1 Joint SMR Approximation algorithm

• Given a sink location k, the problem is a
  maximum concurrent flow problem, and it can be
  approximated by the algorithm of Garg and
  Konemann GK97.
• However, GK algorithm is not enough.
• This assignment is not optimal. Better solution
  (i.e., longer lifetime) can be achieved with a
  more balanced the distribution of the potential.

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Algorithm Illustration for a Mobile Sink
Section 1 Joint SMR Approximation algorithm
Observation potential distribution is evenly
distributed, indicating a evenly distributed flow
(according to complementary slackness, a weight
is positive iff the corresponding nodes uses out
its energy reserves).
Note it can be generalized to approximate the
optimal solution with multiple mobile sinks.
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Line Networks Pause Times
Section 1 Joint SMR Simulation results

• Homogenous nodes (i.e., no quantity depends on i)
• E n
• e eter 1
• l 1

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Line Networks Lifetime Improvements
Section 1 Joint SMR Simulation results
Observation improvement achieved through
substitution effect, rather than load balancing.
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Grid Networks Lifetime Improvements
Section 1 Joint SMR Simulation results
Observation improvements are dramatic due to the
load balancing effect.
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Grid Networks Pause Times
Section 1 Joint SMR Simulation results
Observation sink tends to pause near the network
periphery with an increasing n.
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Our Treatment of the Problem
Outline
Massively Dense Network (Continuum Model)
II
Sparse Networks(Graph Model)
Routing Protocol(Implementation)
III
I
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Section 2 Decomposed Sink Mobility and Routing

• Improving Lifetime of Wireless Sensor Networks
• Using Sink Mobility
• Analysis under a Continuum Model

• Network model
• Optimality results for sink mobility

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A Continuum Model
Section 2 Decomposed SMR A continuum model

• Nodes densely distributed (with an density ? )
  within a circle for radius R
• Constant data rate ? between a node and a sink
  (no data aggregation)
• Fixed transmission and sensing range r
• An overall energy consumption e of to receive
  and transmit a unit of data (no topology control)
• Load-balanced routing following a straight line
• Forwarding load taken by a node is modeled as
  pressure from a sector

Max (Lifetime) MinMax (Energy Consumption)
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Optimal Moving Trace Two Claims
Section 2 Decomposed SMR Optimal moving trace

• By defining periodic mobility as recurrent
  movements with constant period, we can consider
  aperiodic trace as periodic mobility whose period
  is the same as the network lifetime.
• CLAIM 1 Symmetric trace (rotation symmetry of
  all degrees around the center) is at least as
  good as its non-symmetric version.
• CLAIM 2 The best trace is the network periphery.

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Our Treatment of the Problem
Outline
Massively Dense Network (Continuum Model)
II
Sparse Networks(Graph Model)
Routing Protocol(Implementation)
III
I
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Section 3 Protocol to Support Sink Mobility

• MobiRoute Routing towards a Mobile Sink

• Basic idea and simulation results
• Adaptive mobility control
• On-going field tests

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MobiRoute Considering Control Overhead
Section 3 MobiRoute Basics and simulations

• The following features of sink mobility and
  sensor networks allow MobiRoute to suppress its
  overhead in coping with mobility.
• The mobility is controllable and thus
  predictable.
• The pause time is much longer than the actual
  moving time.
• Existing routing protocol for sensor networks
  already have proactive features to cope with the
  dynamics in network topology

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Adaptive Mobility An LP Approach
Section 3 MobiRoute Adaptive mobility
Given MobiRoute, the following LP suggests the
pause times if the profile pik is
time-invariant
However, the profile pik does change with
time due to network dynamics (e.g., fluctuations
of link quality). Solution repetitively solve
the LP with the most recently collected profile
pikt to determine the pause time at the current
location.
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On-going Field Tests
Section 3 MobiRoute Field tests
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On-going Field Tests
Section 3 MobiRoute Field tests
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Summary of Contributions

• A constructive proof of the NP-hardness of
  maximizing network lifetime (MNL) problem
  involving multiple mobile sinks
• An efficient algorithm for the sub-problem
  involving a single sink, which can be generalized
  to approximate the general MNL problem
• A formal proof on the superiority of moving the
  sinks over keeping them static
• A closed-form expression of the optimal sink
  moving trace under a continuum model
• A routing protocol dedicated to support sink
  mobility
• Further information http//sensemob.epfl.ch/
  http//wasal.epfl.ch/