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					Sensor Control and Scheduling
Strategies for Sensor Networks
         Victoria Manfredi
         Thesis Defense
         August 13, 2009

         Advisor: Jim Kurose
       Committee: Andrew Barto
                  Deepak Ganesan
                  Weibo Gong
                  Don Towsley
Motivation                       Wireless, Closed-Loop
   Cameras, radars: cannot
                                    Sensor Network
  collect data simultaneously
from all environment locations
Where to focus sensing?                      Data




                                        Sensor Controls      Multiple users making
  Changing network topology                                conflicting sensor requests
How to make routing robust                                  How to accommodate
  to network changes?                                         multiple users?

        Bursty, high-bandwidth data, many-to-one data routing to sink: congestion
          How to make sensing robust to delayed and dropped packets?
                                                                                    2
Contributions
 Adaptive sensors
   – where to focus sensing in adaptive meteorological radar network?
       • show lookahead strategies useful when multiple small phenomena,
         trade-off between scan quality and re-scan interval
   – accommodating multiple users?
       • identify call admission control problem, give complexity results


 How to make sensing robust to delayed, dropped packets?
   – show good application-level performance possible in closed-loop
     sensor network when congestion if sensor control prioritized


 How to make routing robust to network changes?
   – propose routing algorithm, show can significantly  control
     overhead while minimally degrading % of packets delivered
                                                                            3
Outline
Adaptive sensors
  – where to focus sensing?
  – multiple users
Prioritizing sensor control traffic
Robust routing in dynamic networks
Conclusions




                                       4
Where to focus sensing?
    CASA: Adaptive Meteorological Radar Network




      small scan sectors    large scan sectors
       high quality, but      low quality, but
       may miss storm       miss fewer storms
                                                  5
Sensing Strategies
              What are ``good” sensing strategies?
 sit-and-spin
   – all radars always scan 360

 myopic
   – consider only current environmental state

 limited lookahead
   – Kalman filters to predict storm cell attributes k time-steps ahead

 full lookahead
   – formulate as Markov decision process
   – reinforcement learning to obtain policy: Sarsa()

                                                                          6
Storm Tracking Application
 Radar network


               30km
              30 km

                                               max storm radius: 4km



 Storm model
  – storms arrive according to spatio-temporal Poisson process
  – storm dynamics from Kalman filters

 Radar sensing model
  – observed attribute value = true attribute value + Gaussian noise
                                                 Depends on scan
                                                     quality           7
Performance Metrics
 Re-scan interval 30 km
   – how long before storm first observed or rescanned

 Scan quality
   – how well storm observed
   – function of
       • scan sector size
       • distance from radar
       • % of storm scanned
   – value between 0 and 1


 Cost
   – function of re-scan interval, quality, penalty for missing storms
   – 2-step and full lookahead have similar cost for 2 radars


                                                                         8
          Optimize over all radars?

                  1-Step Lookahead
Average Quality




                  Myopic                            1-Step Lookahead

                                                       Myopic


                   Sit-and-Spin                      Sit-and-Spin




                          Max 1 Storm                      Max 8 Storms
                  No gains in quality as optimize    Decreasing gains as optimize
                        over more radars                  over more radars
                                                                                9
Summary

                Where to focus sensing?

  Showed lookahead strategies useful when multiple
  storms, storm radius (much) smaller than radar radius
    trade-off scan quality and frequency storm scanned
    may not need to optimize over all radars in network


  Related work
    – track ground targets from airplanes [Kreucher, Hero, 2005]
    – our focus: track meteorological phenomena using ground radars



                                                                  10
Outline
Adaptive sensors
  – where to focus sensing?
  – multiple users
Prioritizing sensor control traffic
Robust routing in dynamic networks
Conclusions




                                       11
How to accommodate multiple users?
  Virtualize sensing resources                                                                              Mt. Toby
    – virtualized private sensor network
                                                                                                                   Q uic kT im e™ an d a
                                                                                                                      d ec o mp r es s or
                                                                                                           a re n ee d ed to s e e th is p ictu r e.




  To each user
    – looks like own private network
    – but user only has virtual slice

                                                                                                                                                        MA1
  Users request resources                                                                                                                             Tower
                                                Q uic kT im e™ an d a


    – possibly conflicting requests
                                                   d ec o mp r es s or
                                        a re n ee d ed to s e e th is p ictu r e.




    – which requests to satisfy?                                                   QuickTime™ and a
                                                                                     decompressor

                                                                                                        CS
                                                                             are neede d to se e this picture.




                                                                                                      Building

  Call admission control problem

                                                                                                                                                           12
Call Admission Control Problem
                               Scan 360°
 Sensor request
    – use sensor in particular way possibly during particular time

 Sensing strategy                                Scan 360° every 2 min
    – sequence of requests over time

         Strategy for User 1

         Strategy for User 2




 Utility of request j
                               i
   – to requesting user i: uij      Combine into single utility
                                              i            i
   – to each other user i: uiji      uij = uij +  uij
                                                   i


  Select set of non-interfering requests that maximizes utility
                                                                          13
Space of Problems
     Divisible requests?                  Shifting permitted?
  Utility received if only part    Utility received if request
   of request satisfied?             executed at different time?
  Yes                              Yes
     – scan x of y elevations         – perform surveillance scan
  No                               No
     – obtain full scan of storm      – sense storm expected at
                                        location (x,y) at time t

 User 1 Request
                                   User 1 Request
 User 2 Request
                                   Shifted Request
 Interleaved Requests
                                                       Time
                          Time
                                                                    14
Complexity
                              Divisible requests?

                        Yes                     No


          Shifting permitted?                   Shifting permitted?

          Yes          No                           Yes          No


   Polynomial         Polynomial         NP-Complete            Polynomial



Same as fractional   Interleave sensor                     Interval scheduling
knapsack problem          requests                        [Arkin, Silverberg, 1987]


                                                                                15
Indivisible, Shifting
 NP-complete
  – assume utility independent of when request executed
  – In NP: can check whether solution correct in polynomial time



                                  Sensing Strategy          w1
   Knapsack Problem
                                     for User 1             v1




                                          




                                                           
      Capacity        Reduction                           wN
                                  Sensing Strategy
        W                            for User N            vN

    w1                                                      Time T=W
              wN
    v1           vN                Utility for satisfying user i’s request
                                       – to user i: vi
                                       – to each other user: 0
                                                                             16
Summary
              How to accommodate multiple users?

     Requests divisible or fixed in time  polynomial-time algorithms
     Requests indivisible but may be shifted  NP-complete


 Related work
   – adaptively select set of sensors for task [Jayasumana et al, 2007]
   – our focus: virtualizing sensing resources within a sensor


 Future work
   – online, decentralized algorithms
   – trade-off between maximizing utility and user fairness
   – implement proposed algorithms in deployed network

                                                                          17
Outline
Adaptive sensors
  – where to focus sensing?
  – multiple users
Prioritizing sensor control traffic
Robust routing in dynamic networks
Conclusions




                                       18
Why prioritize sensor control traffic?
 Sensor network              Bursty, high-
                             bandwidth data
                              Many-to-one           Congestion
                             routing to sink
                             Wireless links

 Closed-loop sensor network
           Data                Data spatially,
                                                     Prefer to delay,
                                temporally
                                                     drop data rather
         Sensor                 redundant
                                                       than control
         Controls             Data >> control


  How does prioritizing sensor control traffic over data traffic
          impact application-level performance?
                                                                   19
Closed-loop Sensor Networks
 Prioritizing sensor control
   – impact on packet delays?
   – impact on data collected?
                           Control, data share queues
 Control loop delay          e.g., wireless links

                                     Priority control
                          Data delay     delay     FIFO control delay
  Data
                             Data from                   Data from
                             control k-1                 control k
   Control
                k-1                         k                           k+1
                                                    Update interval

         Small  data delay, large  control delay  more data
           collected in time to compute next sensor control
                                                                         20
Better Quality Data
 More data samples
    Cramer-Rao bound:
              SD(W) ≥ 1 / n I          Fisher        Radars, Sonars,
        Std Dev of W                  information       Cameras, …
           from          # of iid samples
                                                                      Q uic kT im e™ an d a
                                                                         d ec o mp r es s or
                                                              a re n ee d ed to s e e th is p ictu r e.




      Lower bound on std dev of unbiased estimator W
    (sample mean) from parameter  (population mean)

   – accuracy  sub-linearly with  n


 Effect of data packet drops?
   – accuracy  sub-linearly with  n

     Sensing accuracy changes slowly with # of samples
                                                                                                          21
Storm Tracking Application
 Network model
   – obtain sensor control and data packet delays
   – CASA network is closed-loop sensor network


                                 Deterministic      control
        Delays at bottleneck
                                   arrivals
           link dominate,                                           
       assume wireless links
                                                 data
                                      Bursty arrivals    other

 Sensing model
   – convert packet delays into sensing error
 Tracking model
   – convert sensing error into storm location error
   – tracking: compute next scan for radar from 99% confidence ellipse
                                                                         22
Tracking Error
                                                      +
                                         +

RMSE =
     # intervals

      (true -obs )
               t     t
                         2


 √
      t=1
       # intervals



                                 +
                                 +
                             idx = 1   idx = 25    idx = 55


     Per-interval performance gains/losses may accumulate
                 across multiple update intervals
                                                              23
Summary
How to make sensing robust to delayed and dropped packets?

    When network congestion, prioritizing sensor control
     in closed-loop sensor network  quantity, quality of
    data, and gives better application-level performance


 Related work
   – SS7, ATM, [Fredj et al, 2001] [Kyasanur et al, 2005]
   – our focus: prioritizing sensor control (not network control)




                                                                    24
Outline
Adaptive sensors
  – where to focus sensing?
  – multiple users
Prioritizing sensor control traffic
Robust routing in dynamic networks
Conclusions




                                       25
What do we mean by robust?

                     network structure           protocols
                    changing over time          must adapt


 But if frequent changes, adapting is costly: e.g., in MANET
        may have as much routing control traffic as data

 Adapt to every change?
    yes: potentially perform optimally, but more overhead
    no: likely perform sub-optimally, but less overhead

         Robust: solution performs well over many
             scenarios, solution is not fragile
                                                             26
Robust Routing
        Robust routing: routing subgraph has path from
                 src to dest, as links up/down
 src-dest reliability
                                                      But, reliability #P-complete
   – prob instantaneous path in stochastic graph       to compute, can’t search
   – want max reliability sub-graph for overhead          over all sub-graphs


            Identify structural properties that make graph reliable,
                efficiently find subgraph with such properties



 Effect of graph structure on src-dest reliability?
   – show reliability (in limits) dominated by shortest paths, smallest cuts

                Most robust routing subgraph should contain
                   shortest path and have large min cut
                                                                               27
Braid
                 (shortest)
  k-hop braid: most reliable path + all nodes within k-hops

        Most Reliable Path    1-Hop Braid      2-Hop Braid
                s                  s               s




                d                  d                d



  Given fixed amount of overhead, is braid most reliable sub-graph?
             reliability simulations + theoretical analysis


                                                                      28
Theoretical Analysis
                                        Add black node rather
Lemma: Suppose sub-          How Reliable is Braid?nodes?
                                           than blue
graph contains shortest
path and 0<n<N 1-hop
nodes. Given 1 or 2 extra
nodes, to max reliability,
use all 1-hop nodes before       s                                             d
any 2-hop nodes
                                                  N

Note: lemma does not hold when adding links

                                                Partial braid less reliable
                                                than 2-disjoint paths for
     s                d      s              d           1p√2/3
      Partial Braid          2-Disjoint Paths
                                                                              29
Braid Routing
                                                     Use dynamic source
If no path from src to dest:                           routing (DSR)
Step 1: Identify shortest path in network
                                                     Overheard RREQ and RREP
Step 2: Build braid around shortest path               contain 1-hop braid info

Step 3: Perform local forwarding within braid
                                                     When link breaks, use braid
           e.g., flooding, opportunistic routing,
            backpressure                              path back to DSR path


        DSR vs Braid
              – path breaks
                  • use new DSR path or existing 1-hop braid path
              – primary difference
                  • control overhead incurred to find this new path

                                                                             30
Simulation Set-up
 QualNet

 Gauss-Markov mobility
    – BonnMotion to generate traces
    – min 0.5 m/s, max 2 m/s
    – speed, angle updates every 100s

 20-80 nodes
    – 400m transmission radius
    – 2km x 2km area

 1 constant bit-rate flow
    – 4 pkts/s, 1 million seconds

 10 runs, each lasting life of flow


                                        31
Control Overhead

    # of Control Packets                       DS
                                               R



                                            Braid




                              # of Nodes

               As node density increases, braid incurs fewer
                        control packets than DSR
                                                               32
    Control Overhead
                           Route Requests              Route             Route Errors
# of Control Packets




                                                       Replies
                                                                                  DS
                                                                                  R
                                                                                 Braid
                                           DS                     DS
                                            R
                                           Braid                  R
                                                                 Braid
                             # of Nodes             # of Nodes            # of Nodes

                            Up to ~30%              Up to ~40%           Up to ~25%
                          fewer requests           fewer replies         fewer errors


                       Braid incurs fewer route requests, replies, errors than DSR

                                                                                         33
        Packets Delivered and Delay
% of Packets Delivered




                                       DS




                                                Delay (seconds)
                                        R
                                      Braid
                                                                               Braid

                          (4 million packets)

                                                                  DS
                                                                  R

                         # of Nodes                               # of Nodes



                         Braid delivers slightly fewer packets, incurs
                                    higher delay than DSR
                                                                                  34
Summary
      How to make routing robust to network changes?

       Proposed routing algorithm that  control overhead by
       (1) updating routes less frequently
       (2) performing local forwarding within routing sub-graph
              gains depend on network characteristics


 Related work
   – [Shacham et al 1983] [Lee, Gerla, 2000] [Ganesan et al, 2001] [Ghosh et al, 2007]
   – our work: differs in structure and/or usage of routing subgraph

 Future work
   – which network characteristics most impact performance?
   – joint rate control and routing
   – what should be braid width (trade-off with interference)?
                                                                                         35
Outline
Adaptive sensors
  – where to focus sensing?
  – multiple users
Prioritizing sensor control traffic
Robust routing in dynamic networks
Conclusions




                                       36
Conclusions
 Adaptive sensors
   – where to focus sensing in adaptive meteorological radar network?
       • show lookahead strategies useful when multiple small phenomena,
         trade-off between scan quality and re-scan interval
   – accommodating multiple users?
       • identify call admission control problem, give complexity results


 How to make sensing robust to delayed, dropped packets?
   – show good application-level performance possible in closed-loop
     sensor network when congestion if sensor control prioritized


 How to make routing robust to network changes?
   – propose routing algorithm, show can significantly  control
     overhead while minimally degrading % of packets delivered
                                                                            37
Thanks!
 Jim
 Don, Deepak, Andy, Weibo
 Networks Lab
   – Bruno, Mike, Yung-Chih, Daniel2, Majid, Yu, Bo, Patrick, Junning,
     Giovanni, Guto, Elisha, Suddu, Bing, Sookhyun, Chun …
 ALL Lab
   – Sridhar, Mohammad, George, Sarah, Khash, Ash, Ozgur, Pippin …
 Laurie, Tyler, ….


                         Questions?


                                                                         38
Adaptive Sensing




                   39
                                                   sr : radar configuration, start,
Performance Metrics                                     end angles of scan sector
                                                   Sr: set of radar configurations
 Re-scan interval
   – # of decision epochs before storm cell first observed or rescanned

 Quality
   – how well storm cell p observed

                                       distance to storm cell

   Up(p, Sr) = max [ Fc(c(p, sr ))  [  Fd(d(r,p)) + (1-) Fw(w(sr ) / 360)]     ]
                s r Sr
                          % covered                             radar rotation speed


   – how well sector ri scanned

                          Us(ri, sr) = Fw(w(sr ) / 360)]
                                                                                      40
Performance Metrics                                      Pm := penalty for never
                                                               scanning storm
                                                         Pr := penalty for not
 Cost                                                         rescanning storm

  – Re-scan time and quality + penalty for never scanning storm cell


                           Difference between true and
                            observed # of storm cells
                 o         o
               Np    Nd                                  Np
          C =   |dij - dij| +                  Pm + I(tk)Pr
                                             o
                                      (Np -Np)
               i=1   j=1                              k=1

          Difference between observed             Storm scanned within Tr
             and true storm attribute                decision epochs?



         Goal: maximize quality, minimize re-scan time

                                                                                   41
Limited Look-ahead Strategy
      Use Kalman filters to predict storm cell attributes
             1 and 2 decision epochs ahead
 State

                                                           
          y                 True state:     true = [ x, y, x, y ]T
                            Observed state: obs = [ x, y ]T
               
       (x,y) x              Assume:                            A, B, Q, R
                             truet = A truet-1 + N[0, Q]    initialized using
                             obst = B truet + N[0,R]        prior knowledge


 Actions
   – select scan action that minimizes cost
   – additionally scan any sector not scanned in last T=4 decision epochs


                                                                           42
Full Look-ahead Strategy
                  Markov Decision Process Formulation
 State
                                       Storm radius
                  y
                                                        # of storm cells,
                       x
              (x,y)                             +        Up quality of storm cells,
                                                         Us quality of sectors

 Actions


 Transition function
    – encodes observed environment dynamics, obtained from simulator
 Cost function
    – obtained from performance metrics
 Sarsa()
    – linear combination of basis functions to approximate value function
    – tile coding to obtain basis functions, one tiling for each state variable


                                                                                      43
Simulation Set-up
 True state
   – storms arrivals: spatio-temporal                              Poisson
     process                                   10 km or
   – storm attributes from distributions        30 km
     derived from real data
   – max storm radius: 4km
   – max number of storms

 Observed state
   – observed attribute value = true attribute value plus noise ~ N[0, 2]
                       Largest positive value of attribute

                           = (1-u) Vmax / 

                        Us(ri,sr) quality         scaling term
                                                                             44
Scan Quality
     Avg Difference in Quality (250,000 steps)
                                                 Max 1 storm

                                                         2Step - Sarsa



                                                  SitandSpin - Sarsa
                                                                         Max 4 storms




                                                                  1/

  2-Step scans have higher quality than Sarsa(), especially
     when little noise in environment (when 1/ is small)
                                                                                        45
 Cost                                2 radars




      Average
 Difference in Cost            SitandSpin -
# timesteps                   Full Lookahead

   
   t=1
           Ct
              2step
                  - CFull
                     t

         # timesteps

                                     2StepLookahead - FullLookahead




                                               1/


           Full lookahead and 2-step look-ahead have similar costs
                                                                      46
Re-scan Interval
             Sit-and-Spin
             1-Step



              2-Step
                                 Sarsa() more likely than 2-step
                                 look-ahead to scan storm within
   P[X≤ x]




                                      Tr=4 decision epochs
                      Sarsa()




                x = # of decision epochs between storm scans
                                                                    47
Related Work                                       Large State-space
                                                 Reinforcement Learning
            Radar Control                     2005: Stone, Sutton, Kuhlmann
                                                – robot soccer
 2005: Kreucher, Hero                        2004: Ng, Coates, Diel, Ganapathi,
   – look-ahead scheduling of radars on        Schulte, Tse, Berger, Liang
      airplanes for detecting and tracking      – helicopter control
      ground targets
                                              2002: Zilberstein, Washington,
   – information-theoretic reward, Q-          Bernstein, Mouaddib
      learning
                                                – planetary rovers
    We consider tracking meteorological
     phenomena using ground radars

 2005: Suvorova, Musicki, Moran,
  Howard, Scala
                                                    Sensor Networks
   – target radar beams, select waveform      2005: Mainland, Parkes, Welsh
      for electronically steered phased         – game theory + reinforcement
      array radars                                 learning to allocate resources
   – show 2-step lookahead outperforms          – learn profit associated with
      one-step look-ahead for tracking             different actions, rather than profit
      multiple targets                             associated with different state-
    Do not consider infinite-horizon case          action pairs

                                                                                           48
Call Admission Control Problem




                                 49
Divisible, No Shifting
 Polynomial-time
    – assume utility depends on how much of request executed
    – select max utility sensor request during each conflicting interval


Sensing Strategy for User 1


Sensing Strategy for User 2




Interleaved Sensor Requests




                                                                           50
Separation of Control/Data




                             51
Storm Tracking Application: 3 Coupled
Models
                                                                    
Network model: control, data delays,             d                d             
  depend on scheduling (FIFO, priority)

               Timeliness of control, data affects       d             
               amount of sensed data gathered
                                                                                      c

Sensing model: given scan, quantity and
  quality of data, estimated storm location

               Quality of estimated storm location
                         affects tracking

Tracking model: predict storm location
   based on current, past estimates and                                     (xk,yk)
   observations using Kalman filters
                                                              (xk-1,yk-1)
               Quality of tracking affects scan angle,
                        quality of estimates
                                                                                       52
Network Model                                                
                                           d               d           
     Obtain sensor control and
        data packet delays                          d           
                                                                             c
 Wireless network
   – radar data sent to control center, sensor control back to radars
   – much more data traffic than sensor control traffic


 Delays at bottleneck link dominate control-loop delay

                 Deterministic
                                      control
                   arrivals
                                                                     
                                  data
                         Bursty arrivals        other


   Obtain delays for FIFO, priority queuing using simulation
                                                                                  53
Sensing Model
         Convert packet delays into
              sensing error
 Radar
   – transmits pulses to estimate reflectivity at point in space

 Reflectivity
   – # of particles in volume of atmosphere
   – standard deviation,

                 =

                 where N = c (D - (a+)) /           radar SNR
                                               scan angle width
                               sensing time


  Smaller angle, longer time sensing  lower sensing error
                                                                   54
Tracking Model
      Convert sensing error into location             (xk,yk)
            error, perform tracking       (xk-1,yk-1)
 Location of storm centroid
   – equals location of peak reflectivity
   – standard deviation,
                                      distance from radar
                              r d
                      z =
                             30 dBz
                                      mid-range reflectivity value


 Kalman filters
   – generate trajectory of storm centroid       z used in measurement
   – track storm centroid                            covariance matrix



   Goal: track storm centroid with highest possible accuracy
                                                                          55
Kalman filter
 xk := estimated (location, velocity)
                                                          (xk,yk)
 yk := measured (location, velocity)        (xk-1,yk-1)
      noisy, with std deviation r(,a+)

  Measure: radar data
  received, measured
  position yk, with r(,a+)

  Filter: estimate xk
  based on yk, predicted x-k

                                               Estimated state error
                      x-
  Predict: next (k+1) 99%                      covariance matrix, depends
  confidence region, gives k+1                on velocity noise model,
                                                r(,a+)
  to scan next time step
                                                                        56
Simulation Set-up
  Network parameters
                                           Vary burstiness of ``other” traffic,

              control= 1/D pkts/s                           r1 = 1s

 data= 2000/30                                1= po    off         on   2= (1-p)o
                                     
     pkts/s
                                                                r2 = 1s
                   other= 2000/30
                        pkts/s
                                           Index of dispersion
  control+ data+other  133.37 pkts/s
                       = 148.5 pkts/s         idx =

         avg load  0.90

  Kalman filter parameters
     – initialize based on storm data

  10 NS-2 simulation runs, 100,000 sec each
                                                                                  57
Data Quantity

                             Number of times more
                idx = 55     voxels scanned under
                            priority than under FIFO


              idx = 25




             idx = 1


                           D (seconds)

  As D  and burstiness , gains from prioritizing increase
                                                              58
  Data Quality
   Assuming  = 360

                                                          Reflectivity Standard
           Number of Pulses                                    Deviation
F(x)




                   D = 30sec                                          D = 30sec




                                              F(x)
                                      idx1                                              idx1

                            idx55                            D = 5sec         idx55
            D = 5sec
                                                                  idx55
                 idx55
                              idx1                                                  idx1

              x = NFIFO / NPriority                          x = r,Priority / r,FIFO

   Small decision epoch, bursty traffic:          Small decision epoch, bursty traffic:
  FIFO achieves ~80% as many pulses                priority has at least 90% as much
        as priority ~80% of time                 uncertainty as FIFO ~90% of the time

                                                                                            59
Number of Pulses




     FIFO and Priority each achieve about 6x as many
   pulses per voxel for D = 30 sec vs D = 5 sec, and total
               # of pulses is independent of D               60
Data Quantity vs Quality
                     360 scans, D = 5sec,
                       very bursty traffic
   CDF




                       FIFO achieves at least          Priority has at least
                      80% as many samples as              90% as much
                        priority ~80% of time          uncertainty as FIFO
                                                        ~90% of the time
                            NFIFO / Npriority
                                                **   r,Priority / r,FIFO



         During times of congestion, prioritizing sensor
               control  quantity, quality of data                           61
Effect of Packet Loss
     r (with loss) / r (no loss)
                                                              FIFO: sensor control
                                                                packets dropped

                                     Capacity: when >1000,
                                         data dropped



                                                              Priority: no sensor control
                                                                   packets dropped




                                                         = pkts / second

  As system goes into overload sensing accuracy degrades
     (more) gracefully when sensor control is prioritized                                   62
Related Work                                                   Prioritize Network Control
                                                       SS7 telephone signaling system
    Service Differentiation for                        ATM networks, IP networks
    Different Classes of Traffic                       1998: Kalampoukas, Varma, Ramakrishan,
 2001: Bhatnager, Deb, Nath                            2002: Balakrishnan et al,
    –   assign priorities to packets, forwarding          –    priority handling of TCP acks
        higher-priority packets more frequently        2005: Kyasanur, Padhye, Bahl
        over more paths to achieve higher                 –    separate control channel for controlling
        delivery prob                                          access to shared medium in wireless
 2005: Karenos, Kalogeraki,
  Krishnamurthy
                                                       Our focus: prioritize sensor control
    –   allocate rates to flows based on class of
        traffic and estimated network load                    Networked Control Systems
 2006: Tan, Yue, Lau                                  data, sensor control sent over network
    –   bandwidth reservation for high-priority           –    constrained to be feedback and
        flows in wireless sensor networks                      measurements of classical control system
 2008: Kumar, Crepadir, Rowaihy, Cao,                    –    ratio of data to control much smaller than that
  Harris, Zorzi, La Porta                                      of closed-loop sensor network
    –   differential service for high priority data    2001: Walsh, Ye
        traffic versus low-priority data traffic in       –    put error from network delays in control eqns
        congested areas of sensor network              2003: Lemmon, Ling, Sun
     Do not consider effects of                           –    drop selected data during overload by
   prioritizing only sensor control                            analyzing effect on control equations

         in a sensor network                                   We assume amount of
                                                               data  sensor control                     63
Robust Routing




                 64
What do we mean by robust?
    Robust routing: routing subgraph has path from
             src to dest, as links up/down

                                           2/4
                                       
                           
                                       
                                             3/4



                                           4/4
                                       
          T=1      T=2      T=3      T=4             65
Some Intuition
   What is effect of graph structure on src-dest reliability?
    Given graph G, src, dest, assume links iid and up with prob p

 Paths                                              Small p limit:
                                                     reliability
                                                   dominated by
                                                   shortest paths

 Cuts                                             Small q=1-p limit:
                                                     un-reliability
                                                    dominated by
                                                    smallest cuts


 Most robust routing subgraph should contain shortest/most
            reliable path and have large min cut                      66
Theoretical Analysis
Proof:

             s1        s1     q1       q1        d1     d1

    s        s0       s0      q0       q0        d0     d0      d


 P(d|s) = P(d | s0 s1) P(s0 s1|s)
                    -        -               Recursively iterate:
         + P(d | s0 s1) P(s0 s1|s)          get eqn with 27 terms
                 -         -
         + P(d | s0 s1) P(s0 s1|s)


 P({q0,q1} | {s0,s1}) P(d | {d0,d1})        Product always  for
                                             adding black node
                                                                    67
Conjectures

Conjecture 1: N extra nodes: 1-hop braid most reliable
              From lemma: true for N ≤ 5


Conjecture 2: 2N extra nodes: 2-hop braid most reliable


  Experimentally: for
 N=6, 2-hop braid more
  reliable than pyramid   s              d   s               d
                                 N=6               N=6




   Generally: conjecture no “holes” in most reliable graph
                                                                 68
Conjectures
Conjecture 2: 2N extra nodes: 2-hop braid most reliable
       experimentally: for N=6, 2-hop braid more reliable than pyramid

            reliability




                                    p                                 69
Adding edges rather than nodes

 Conjecture 3: N+1 extra edges: partial 1-hop braid most reliable
                  not true, see counterexamples


      Partial Braid       2-Disjoint Paths
                                                    Partial braid less
N=3                                              reliable than 2-disjoint
      s           d       s           d              paths for 1p0


                                                    Partial braid less
N=4                                              reliable than 2-disjoint
      s               d   s                  d     paths for 1p√2/3


                                                                        70
Adding edges rather than nodes

  Conjecture 3: N+1 extra edges: partial 1-hop braid most reliable
                      not true, see counterexamples


            Scaling behavior



link up prob above which
   2-disjoint paths more
reliable than partial braid

                                                        N


                 As N increases, partial braid more reliable
                           for more values of p
                                                                     71
Reliability Experiments
    Have intuition that braids have good reliability properties

 But,
   – how does reliability of braid compare with other routing subgraphs?
   – what is impact of time between braid re-computations T on reliability?



 Experiment set-up
   – model                                             Link model
         • 100 nodes, random graph                          1-p
         • links iid, 2-state link model
         • src, dest randomly chosen
                                                   p   up         down        q
   – Monte Carlo simulation
         • 500 runs, each lasting 100 time-steps
                                                            1-q


                                                                                  72
Link Failures




                                                      Gain in Reliability over Shortest Path
                               full graph

                          1-hop braid                                                               2-shortest
                                                                                                  disjoint paths
Reliability




                                                                                                                            full graph
                      2-shortest disjoint paths

                      shortest path
                                                                                                              1-hop braid




              T = length of routing update interval                                            # of Nodes Used in Addition to Shortest Path
                         p=0.85, q=0.5                                                                      p=0.85, q=0.5, T=5



                   Braid reliability close to full graph, braid overhead
                             significantly less than full graph
                                                                                                                                         73
  Node vs Link Failures
              Node failures imply correlated link failures, as in mobility




                                                         Gain in Reliability over Shortest Path
Reliability




                               1-hop braid
                full graph                                                                             2-shortest                    full graph
                                                                                                     disjoint paths



                                                                                                                      1-hop braid
                        2-shortest       shortest path
                      disjoint paths


              T = length of routing update interval                                               # of Nodes Used in Addition to Shortest Path
                             p=0.85, q=0.5                                                                     p=0.85, q=0.5, T=5


                  All algorithms have lower reliability, braid overhead
                                 still less than full graph
                                                                                                                                         74
Routing Experiments
 GloMoSim
   –   60 nodes, 250m transmission radius
   –   1km x 1km area
   –   1 cbr flow: 5 million pkts (~29 days)
   –   random waypoint, Gauss Markov mobility


 Compare throughput, overhead
   – AODV
   – 1-hop braid
      built around AODV path
      choose next hop based on last successful use


 10 runs, each lasting life of flow


                                                      75
Random Waypoint Mobility




   T = routing update interval (seconds)   T = routing update interval (seconds)


     Packets delivered: braid              Braid overhead: ~25% more
     delivers up to 5% more                control overhead than AODV
       packets than AODV

                                                                                   76
Gauss-Markov Mobility




  Insights: braids work well when
   links can reappear in T
   Independent link failure


      T = routing update interval (seconds)   T = routing update interval (seconds)

     Packets delivered: braid                 Braid overhead: ~40% more
     delivers up to 5% more                   control overhead than AODV
       packets than AODV



                                                                                  77
Reliability vs Routing
           Reliability gains  Throughput gains

  Reliability experiments
     iid links
     shortest path = most reliable path

  Routing experiments
     non-iid links
     shortest path ≠ most reliable path


    Braid construction independent of “best” path algorithm
       don’t use AODV, instead estimate link reliability

                                                              78
Reliability vs Routing
           Reliability gains  Throughput gains

  Reliability experiments
     iid links
     rate at which down links re-appear is “high”
         prob down link reappears = 0.5
     broken link likely re-appears during T

  Routing experiments
     non-iid links
     rate at which down links re-appear is “low”
         2 nodes meet on avg once every 22.7 min
     broken link likely does not re-appear during T

       Consider link correlations, mobility characteristics   79
Link Failures and Braid Attempts




                                   80

				
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