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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

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 NetworksDIWANS 2004

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

Problem Statement(s)

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

Problem Statement(s)

- 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
- 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

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

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

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

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

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

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

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

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

Virtual Grid Size Determination

- r: grid size, R: deterministic radio range
- r2 + (2r)2 R2
- r R/sqrt(5)

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

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

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

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Challenges for local healing of solid-disc clustering- Equi-radius solid-disc clustering with bounded overlaps is not achievable in a distributed and local manner

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

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

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

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

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new node subsumed

Justification for stretch factor > 2- 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

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new cluster

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:

FLOC actions

- idle Λ random wait time from [0…T] expired become a cand and bcast cand msg
- receiver of cand msg is within in-band Λ its status is i_band receiver sends a conflict msg to the cand
- candidate hears a conflict msg candidate becomes o_band for respective cluster
- candidacy period Δ expires cand becomes c_head, and bcasts c_head message
- idle Λ c_head message is heard become i_band or o_band resp.
- receiver of c_head msg is within in-band Λis o_band receiver joins cluster as i_band

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 Δtime
- 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

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

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

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

Implementation

- Mica2 mote platform, 5-by-5 grid
- Confirms simulation

GS3: Scalability via locality

- Locality is hard for some graph problems
- e.g., self-configuration and self-healing of routing tree
- An ideal goal for locality: self-healing should be a function of the size of perturbation (in time, space, and energy)
- Locality depends on model

System model

- System
- multiple “small” nodes and one “big” node, on a plane
- node distribution
- density: ( Rts.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

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

Static networks

- An ideal case:
- 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

(IL = Ideal Location)

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
- but, accumulation in deviation of head location from IL is a problem

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Organizing neighboring clusters & heads

Deviation problem is handled locally

- instead of using real locations, node i uses its and its parent’s ILs
- i calculates the ILs of next band cells in its search region < LD , RD >
- big node: <0o , 360o>
- other nodes: <-60o-a , 60o+a> , where a Sin-1(Rt / R)
- for each IL, i ranks nodes within Rt radius of the IL (by <D, A>), and selects the highest ranked node as the corresponding cluster head

Summary: static networks

- Cell structure is hexagonal
- cell radius:
- 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:
- local coordination: only with nodes within range
- local knowledge: each node maintains info about a constant number of nearby nodes

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)

Local intra-cell healing

- Head shift
- upon head leaving (death)
- local in a radius of Rt
- Cell shift
- upon the death of all the nodes in an area of radius Rt
- local in a radius of R
- independent but consistent shift at individual cells sliding of the global head level structure

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

Summary: dynamic networks

- Cell radius
- for cells not adjoining any gap:
- for cells adjoining a gap:
- 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

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

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

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

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

Messages

Help Messages

Data Message

Data Message

Source

Source

Sink

Sink

Sink

Source

Passive Neighbor

Active Neighbor

(a) Communication Hole

(b) Self-configuration transition

(c) Final State

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)

Test

Active

- neighbors < NT
- and
- loss > LT
- loss < LT & help

neighbors > NT (high ID for ties)

or

loss > loss T0

after Tp

Sleep

Passive

after Ts

State Transitions

NT: neighbor threshold

LT: loss threshold

Tx: state timer values (x = p: passive, s: sleep, t: test)

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

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

ASCENT Energy Savings Analysis

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

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

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

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

nr2 ≥ 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

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

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)

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