Smart Sleeping Policies for Wireless Sensor Networks

1
Smart Sleeping Policies for Wireless Sensor
Networks

• Venu Veeravalli
• ECE Department Coordinated Science Lab
• University of Illinois at Urbana-Champaign
• http//www.ifp.uiuc.edu/vvv
• (with Jason Fuemmeler)
• IPAM Workshop on Mathematical Challenges and
  Opportunities in Sensor Networks, Jan 10, 2007

2
Saving Energy in Sensor Networks

• Efficient source coding
• Efficient Tx/Rx design
• Efficient processor design
• Power control
• Efficient routing

3
Active Sleep Transition

• Paging channel to wake up sensors when needed
• But power for paging channel is usually not
  negligible compared to power consumed by active
  sensor
• Passive RF-ID technology?

4
Active Sleep Transition

• Practical Assumption
• Sensor that is asleep cannot be communicated
  with or woken up prematurely ? sleep duration
  has to be chosen when sensor goes to into sleep
  mode
• Having sleeping sensors could result in
  communication/sensing performance degradation
• Design Problem
• Find sleeping policies that optimize
  tradeoffbetween energy consumption and
  performance

5
Sleeping Policies
Duty Cycle Policy

• Sensor sleeps with deterministic or random (with
  predetermined statistics) duty cycle
• Synchronous or asynchronous across sensors
• Duty cycle chosen to provide desired tradeoff
  between energy and performance
• Simple to implement, generic

6
Smart (Adaptive) Policies

• Use all available information about the state of
  the sensor system to set sleep time of sensor
• Application specific ? system-theoretic approach
  required
• Potential energy savings over duty cycle policies

7
Tracking in Dense Sensor Network

• Sensor detects presence of object within close
  vicinity
• Sensors switch between active and sleep modes to
  save energy
• Sensors need to come awake in order to detect
  object

8
Design Problem

• Having sleeping sensors could result in tracking
  errors
• Design Problem
• Find sleeping policies that optimize tradeoff
  between energy consumption and tracking error

9
General Problem Description

• Sensors distributed in two-dimensional field
• Sensor that is awake can generate an observation
• Object follows random (Markov) path whose
  statistics are assumed to be known

10
General Problem Description

• Central controller communicates with sensors that
  are awake
• Sensor that wakes up remains awake for one time
  unit, during which it
• reports its observation to the central controller
• receives new sleep time from central controller
• sets its sleep timer to new sleep time and enters
  sleep mode

11
Markov Decision Process

• Markov model for object movement with absorbing
  terminal state when object leaves system
• State consists of two parts
• Position of object
• Residual sleep times of sensors
• Control inputs
• New sleep times
• Exogenous input
• Markov object movement

12
Partially Observable Markov Decision Process
(POMDP)

• The state of the system is only partially
  observable at each time step (POMDP)
• Object position not known -- only have
  distribution for where the object might be
• Can reformulate MDP problem in terms of this
  distribution (sufficient statistic) and residual
  sleep times

13
Sensing Model and Cost Structure

• Sensing Model Each sensor that is awake provides
  a noisy observation related to object location
• Energy Cost each sensor that is awake incurs
  cost of c
• Tracking Cost distance measure d(.,.) between
  actual and estimated object location

14
Dynamic System Model
Sensor Observations
Nonlinear Filter
Posterior
15
Simple Sensing, Object Movement, Cost Model

• Sensors distributed in two-dimensional field
• Sensor that is awake detects object without error
  within its sensing range
• Sensing ranges cover field of interest without
  overlap
• Object follows Markov path from cell to cell
• Tracking cost of 1 per unit time that object not
  seen

16
What Can Be Gained
1
Duty Cycle
Tracking errors per unit time
Always Track
n
0
Number of sensors awake per unit time
17
Always Track Policy
Unit random walk movement of object
18
Always Track Asymptotics
E awake per unit time O(log n)
E awake per unit time n0.5
19
Dynamic System Model
Sensor Observations
Nonlinear Filter
Posterior
20
Nonlinear filter (distribution update)
21
Optimal Solution via DP

• Can write down dynamic programming (DP) equations
  to solve optimization problem and find Bellman
  equation
• However, state space grows exponentially with
  number of sensors
• DP solution is not tractable even for relatively
  small networks

22
Separating the Problem

• Problem separates into set of simpler problems
  (one for each sensor) if
• Cost can be written as sum of costs under control
  of each sensor (always true)
• Other sensors actions do not affect state
  evolution in future (only true if we make
  additional unrealistic assumptions)
• We make unrealistic assumptions only to generate
  a policy, which can then be applied to actual
  system

23
FCR Solution

• At time sensor is set to sleep assume we will
  have no future observations of object (after
  sensor comes awake)
• Policy is to wake up at first time that expected
  tracking cost exceeds expected energy cost
• Thus termed First Cost Reduction (FCR) solution

24
QMDP Solution

• At time sensor is set to sleep, assume we will
  know location of object perfectly in future
  (after sensor comes awake)
• Can solve for policy with low complexity
• Assuming more information than is actually
  available yields lower bound on optimal
  performance!

25
Line Network Results
26
Line Network Results
27
Line Network Results
28
Two Dimensional Results
29
Offline Computation

• Can compute policies on-line, but this requires
  sufficient processing power and could introduce
  delays
• Policies need to be computed for each sensor
  location and each possible distribution for
  object location
• Storage requirements for off-line computation may
  be immense for large networks
• Off-line computation is feasible if we replace
  actual distribution with point mass distribution
• Storage required is n values per sensor

30
Point Mass Approximations

• Two options for placing point mass
• Centroid of distribution
• Nearest point to sensor on support of distribution

31
Distributed Implementation

• Off-line computation also allows for distributed
  implementation!

32
Partial Knowledge of Statistics

• Support of distribution of object position can be
  updated using only support of conditional pdf of
  Markov prior!
• Thus nearest point point mass approximation is
  robust to knowledge of prior

33
Point Mass Approximation Results
34
Point Mass Approximation Results
35
Conclusions

• Tradeoff between energy consumption and tracking
  errors can be considerably improved by using
  information about the location of the object
• Optimal solution to tradeoff problem is
  intractable, but good suboptimal solutions can be
  designed
• Methodology can be applied to designing smart
  sleeping for other sensing applications, e.g.,
  process monitoring, change detection, etc.
• Methodology can also be applied to other control
  problems such as sensor selection

36
Future Work

• More realistic sensing model
• More realistic object movement models
• Object localization using cooperation among all
  awake sensors at each time step
• Joint optimization of sensor sleeping policies
  and nonlinear filtering for object tracking
• Partial known or unknown statistics for object
  movement
• Decentralized implementation
• Tracking multiple objects simultaneously