Title: Constrained Random Walks on Random Graphs: Routing Algorithms for Large Scale Wireless Sensor Networ
1Constrained Random Walks on Random Graphs
Routing Algorithms for Large Scale Wireless
Sensor Networks
Sergio D. Servetto, Cornell University
Guillermo Barrenechea, Ecole Polytechnique
Federale de Lausanne
- Presented by Guangyu Dong
2Outline
- Contribution
- Motivation Background
- Related Work
- Random Walk Approaches
- For regular and static graphs
- For irregular and static graphs
- For dynamic graphs
- Summary Comments
3Contribution
- A routing protocol for WSN that tries to do load
balancing among intermediate nodes. - Making use of multiple paths that exist from
source to destination by making local packet
forwarding decisions A novel approach to
implicitly maintain multipath - Current algorithm is only valid for grid-topology
sensor network
4Motivation
- Consider the routing in a large-scale WSN with
unreliability and dynamics - A single node has limited capacity
- The unique characteristics of WSN calls for
multipath routing techniques - Searching for possible routes?
- Route creation and destruction?
- Random walk approach use an implicit way to solve
these two problems
5Multiple Paths Routing
- Advantages
- Minimize critical points of failure
- Achieve load-balancing
- Disadvantages
- More energy consumption
- Not Clear
- Performance?
- Security?
6Ways to Do Multipath Routing
- Highly-resilient, energy-efficient multipath
routing - Routes packet through a primary path while
maintaining several other paths as backup. - Trajectory-based routing
- Each time source can randomly select a path for
the packet - Stateless
- SPEED
- Each packet has an unanticipated path.
- Stateless
- Is it really a multipath routing protocol?
- Random Walk
- Packet goes to a random direction at each node
- Not stateless
7Random Walk Approach
- Decentralized algorithms
- Complexity independent of the size of the network
- Dependence on the state of other nodes decays
with separation distance - Taking advantage of a vast number of multiple
paths without explicitly listing them. - Walking is constrained
- Packets visit nodes on short (low delay) routes??
- The number of packets that visit a node is
independent of the particular node
8Assumptions and goals
- Infinite lifetime via renewable energy source
- Goal is to preserve energy to maximize node
throughput while still alive - As opposed to finite lifetime where the goal is
to preserve energy to prolong existence of the
network - So will it still work when some kind of power
control mechanism is used? For example, ASCENT or
SPAN? - The network is a grid
- The approach has a big dependence on graph
structure - No straightforward way to extend to a random
graph - Every node know its distance to source and
destination
9Forwarding Decision based on PDF
u1
p1
u2
p2
v
..
pn
un
10Forwarding Decision in Grid
u4
p4
p1
v
u3
u1
p3
i,j
p2
u2
11Notation and Terminology
- N(v)u1,,un_v-neighbors of v
- ?vp1,,pn_v-pdf over neighbors of v
- GNgrid of size NxN
- D(l)-set of nodes on lth diagonal
- dei,j-distance from node i,j to nearest
boundary node - Expansion region packets move across diagonals
with increase in number of nodes (decrease in
pkt/node density) - Compression region opposite of expansion
12Graph GN
13Expansion Compression Regions
Compression Region
Expansion Region
14Regular, static graphs (RSG)
- Network is grid such that each interior node has
4 neighbors - Constraints
- (c.1) Packet will not go backward
- (c.2) For nodes on a same diagonal, they must be
visited equally often
The diagonals close to source and destination
only have a few nodes. Does it still make sense
to do load balancing?
15Sampling pdf for uniform packet distribution
- A packet at node i,j makes a binary decision to
move to i1,j or i,j1 (c.1) with some
probability p (by convention, to node closer to
boundary)
16RSG Examples (N4)
- In the expansion stage, packet is more likely to
be forwarded toward the boundary - In the compression stage, packet is more likely
to be forwarded apart from the boundary - All possible paths have the same length
17Simulation Results (RSG)
A Random walk based on flipping a fair coin.
A Random walk based on RSG algorithm
18Distributed Computation of Coordinates
- Each node simply needs to know its own
coordinates - Find coordinates using Distributed Bellman Ford
algorithm (local message exchange) - Only good for a grid
- An initializing process necessary
- Introduces delay for initial packets
19Irregular, static graphs (ISG)
- Same as RSG but delete a random set of nodes
permanently - Impossible to achieve exact load balancing
- Use node labels (s,d)( routes to source,
routes to destination) - Can compute labels using recursion
- number of routes to a node is the sum of the
numbers of routes at the two previous nodes - Still a GRID!
20Example of Node Labels (N4)
21Forwarding pdf on a best-effort basis
- The probability that v will forward packet to the
node (s1, d1) and (s2, d2) - Pex (s lt d) Packet more likely forwarded to node
with less source routes - Pcmp(sgtd) Packet more likely forwarded to node
with more destination routes
22ISG Examples (N4)
Ideal Case Equivalent to RSG
General Case
23Simulation Results (ISG)
A Random walk based on flipping a fair coin.
A Random walk based on ISG algorithm
24Dynamic Graphs (DG)
- Same as ISG but nodes turn ON/OFF independently
over - When a node changes state the one-hop neighbors
change labels and possibly trigger further label
changes - More than half of the NN nodes will be affected
- Packet may be routed to a dead end due to delayed
propagation of labels change, which will result
in packet delay or loss. - Concerns
- Delays in propagating updates
- Sensitivity to inaccuracies in labels
Remember the first assumption?
25The Overhead
- A large number of nodes need to keep a state for
each stream - An initializing process to compute labels for all
nodes - Beacon messages exchanged between neighboring
nodes - Check if neighbors are alive
- Exchanging labels
- State change of a node will affect a large part
of the network. The degree of influence depends
on the distance between changing node and
source/destination.
26Simulation Results (DG)
A Random walk based on DG algorithm
A Random walk based on flipping a fair coin.
27More Simulation Results (DG)
28Open Issues
- Extends to general graph?
- Each node has arbitrary number of neighbors
- How to trade off between delay and load
balancing? - The overhead to compute and maintain the labels
depends on how many nodes are in the rectangle
area - Design algorithm under the same principles
- Pex (s lt d) Packet more likely forwarded to node
with less source routes - Pcmp(sgtd) Packet more likely forwarded to node
with more destination routes
29Summary Comments
- A decentralized random walk algorithm to do
multipath routing - Highly topology dependent algorithm is hard to
extend to generally random graph - Mobility not addressed
- All intermediate nodes have to keep routing state
(NN) with considerable overhead - A large number of nodes will be affected when a
node switch between ON/OFF. - An unrealistic energy model
- Inappropriate for multiple or dynamic packet
streams
30GS3 Scalable Self-configuration and Self-healing
in Wireless Networks
- Hongwei Zhang, Anish Arora
- Computer Science Department
- The Ohio State University3
31Outline
- Contributions
- System models and goals
- GS-3 Algorithms
- For static network
- For dynamic network
- For dynamic and mobile network
- Problems
- Conclusion
32Contributions
- An algorithm aiming to organize wireless network
into a ideal cellular hexagonal structure - Self-healing under perturbations
- The clustering criteria, Geographic radius , is
taken into consideration which many previous
works didnt - Scalability in large scale multi-hop wireless
networks achieved by divide and conquer strategy
33Geographic Radius Cluster
Density of wireless network increases
Cluster with fixed radius
Radius is limited by maximum transmit range
Head Graph
34Related Work
- SPAN ASCENT
- Kind of clustering protocol (active node is
cluster head) - No big node
- For power control purpose, other nodes will sleep
- What if other nodes dont sleep?
- Can GS-3 be used for power control?
- Many Other Clustering Algorithms
- Geographic radius or Logical radius
- Local or Global self-stabilizing
- Some of them are for energy saving
35Cellular Structure
36System Models
- Node Distribution Assumption
- there are multiple nodes in each circular area of
radius Rt (radius tolerance) - Every node know its location
- Wireless Transmission Assumption
- Nodes adjust the transmission range
- Message transmission is always reliable
- Perturbation Models
- Dynamics nodes leaving, joins, deaths and state
corruptions - Mobility nodes movements.
- Perturbation Frequency
- Joins, leaves and death are unanticipated and
rare, while node death is predictable - The probability that a node moves distance d is
proportional to 1/d
37Goals
- Each cell has radius of Rc (c is a function of
Rt)?? - Each node in at most one cell
- A node in a cell if and only if its connected to
the big node - Number of children for each node in head graph is
bounded (6) - Self-healing in the presence of dynamics and
mobility
38Definitions
39Algorithm for Static Networks
- No perturbation, no Rt gap
- Always H0 starts to be a head
- A head search for new heads in search region
- For H0, the search region is the whole 1-band
- Cell heads in search region are selected by i
- Nodes not selected as head choose their best heads
Will a node in k-band always have a parent from
(k-1)-band?
40Dynamic Network
- Perturbations
- Joining, leaving and death of nodes
- State corruption
- Rt gap
- Maintenance Mechanisms
- Head shift
- Cell shift
- Cell abandonment
- State check
41Algorithm for Dynamic Network
- Head selection same as GS-3 S
- Rt gap
- No head is selected
- Nodes become associates of neighboring cells
- Parent does periodical check
- Node join
- Try to find the best head
- If fails, try to find a potential head from
associates - If still fail, retries later.
- If a head is announcing itself, it selects this
head as its head - Node leaves or dies
- Intra-cell maintenance head shift, cell shift,
cell abandon - Inter-cell maintenance cell is monitored and
recovered by parent and children heads if
intra-call operation fails - It the parent fails then the children finds other
parents
Why not RtR?
42Cell Maintenance
- Cell will be abandoned when distance between IL
and IL of some neighbor is beyond v3R-2Rt,
v3R2Rt. (Rt gap!!) - Abandoned cell will be restored later if possible
- The whole head graph will slide as a whole?
- Traffic load cannot be uniform
- Density varies across the network
- Central cell usually will not shift
43Algorithm for Dynamic Network (cont)
- Associate node always tries to find better head
- Head node always tries to find better parent
- State corruption (done by head)
- Periodical sanity checking (for invariants and
fixpoint) on hexagonal relation. - If checking fails, ask neighboring heads to check
their state - If all neighboring heads are valid, its state is
corrupted, then node becomes an associate - Otherwise, cannot decide????
- What if perturbations are not isolated??
- Will the algorithm still converge?
- Need theoretical verification or validation from
simulations
44Problems
- Continuous Rt gap? (see next page picture)
- A connectable node is possibly not connected to
the big node. So the third goal cannot be
achieved - How can we guarantee a safe leaving?
- Whats the transmission range of associate node
and head node? Is there difference between them?
45Coutinuous Rt Gap
46Mobile Dynamic Network
- Small node movements leaves at old location,
joins at new location - Big node movements
- The closest head becomes the proxy of big node
- The proxy becomes the root of the head graph
What if big node moves to a null cell?
47Example of Big Node Movement
48Problems
- How to put all these complicated mechanisms
together? - What if perturbations are not isolated? Will the
algorithm still converge?? - Control overhead
- Need to be validated by simulations
49Summary Comments
- Algorithm tries to organize wireless network into
a ideal cellular hexagonal structure with fixed
cell radius - Try to do self-healing when assuming isolated
perturbations - Some of the mechanisms are not likely to work
- A complicated theoretical protocol without clear
analysis or validation by simulation result - What kind of application can we run on this
structure? - Whats the overhead to maintain this structure?
50Roads of Developing Algorithm