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									                      Lecture 5:
                Topology Control



                             Anish Arora

                             CIS788.11J

Introduction to Wireless Sensor Networks



Material uses slides from Paolo Santi and
                            Alberto Cerpa
         Problems affected by link quality


•   Topology Control
•   Neighborhood Management
•   Routing
•   Time Synchronization
•   Aggregation
•   Application Management




                                             2
                            References


• Topology Control tutorial, Mobihoc’04, Paolo Santi

• SPAN, Benjie Chen, Kyle Jamieson, Robert Morris, Hari Balakrishnan,
MIT

• GAF/CEC, Y. Xu, S. Bien, Y. Mori, J . Heidemann & D. Estrin, USC/ISI –
UCLA

• ASCENT, Alberto Cerpa and Deborah Estrin, UCLA

• GS3: Scalable Self-configuration and Self-healing in Wireless
Networks, PODC 2002, Hongwei Zhang, Anish Arora

• M. Demirbas, A.Arora, V.Mittal, FLOC: A Fast Local Clustering Service
for Wireless Sensor Networks DIWANS 2004

                                                                          3
         Why Control Communications Topology

• High density deployment is common
      • Even with minimal sensor coverage, we get a high density
        communication network (radio range > typical sensor range)
• Energy constraints
      • When not easily replenished
• Power usage
      • Observation: radios consume about the same power in idle
        state than Tx and Rx state
      • Chicken & egg problem: to save energy, radios must be
        turned off (not simply reduce packet transmissions); but if
        radios are turned off, nodes cannot receive messages

                                                                      4
                       Problem Statement(s)

1.   Find an MCDS, i.e. a minimum subset of nodes that is both:
        Set cover
        Connected

2.   Choose a transmit-power level whereby network is connected
     •   per node or same for all nodes
     •   with per node there is the issue of avoiding asymmetric links
     •   cone-based algorithm:
          node u transmits with the minimum power ρu s.t. there is at least
            one neighbor in every cone of angle x centered at u
        k-neighbors algorithm:
          each node chooses nearest k neighbors for its subgraph
          k is chosen s.t. the graph generated is connected w.h.p.
                                                                               5
                        Problem Statement(s)

3.   Find a minimum subset of nodes that provides some density
        in each geographic region  connectivity
        we’ll look at the examples of GAF, SPAN, GS3, ASCENT


4.   Given a connected graph G, find a subgraph G’ which can
     route messages between nodes in energy-efficient way
        both unicast and broadcast spanners
        reduces interference as well


Sub-problems:
     •   Prune asymmetric links
     •   Tolerate node perturbations
     •   Load balance
                                                                 6
Where should TC be positioned in the protocol stack?


No clear answer in the literature

One view:
                     Routing Layer
                       TC Layer
                     MAC Layer

Routing protocol may trigger TC execution (to get better routes)
    Routing (structure) involves only active nodes


MAC protocol may trigger TC execution (if neighborhood changes)
    TC controls coarse-grain duty-cycling, MAC controls fine-grain
    Mode changes need to be coordinated to avoid conflicts
                                                                      7
                   Assumptions: Radio/MAC



•   Circular or Isotropic Models: GS3

•   Grid-based connectivity: GAF, GS3

•   Radio/MAC dependencies:

     802.11 Power Saving mode: Span

     Promiscuous mode: ASCENT, CEC




                                            8
           Assumptions: Neighbor Information


•   Locality:

     1-hop neighbor: GS3, ASCENT

     n-hop neighbor (with various n > 1): GAF, CEC, Span …

     Dependency on routing: GS3, Span




•   Measurement-based: ASCENT, CEC




                                                              9
Properties: Reactivity to dynamics & load balancing


 •   Local re-calculation of state: GS3

 •   Global re-calculation of state: Span

 •   Local recovery: GS3, GAF, CEC, ASCENT

 •   Explicit load balancing mechanisms: GS3, Span, GAF, CEC




                                                           10
                                  SPAN


•   Goal: preserve fairness and capacity & still provide energy savings

•   SPAN elects “coordinators” from all nodes to create backbone

    topology

•   Other nodes remain in power-saving mode and periodically check if

    they should become coordinators

•   Tries to minimize # of coordinators while preserving network capacity

•   Depends on an ad-hoc routing protocol to get list of neighbors & the

    connectivity matrix between them

•   Runs above the MAC layer and “alongside” routing
                                                                           11
          Coordinator Election & Announcement


•   Rule: if 2 neighbors of a non-coordinator node cannot reach each
    other (either directly or via 1 or 2 coordinators), node becomes
    coordinator

•   Announcement contention is resolved by delaying coordinator
    announcements with a randomized backoff delay

•   delay = ((1 – Er/Em) + (1 – Ci/(Ni pairs)) + R)*Ni*T
        Er/Em: energy remaining/max energy
        Ni: number of neighbors for node i
        Ci: number of connected nodes through node i
        R: Random[0,1]
        T: RTT for small packet over wireless link
                                                                       12
                       Coordinator Withdrawal



•   Each coordinator periodically checks if it should withdraw as a coordinator


•   A node withdraws as coordinator if each pair of its neighbors can reach
    each other directly of via some other coordinators


•   To ensure fairness, after a node has been a coordinator for some period of
    time, it withdraws if every pair of nodes can reach each other through
    other neighbors (even if they are not coordinators)


•   After sending a withdraw message, the old coordinator remains active for
    a “grace period” to avoid routing loses until the new coordinator is elected

                                                                              13
Performance Results




                      14
        GAF/CEC: Geographical Adaptive Fidelity


•   Each node uses location information (provided by some orthogonal
    mechanism) to associate itself to a virtual grid


•   All nodes in a virtual grid must be able to communicate to all nodes
    in an adjacent grid


•   Assumes a deterministic radio range, a global coordinate system
    and global starting point for grid layout


•   GAF is independent of the underlying ad-hoc routing protocol


                                                                       15
           Virtual Grid Size Determination




•   r: grid size, R: deterministic radio range

•   r2 + (2r)2  R2

•   r  R/sqrt(5)
                                                 16
                          Parameters settings


•   enat: estimated node active time

•   enlt: estimated node lifetime

•   Td,Ta, Ts: discovery, active,

    and sleep timers

•   Ta = enlt/2

•   Ts = [enat/2, enat]

•   Node ranking:

        Active > discovery (only one node active per grid)

        Same state, higher enlt --> higher rank (longer expected time first)

        Node ids to break ties

                                                                                17
Performance Results




                      18
                             CEC

•   Cluster-based Energy Conservation
•   Nodes are organized into overlapping clusters
•   A cluster is defined as a subset of nodes that are
    mutually reachable in at most 2 hops




                                                         19
                       Cluster Formation


•   Cluster-head Selection: longest lifetime of all its neighbors
    (breaking ties by node id)



•   Gateway Node Selection:

     primary gateways have higher priority

     gateways with more cluster-head neighbors have higher priority

     gateways with longer lifetime have higher priority




                                                                    20
Network Lifetime




                   21
    Challenges for local healing of solid-disc clustering



     (             ) (              ) (             )(        )


                                cascading
             ) (           )(                 ) (        )(
                                A         B
                                new node


•   Equi-radius solid-disc clustering with bounded overlaps
    is not achievable in a distributed and local manner




                                                                  22
                        FLOC protocol


•   Solid-disc clustering with bounded overlaps is achievable
    in a distributed and local manner for approximately equal
    radius
      Stretch factor, m≥2, produces partitioning that respects
       solid-disc
         Each clusterhead has all the nodes within unit radius of itself as
          members, and is allowed to have nodes up to m away of itself




•   FLOC is locally self-healing, for m≥2
      Faults and changes are contained within the respective
       cluster or within the immediate neighboring clusters                    23
                      FLOC program …


•   By taking unit distance to be reliable comm. radius & m
    be maximum comm. radius, FLOC
     exploits the double-band nature of wireless radio-model
     achieves communication- and energy-efficient clustering



•   FLOC achieves clustering in O(1) time regardless of the
    size of the network
     Time, T, depends only on the density of nodes & is constant
     Through simulations and implementations, we suggest a
      suitable value for T for achieving fast clustering without
      compromising the quality of resulting clusters

                                                                    24
                            Model


•   Geometric network, e.g., 2-D coordinate plane

•   Radio model is double-band *
     Reliable communication within unit distance = in-band
     Unreliable communication within 1 < d < m = out-band


•   Nodes have i-band/ o-band estimation capability
     RSSI-based using signal-strength as indicator of distance
     Statistics-based using average link quality as an indicator


•   Fault model
     Fail-stop and crash
     New nodes can join the network
                                                                    25
                  Problem statement


•   A distributed, local, scalable, and self-stabilizing
    clustering program, FLOC, to construct network partitions
    such that
     a unique node is designated as a leader of each cluster

     all nodes in the i-band of each leader belong to that cluster

     maximum distance of a node from its leader is m

     each node belongs to a cluster

     no node belongs to multiple clusters




                                                                      26
            Justification for stretch factor > 2


                ) (                   )(         )(          )
                        new node subsumed


•       For m≥2 local healing is achieved: a new node is
         either subsumed by one of the existing clusters,
         or allowed to form its own cluster without disturbing
          neighboring clusters




    (             ) (                 ) (             )(         )

    (             ) (            )(         )(        )(         )
                                  new cluster
                                                                     27
                     Basic FLOC program

•   Status variable at each node j:
      idle : j is not part of any cluster and j is not a candidate
      cand : j wants to be a clusterhead, j is a candidate
      c_head : j is a clusterhead, j.cluster_id==j
      i_band : j is an inner-band member of a clusterhead
       j.cluster_id; a clusterhead itself is an i_band member
      o_band :j is an outer-band member of j.cluster_id
•   The effects of the 6 actions on the status variable:




                                                                      28
                      FLOC actions


1.   idle Λ random wait time from [0…T] expired                 
     become a cand and bcast cand msg

2.   receiver of cand msg is within in-band Λ its status is i_band
         receiver sends a conflict msg to the cand

3.   candidate hears a conflict msg                             
     candidate becomes o_band for respective cluster

4.   candidacy period Δ expires                                 
     cand becomes c_head, and bcasts c_head message

5.   idle Λ c_head message is heard                             
     become i_band or o_band resp.

6.   receiver of c_head msg is within in-band Λ is o_band
         receiver joins cluster as i_band                       29
                              FLOC is fast


•   Assumption: atomicity condition of candidacy is observed by T


•   Theorem: Regardless of the network size FLOC produces the
    partitioning in T+Δ time


•   Proof:
     An action is enabled at every node within at most T time
     Once an action is enabled at a node, the node is assigned a
      clusterhead within Δ time
     Once a node is assigned to a clusterhead, this property cannot be
      violated
         action 6 makes a node change its clusterhead to become an i-band
         member, action 2 does not cause clusterhead to change

                                                                             30
                 FLOC is locally-healing


•   Node failures
     inherently robust to failure of non-clusterhead members

     clusterhead failure detected via “lease” mechanism, the
      orphaned nodes execute clustering ---see node additions



•   Node additions
     either join existing cluster, or

     form a new cluster without disturbing immediate neighboring
      clusters



                                                                31
             Extensions to basic FLOC algorithm


•   Extended FLOC algorithm ensures that solid-disc property is
    satisfied even when atomicity of candidacy is violated
    occasionally


•   Insight: Bcast is an atomic operation
     Candidate that bcasts first locks the nodes in the vicinity for Δ
      time
     Later candidates become idle again by dropping their candidacy
      when they find some of the nodes are locked


•   4 additional actions to implement this idea



                                                                          32
                   Simulation for determining T


•   Prowler, realistic wireless sensor network simulator
      MAC delay 25ms


•   Tradeoffs in selection of T
      Short T leads to network contention, and hence, message losses
      Tradeoff between faster completion time and quality of clustering


•   Scalability wrt network size
      T depends only on the node density
         In our experiments, the degree of each node is between 4-12
      a constant T is applicable for arbitrarily large-scale networks



                                                                           33
     Tradeoff in selection of T

                                      40

                                      35




                                           Number of atomicity violations
                                      30

                                      25

                                      20

                                      15

                                      10

                                      5

                                      0
20    15             10     5     0
           T (sec)                                                          34
Constant T regardless of network size




                                        35
                   Implementation




•   Mica2 mote platform, 5-by-5 grid
•   Confirms simulation
                                       36
Sample clustering with FLOC




                              37
                    GS3: Scalability via locality


•   Locality is hard for some graph problems                                    14 0
       e.g., self-configuration and self-healing of
        routing tree                                                    1                       1
                                                                0                           5


                                                            2                           2                  2
                                                    7                              8                   3
•   An ideal goal for locality:
    self-healing should be a function of the                        3
                                                                                                3              3

    size of perturbation (in time, space,                   9                               1                  6

    and energy)
                                                                                 10 4                  12 4


                                                                    2       5
                                                                                                13 5
•   Locality depends on model
                                                4       6                              11 6


                                                                                                                   38
                               System model


•   System
     multiple “small” nodes and one “big” node, on a plane
     node distribution
          density: ( Rt s.t. with high probability,
                        there are multiple nodes in any circular area of radius Rt)
          localization: relative location between nodes can be estimated


•   Perturbations
       dynamic nodes
          joins, leaves (deaths), state corruptions
       mobile nodes




                                                                                 39
    Problem: Geography-aware self-configuration


•   Geographic radius of clusters is crucial
       for communication quality, energy dissipation, data aggregations &
        applications



•   Problem statement
       Given
         R: ideal cell radius (R > Rt)

       Construct a set of cells , connected via a “head” node in each cell s.t.
          radius of each cell is in [ R-c , R+c ] , where c = f (Rt)
          each node belongs to only one cell
          cells and the connectivity graph over head nodes self-heal locally


                                                                                   40
                       Static networks


•   An ideal case:

                                               (IL = Ideal Location)

                                          Rt
                                 IL2
                     R 3R
                      IL1


•   In reality: no node may exist at some geometric centers (ILs),
    but, with high probability there are nodes no more than Rt away
    from any IL
                                                                       41
           How to find the set of cell heads


•   Bottom-up ?
       hard to guarantee the
        placement and size of
        clusters


•   Top-down w.r.t. big node
       use diffusing computation
                                           H0
       but, accumulation in

                                                i
                                     GAP
        deviation of head location
        from IL is a problem
                                     Rt




                                                    42
            Organizing neighboring clusters & heads

                                                                   IL(p.i)
Deviation problem is handled locally
      instead of using real locations, node i
                                                                    IL(i)
       uses its and its parent’s ILs                          -60o 60o      a
      i calculates the ILs of next band cells in        Rt         3R             RD
                                                    LD
       its search region < LD , RD >
         big node:     <0o , 360o>
                                                                   i2     search region

         other nodes: <-60o-a , 60o+a> , where
                               a  Sin-1(Rt / R)                   GR

      for each IL, i ranks nodes within Rt
                                                              Rt    A       j
       radius of the IL (by <D, A>), and selects
                                                                   i2 D
       the highest ranked node as the
       corresponding cluster head                                                   43
                   Summary: static networks


•   Cell structure is hexagonal
        cell radius:   [ R  (2   3) Rt , R  (2   3) Rt ]

•   Time taken to form the structure is (Db), where Db = the maximum
    distance between the big node and the small nodes


•   Scalability in self-configuration:          3R  2Rt
        local coordination: only with nodes within range
        local knowledge: each node maintains info about a constant number of
         nearby nodes




                                                                                44
                     Dynamic networks


•   Dynamics include:
       node join, leave (death), state corruption


•   Common vs. rare
     common perturbations: node density is preserved
     rare perturbations: node density is destroyed



•   Scalable self-healing is achieved via locality in:
     intra-cell healing
     inter-cell healing
     sanity checking of state (invariants)

                                                         45
                          Local intra-cell healing


•   Head shift                                                      GR


        upon head leaving (death)                    R
                                                                     IL
        local in a radius of Rt                               Rt




•   Cell shift
        upon the death of all the nodes in an area        GR
         of radius Rt                                                0
        local in a radius of R                                           1
                                                                              2
        independent but consistent shift at
                                                      Rt            OIL
         individual cells  sliding of the global
                                                           R
                                                                          1
         head level structure                                                 2

                                                                                  46
       Local inter-cell healing & sanity checking


•   Local inter-cell healing :
    upon failure of intra-cell healing at head j,
     first, the parent of j tries to find a new head j’
     if that fails, the children of j find new parents


•   Local sanity checking of state invariants :
    upon detecting violation of the hexagonality property,
     node corrects itself after checking with its neighbors
     when state perturbation includes several nodes, the
      perturbed region corrects itself from the outside going
      in, and all nodes are corrected within time proportional
      to size of perturbed region
                                                                 47
              Summary: dynamic networks


•   Cell radius
     for cells not adjoining any gap: [ R  (2    3) Rt , R  (2   3) Rt ]
     for cells adjoining a gap:        [ R  (2   3) Rt , R  (2    3) Rt  d p ]


•   Head tree is now minimum distance tree rooted at the
    big node


•   Stabilization time from perturbed state: (Dp), where
    Dp = diameter of the continuously perturbed area




                                                                                     48
        Summary: dynamic networks             (contd.)



•   Scalability in self-healing:
     local fault-containment and healing
     local knowledge


•   Local healing and fault-containment enables
     stable cell structure
     lengthened lifetime: (nc) , where nc = the number of nodes
       in a cell




                                                                49
                            Related work


•   Cellular hexagon structure (Mac Donald ’79)
     Preconfigured & not considering self-healing


•   LEACH (Heinzelman et al ’00)
     No guarantee about the placement and size of clusters
     Perturbations dealt with by globally repeating the whole
       clustering process

•   Logical-radius based clustering (in Banerjee ’01)
     non-local cluster maintenance, and no consideration of state
       corruption
     only logical radius  long links and link asymmetry are possible
     multiple rounds of diffusion
                                                                         50
                                     ASCENT

•   Adaptive Self-Configuring sEnsor Networks Topologies

•   Observation: different applications may require the underlying
    topology to have different characteristics. For example:
       Minimal
       Homogeneous with a certain degree of connectivity
       Heterogeneous with different degrees of connectivity in different regions


•   Examples of these different regions may be:
       Along a data flow path
       Avoiding a data flow path
       In the border of an event of interest

•   Input: application tolerance specified in terms of acceptable loss rate
    at any node
                                                                                    51
                                 Model


•   Adapt to empirical measurements of link quality: each node assesses
    its connectivity & adapts its participation in the multi-hop topology
    based on the measured operating region


•   Assumptions: ASCENT needs to
     turn off the radio (sleep state)

     turn the NIC/MAC in promiscuous mode (passive state)



•   ASCENT runs on top of MAC and below routing; does not uses any
    information gathered by routing

                                                                            52
                                      ASCENT Basics

• Node state: active or passive
   – Active nodes are in topology & forward data packets (using
     orthogonal routing mechanism that runs on topology)
   – Passive nodes can sleep or collect network measurements

• Each node measures # of neighbors and packet loss locally

• Each node then decides to join the network topology or to adapt
  (e.g. reducing its duty cycle to save energy)
                        Help          Neighbor
                        Messages      Announcements                          Data
     Data Message                     Messages                               Message

     Source                    Sink                           Sink         Source                 Sink
                                       Source

                                      Passive Neighbor      Active Neighbor

      (a) Communication Hole           (b) Self-configuration transition        (c) Final State          53
                       State Transitions


                                            after Tt
                              Test                          Active

neighbors < NT
                                   neighbors > NT (high ID for ties)
and
                                   or
• loss > LT
                                   loss > loss T0
• loss < LT & help
                                             after Tp

                           Passive                               Sleep
                                              after Ts
    NT: neighbor threshold
    LT: loss threshold
    Tx: state timer values (x = p: passive, s: sleep, t: test)

                                                                         54
                                  Details


•   Each node adds a sequence number per packet (for loss detection)

•   Neighbor estimator: based on a neighbor loss threshold (NLT) = 1 –
    1/N (N: number of neighbors in the previous cycle)

•   Neighbor threshold value (NT) determines the average degree of
    connectivity in the network


•   Loss threshold determines the maximum data loss application can
    tolerate


•   Relation between Tp/Ts (passive & sleep timers) determines amount
    of energy savings and convergence time                               55
                         Performance Results




Energy Savings (normalized to the Active case, all nodes turn on) as a function of
density. ASCENT provides energy savings up to 5.5 times for high density scenarios
                                                                                56
                 ASCENT Energy Savings Analysis

                                            n * Idle
ES (n ) 
                                               Tp                            Ts
             NT * Idle  (n  NT ) * Idle *           (n  NT ) * Sleep *
                                            Tp  Ts                        Tp  Ts
NT: neighbor threshold
Tp: passive state timer
Ts: sleep state timer
Sleep: power radio off
Idle: power radio on
 = Tp/Ts
 = Sleep/Idle = 0.004
                        n
ES ( n ) 
                                 
             NT  ( n  NT ) *
                                  1
               1
 lim ES 
n           
                                                                                     57
    Topology Control from a Sensing Perspective

So far we have considered only the communications perspective

Sensing coverage model:
    typically unit disk sensing
    note: depends on object being sensed


Node deployment model:
    deterministic with (no failures or with isolated failures)
    approximated by a pdf or is random (as a result of rampant errors)


Coverage requirements:
    Point coverage (deterministic or probabilistic guarantee)
    Barrier coverage (deterministic or probabilistic guarantee)
    Worst-case coverage: least exposed path
    Tracking coverage: any uncovered path has length at most l           63
                Sensing Coverage References


•   Survey:
        “Coverage in Wireless Sensor Network”, Mihaela Cardei, Jie Wu

•   For 1-coverage:
        Pater Hall, "An Introduction to the Theory of Coverage
    Processes”, 1988


•   For k-coverage:
        Santosh Kumar and Balogh, Mobisys 2004


•   For k-coverage poisson deployment:
        Honghai Zhang and Jennifer Hou, Mobihoc 2004


                                                                    64
                         Coverage Results


•   1-point coverage with deterministic placement:
     hexagonal layout is optimal


•   k-point coverage with deterministic placement :
     question of optimal placement is open


•   k-point probabilistic coverage:
     almost always k-coverage for poisson deployment

               nr2 ≥ ln(n) + k ln(ln(n)) + … (error term)
        where n is #sensors and r is sensing radius

     almost always k-coverage for random uniform deployment
        has essentially same result                            65
                       Coverage Algorithms


•   Checking whether network is not suitably covered
       point coverage violation check is possible locally



•   Maintaining coverage via sleep-wakeup
       optimal scheme is NP-Complete, if deployment unknown
        (so heuristics used)
       random independent scheduling, if deployment uniformly random
       sentry rotation between redundant nodes in each cluster/region




                                                                         66
    Both Communication and Sensing Topology Control


•   Relation between sensing radius and communication radius


•   If        Comm radius ≥ 2 x Sensing radius
    then      (k-coverage  k-connectivity)




                                                               67

								
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