Network Routing: Metrics and NonTraditional Routing

1
Network Routing Metrics and Non-Traditional
Routing

• Y. Richard Yang
• 2/26/2009

2
Admin.

• Project propose due
• Friday

3
Recap Key Problems

• Forwarding and location management
• Routing
• due to node mobility/wireless connectivity, link
  connectivity/quality can be highly dynamic
• need to design routing protocols that are
  effective in handling dynamic topologies
• there can be interference among links and paths
• need good link performance metrics or scheduling

4
Recap Routing Protocols

• Proactive protocols
• distance vector
• e.g., DSDV
• link state
• link reversal
• e.g., partial link reversal, TORA
• Reactive protocols
• DSR
• AODV

5
Recap ETX

• ETX The predicted number of data transmissions
  required to successfully transmit a packet over a
  link
• Link loss rate p
• Expected number of transmissions
• Problems of using ETX in 802.11 networks?

6
Problems of ETX

• ETX does not handle multirate 802.11 networks
• ETX does not work out well when nodes have
  multiple radios working on different channels

7
Extending ETX Multirate

• In a multirate environment, need to consider link
  bandwidth
• packet size S, Link bandwidth B
• each transmission lasts for S/B

Routing in Multi-radio, Multi-hop Wireless Mesh
Network, Richard Draves, Jitendra Padhye, and
Brian Zill. Mobicom 2004.
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Extending ETX Multirate

• Add ETTs of all links on the path
• Use the sum as path metric
• Interpretation pick a path with the lowest total
  network occupation time
• Q under what condition is SETT total network
  occupation time?

9
Extending ETX Channel Diversity with Multiradio
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Impact of Interference

• Interference reduces throughput
• throughput of a path is lower if many links are
  on the same channel
• path metric should be worse for non-diverse paths

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Combining Link Metric into Path Metric Proposal 2

• Group links on a path according to channel
• assumes links on the same channel interfere with
  one another
• pessimistic for long paths
• Add ETTs of links in each group
• Find the group with largest sum (BG-ETT)
• this is the bottleneck group
• too many links, or links with high ETT (poor
  quality links)
• Use this largest sum as the path metric
• Lower value implies better path

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BG-ETT Example
0
5.33 ms
5.33 ms
1.5 Mbps
1.33 ms
4 ms
4 ms
2 Mbps
2.66 ms
2.66 ms
2.66 ms
3 Mbps
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BG-ETT May Select Long Paths
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Path Metric Putting it all together

• SETT favors short paths
• BG-ETT favors channel diverse paths
• ß is a tunable parameter
• Higher value more preference to channel
  diversity
• Lower value more preference to shorter paths

15
Implementation and such

• Measure loss rate and bandwidth
• loss rate measured using broadcast probes similar
  to ETX
• updated every second
• bandwidth estimated using periodic packet-pairs
• updated every 5 minutes
• Implemented in a source-routed, link-state
  protocol, Multi-Radio Link Quality Source Routing
  (MR-LQSR)
• nodes discover links to its neighbors, measure
  quality of those links
• link information floods through the network
• each node has full knowledge of the topology
• sender selects best path
• packets are source routed using this path

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Evaluations
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Media Throughput (Baseline, single radio)
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Media Throughput (Baseline, two radios)
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Impact of ß value
Channel diversity is important especially for
shorter paths
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Summary

• Link metrics are still an active research area

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Summary Traditional Routing

• So far, all routing protocols in the framework of
  traditional wireline routing
• a graph representation of underlying network
• point-to-point graph edges with costs
• select a lowest-cost route for a src-dest pair
• commit to a specific route before forwarding
• Problems dont fully exploit path (spatial)
  diversity and wireless broadcast opportunities

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Outline

• Admin.
• Link metrics
• Non-traditional routing

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Motivating Scenario I

• Assumes independent loss
• Tradition routing has to follow one pre-committed
  route
• Does not allow exploration of opportunities

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Motivating Scenario II

• Traditional routing picks a single route, e.g.,
  src -gt B -gt D -gt dst
• packets received off path are useless
• However, one should take advantage of
  transmissions that reach unexpectedly far or
  unexpectedly short

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Motivating Scenario III

• A sends 1 packet to B B sends packet 3 to A
• If R has both packets 1 and 3, it can combine
  them and explore coding and broadcast nature of
  wireless

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Outline

• Admin.
• Link metrics
• Non-traditional routing
• motivation
• network coding exploiting network broadcast

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Coding

• We have covered source coding (FEC, compression)
• The new approach uses opportunistic network
  coding
• goal increase the amount of information that is
  transported

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Opportunistic Coding
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Outline

• Admin.
• Link metrics
• Non-traditional routing
• motivation
• network coding exploiting network broadcast
• opportunistic routing ExOR

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Opportunistic Routing (ExOR)

• Group packets into batches
• Instead of choosing a fix sequential path (e.g.,
  src-gtB-gtD-gtdst), the source chooses a list of
  forwarders (a forwarder list in the packets)
  using ETX-like metric
• a background process collects ETX information via
  periodic link-state flooding
• Forwarders are prioritized by ETX-like metric to
  the destination

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ExOR Forwarding

• The highest priority forwarder transmits when the
  batch ends
• The remaining forwarders transmit in prioritized
  order
• each forwarder forwards packets it receives yet
  not received by higher priority forwarders
• status collected by batch map
• A nodes stops sending the remaining packets in
  the batch if its batch map indicates over 90 of
  this batch has been received by higher priority
  nodes
• the remaining packets transferred with
  traditional routing

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Batch Map Example

• Batch map indicates, for each packet in a batch,
  the highest-priority node known to have received
  a copy of that packet

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Example Timeline
Forwarder list N24(dst), N20, N18, N11, N8, N17,
N13, N5(src)
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Evaluations

• 65 Node pairs
• 1.0MByte file transfer
• 1 Mbit/s 802.11 bit rate
• 1 KByte packets
• EXOR bacth size 100

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Evaluation 2x Overall Improvement
1.0
0.8
0.6
Cumulative Fraction of Node Pairs
0.4
0.2
ExOR
Traditional
0
0
200
400
600
800
Throughput (Kbits/sec)

• Median throughputs 240 Kbits/sec for ExOR,
• 121 Kbits/sec for Traditional

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25 Highest throughput pairs
1 Traditional Hop 1.14x
2 Traditional Hops 1.7x
3 Traditional Hops 2.3x
1000
ExOR
Traditional Routing
800
600
Throughput (Kbits/sec)
400
200
0
Node Pair
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ExOR uses links in parallel

• ExOR
• 7 forwarders
• 18 links

• Traditional Routing
• 3 forwarders
• 4 links

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ExOR moves packets farther
0.6
ExOR
Traditional Routing
Fraction of Transmissions
0.2
0.1
0
0
100
200
300
400
500
600
700
800
900
1000
Distance (meters)

• ExOR average 422 meters/transmission
• Traditional Routing average 205 meters/tx

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Comments

• Pros
• takes advantage of link diversity (the
  probabilistic reception) to increase the
  throughput
• does not require changes in the MAC layer
• can cope well with unreliable wireless medium and
  mobility
• Cons
• maybe hard to scale to a large network
• overhead in packet header (batch info)
• batches increase delay

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Outline

• Admin.
• Link metrics
• Non-traditional routing
• motivation
• network coding exploiting network broadcast
• opportunistic routing ExOR
• opportunistic routing MIXIT

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Mesh Networks Borrowed the Internet API
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Wireless Naturally Provides Reliability Across
Links
99 (10-3 BER)
0
D
S
0
99 (10-3 BER)
Even 1 bit in 1000 incorrect ? Packet loss of 99
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Implication
99 (10-3 BER)
Loss
0
D
S
Loss
0
99 (10-3 BER)
Link by link reliability ? 50 transmissions
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Wireless Naturally Provides Reliability Across
Links
99 (10-3 BER)
0
D
S
0
99 (10-3 BER)
Spatial diversity Even if no correct packets,
every bit is likely received correctly at some
node
Current contract ? 50 tx ? Low throughput
Exploit wireless characteristics ?3 tx ? High
throughput
Exploit wireless characteristics ?3
transmissions
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Useful with High Quality Links?
R1
1
0
Loss
Sa
Da
0
Pa
2
R2
Loss
R3
1
Loss
0
Db
Sb
0
R4
3
Pb
Loss
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Useful with High Quality Links?
R1
1
0
Sa
Da
0
Pa
2
R2
R3
1
0
Current contract ? Inhibits concurrency Exploit
wireless characteristics ? Enables high
concurrency
Db
Sb
0
R4
3
Pb
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Current Contract

• Limits throughput, inhibits concurrency

New Contract Exploiting Wireless Characteristics

• High throughput, high concurrency

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MIXIT

• New contract between layers to harness wireless
  characteristics
• Novel symbol-level network code that scalably
  routes correct symbols
• High concurrency MAC
• Implementation and evaluation
• 3-4x gain over shortest path routing
• 2-3x gain over packet-level opp. routing

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How does a Router Identify Correct Symbols?

• PHY already estimates a confidence for every
  decoded symbol JB07
• PHY LL delivers high confidence symbols to
  network layer

PHY Confidence
Packet
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What Should Each Router Forward?
D
S
P1
P2
P1
P2
P1
P2
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What Should Each Router Forward?
D
S
P1
P2
P1
P2
P1
P2

• But overlap in correctly received symbols
• Potential solutions
• Forward everything ? Inefficient
• Coordinate ? Unscalable

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MIXIT Prevents Duplicates using Symbol Level
Network Coding
D
S
P1
P2
P1
P2
P1
P2
Forward random combinations of correct symbols
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MIXIT Prevents Duplicates using Symbol Level
Network Coding
Routers create random combinations of correct
symbols
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MIXIT Prevents Duplicates using Symbol Level
Network Coding
Solve 2 equations
Randomness prevents duplicates without
co-ordination
Destination decodes by solving linear equations
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MIXIT Prevents Duplicates using Symbol Level
Network Coding
Routers create random combinations of correct
symbols
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MIXIT Prevents Duplicates using Symbol Level
Network Coding
Solve 2 equations

• Symbol Level Network Coding
• No duplicates ? Efficient
• No coordination ? Scalable

Destination decodes by solving linear equations
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Destination needs to know which combinations it
received
(if both symbols were correct)
(if only s1 was correct)
(if only s2 was correct)
Nothing
(if neither symbol was correct)
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Destination needs to know which combinations it
received
Use run length encoding
Coded Packet
Original Packets
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Destination needs to know which combinations it
received
Use run length encoding
Coded Packet
Original Packets
60
Destination needs to know which combinations it
received
Use run length encoding
Coded Packet
Original Packets
61
Destination needs to know which combinations it
received
Use run length encoding
Coded Packet
Original Packets
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Destination needs to know which combinations it
received
Use run length encoding
Run length encoding efficiently expresses
combinations
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Symbol-level Network Coding
Forward random combinations of correct symbols
Coded Packet
Original Packets
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Symbol-level Network Coding
Forward random combinations of correct symbols
Coded Packet
Original Packets
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Symbol-level Network Coding
Forward random combinations of correct symbols
Coded Packet
Original Packets
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Symbol-level Network Coding
Forward random combinations of correct symbols
Coded Packet
Original Packets
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Symbol-level Network Coding
Forward random combinations of correct symbols
Use run length encoding to efficiently expresses
combinations in header
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MIXIT Efficient and Scalable Symbol-level
Opportunistic Routing
Solve 2 equations
Original Symbols

• Symbol Level Network Coding
• No duplicates ? Efficient
• No coordination ? Scalable

Destination decodes by solving linear equations
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Routers May Forward Erroneous Bits Despite High
Confidence
MIXIT has E2E error correction capability!
Decode ECC
Symbol-Level Network Coding
ECC
Data
Data
Source
Destination

• MIXITs Error Correcting Code (ECC)
• Routers are oblivious to ECC
• Optimal error correction capability
• Rateless

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High Concurrency MAC
w x ? NO! w u? YES!
u
w
x

• Each node maintains a map of conflicting
  transmissions
• Map is based on empirical measurements and built
  in distributed, online manner

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Evaluation

• Implementation on GNURadio SDR and USRP
• Zigbee (IEEE 802.15.4) link layer
• 25 node indoor testbed, random flows
• Compared to
• Shortest path routing based on ETX
• MORE Packet-level opportunistic routing

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Throughput Comparison
CDF
2.1x
MIXIT
3x
MORE
Shortest Path
Throughput (Kbps)
Throughput increase 3x over SPR, 2x over MORE
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Where do the gains come from?
CDF
MIXIT
MORE
Shortest Path
Throughput (Kbps)
Take concurrency away from MIXIT
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Where do the gains come from?
CDF
MIXIT without concurrency
1.5x
MORE
Shortest Path
Throughput (Kbps)
Without concurrency, 1.5x gain over MORE
Take concurrency away from MIXIT
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Where do the gains come from?
MIXIT
CDF
MIXIT without concurrency
MORE
Shortest Path
Gains come from both moving to the symbol level
and high concurrency
Throughput (Kbps)
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Where do the gains come from?Higher Concurrency?
CDF
1.4x
Throughput (Kbps)
MORE, enhanced with higher concurrency is only
1.4x better
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Where do the gains come from?
CDF
1.5x
2.1x
Higher concurrency MAC fully exploits
symbol-level diversity
Throughput (Kbps)
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Multiple Flows
MORE/SPR Higher congestion ? Lower
concurrency MIXIT Higher congestion ? High
concurrency
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(No Transcript)
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Geographical Routing
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Motivations

• A need for geographical based distribution
• e.g., sensornets and location-based services
• Reducing state overhead
• the routing protocols we discussed so far may not
  scale to large-scale networks
• maintain (end-to-end) routing states for each
  destination
• thus overhead proportional to network size

82
GeoRouting Greedy Distance
S
D

• Find neighbors who are the closest to destination
  D
• To make progress, the chosen neighbor should be
  closer to destination

83
Geographical Routing

• Each node only needs to keep state for its
  neighbors
• Beaconing mechanism
• each node broadcasts its MAC and position
• to minimize costs piggybacking

84
Greedy Routing Not Always Works
D
85
Greedy Routing Works Well in Dense Networks
D

• If node density is high, it is a low probability
  event for the region to have no nodes

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Dealing with Void Right-Hand Rule
Right-hand rule When arriving at node x from
node y, the next edge traversed is the next one
sequentially counterclockwise about x from edge
(x,y)
87
Right Hand Rule on Convex Subdivision
Applying the right hand rule to convex
subdivision (namely a planar graph where every
internal face is a polytope) first remove the
edges crossing the line from source to
destination, and then apply the right hand rule
If not convex subdivision, removing crossing
edges may not work
88
Right-Hand Rule Does Not Work Well with Cross
Edges
z
v
D
u

• x originates a packet to u
• Right-hand rule results in the long detour
  x-u-z-w-u-x

w
x
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Removing Cross Edges
z
v
D
u
w

• Remove (w,z) from the graph
• Right-hand rule results in the route x-u-z-v-D

x
90
How to Make a Graph Planar?

• Convert a connectivity graph to planar
  non-crossing graph by removing bad edges
• make sure the original graph will not be
  disconnected
• two types of planar graphs
• Relative Neighborhood Graph (RNG)
• Gabriel Graph (GG)

91
Relative Neighborhood Graph

• Edge uv can exist only if there does not exist
  another node w inside the intersection of the
  two circles centered at u and v with radius d(u,
  v)
• i.e., no w such that d(w, u) lt d(u, v) and d(w,
  v) lt d(u, v)
• Or equivalently ?w ? u, v d(u,v)
  maxd(u,w),d(v,w)

not empty ? remove uv
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Gabriel Graph

• An edge (u,v) exists between vertices u and v if
  no other vertex w is present within or on the
  circle whose diameter is uv.
• ?w ? u, v d2(u,v) lt d2(u,w) d2(v,w)

Not empty ? remove uv
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Examples
Full graph
GG subset
RNG subset

• 200 nodes
• randomly placed on a 2000 x 2000 meter region
• radio range of 250 m
• Bonus remove redundant, competing path ? less
  collision

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Properties of GG and RNG
RNG

• RNG is a sub-graph of GG
• because RNG removes more edges
• GG is a planar graph
• and thus RNG is also planar
• Connectivity
• if the original graph isconnected, RNG is also
  connected

GG
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Connectedness of RNG Graph

• Key observation
• any edge on the minimumspanning tree of the
  originalgraph is not removed
• Assume (u,v) is such an edge but removed in RNG
  due to w

u
v
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Delaunay Triangulation

• Let disk(u,v,w) be a disk defined by the three
  points u,v,w
• The Delaunay Triangulation (Graph)
• There is a triangle of edges between three nodes
  u,v,w iff the disk(u,v,w) contains no other
  points
• Properties of the Delaunay Triangulation graph
• it is the dual of the Voronoi diagram
• DT graph is planar

97
Some Interesting Properties

• Since the MST(V) is connected and the DT(V) is
  planar, all the planar graphs above are connected
  and planar

98
Final Algorithm Greedy Perimeter Stateless
Routing (GPSR)

• Maintenance
• all nodes maintain a single-hop neighbor table
• Use RNG or GG to make the graph planar
• Routing
• use greedy forwarding whenever possible
• resort to perimeter routing when greedy
  forwarding fails and record current location Lc
• resume greedy forwarding when we are closer to
  destination than Lc

99
Example
d
d
D
D
e
e
c
c
a
a
f
S
S
b
For details about GPSR algorithm, please GPSR.
100
Evaluations

• 50, 112, and 200 nodes with 802.11 WaveLAN radios
• Maximum velocity of 20 m/s
• 30 CBR traffic flows, originated by 22 sending
  nodes
• Each CBR flows at 2 Kbps, and uses 64-byte
  packets

101
Packet Delivery Success Rate
Very dense network 20 neighbors
102
Routing Protocol Overhead
103
Routing State

• State per router for 200-node
• GPSR node stores state for 26 nodes on average in
  pause time-0

104
Path Length
105
Worst Case of GeoRouting in Terms of Hop Count

• A worst case scenario
• destination is central node
• source is any node on ring
• any spine can go to middle
• O(c) nodes along ring and O(c) nodes along each
  spine
• Best path length O(c)O(c)
• Geographic routing
• Test O(c) spines of length O(c)
• Cost O(c2) instead of O(c)

106
Geographic Routing
107
Pros and Cons of GPSR

• Pros
• low routing state and control traffic
• scalable
• handles mobility well
• Cons
• planarized graph is hard to guarantee under
  mobility
• location might not be available everywhere (we
  will see the problem next week)
• geographic distance does not correlate well with
  network proximity

108
Why Geographic Routing Without Location?

• Location is hard to get
• GPS takes power, doesnt work indoors, difficult
  to incorporate in small sensors
• the network localization problem is difficult
• True location may not be useful if there are
  obstacles

In the connectivity space, B is closer to
destination!!
109
Overview

• Objective assign virtual coordinates to nodes
  so that
• the coordinates are computed efficiently,
• routing works well using the computed coordinates
• Progress in three steps
• the perimeter nodes and their locations are known
• the perimeter nodes are known but not their
  coordinates are not known
• nothing is known
• We cover the first two steps

110
The Perimeter Nodes and Their Locations Are Known

• Image a rubber band from each node to each
  (connected) neighbor
• The force of a rubber band is proportional to
  its length, directedto the neighbor

111
The Perimeter Nodes and Their Locations Are Known

• The equilibrium is achievedwhen the position p
  of a node is equal to the average of its
  neighbors
• where n is number of neighbors
• Algorithm
• each node sends its position to its neighbors
• a node updates its new position to be the average
  of those of its neighbors

112
Perimeter Nodes Are Known (True Positions)
3200 nodes 64 perimeter nodes on the boundary
113
Perimeter Nodes Are Known (10 iterations)
Internal nodes initialized as the center of the
square
114
Perimeter Nodes Are Known (100 iterations)
Internal nodes initialized as the center of the
square
115
Perimeter Nodes Are Known (1000 iterations)
Internal nodes initialized as the center of the
square
116
Routing Performance

• 32000 packets with random source-destination pairs

Success rate using (distance) greedy routing
117
Two More Scenarios
Success rate 0.981 Avg. path length 17.3
Success rate 0.99 Avg. path length 17.1
118
Weird Shapes
119
The Perimeter Nodes Are Known But Their Locations
Are Not Known

• Assume the distance between two nodes is the
  (minimum) number of hops to go from one to the
  other
• Distances can be derived by flooding the network
• each perimeter node sends a HELLO message with a
  hop counter of 0
• when seeing a message from a perimeter node with
  a lower hop counter, a node increases the counter
  by 1 and forwards it

120
Virtual Coordinates by Triangulation

• Each perimeter node solves the minimization
  problem
• Detail

121
Convergence and Performance
One iteration success rate 0.992 avg. path
length 17.2 Ten iterations success rate
0.994 avg. path length 17.2
122
Backup Slides
123
Improving Resiliency

• If perimeter vector is inaccurate, it results in
  inconsistent information
• Augment with two beaconing nodes which provide
  two coordinate axes
• special perimeter nodes or run leader election to
  select the two nodes
• Origin is chosen as the center of gravity of all
  perimeter nodes
• more robust to lost information

124
Selecting Perimeter Nodes

• Rule A node is a perimeter node if
• It is farthest away from the first beacon node
  among all its one-hop neighbors

125
Perimeter Node Detection
126
Convergence and Performance
Ten iterations success rate 0.996 avg. path
length 17.3
127
Projecting on Circle After First Computation

• Circle center is center of gravity radius is
  average of distance of the perimeter nodes to the
  CG
• Motivation maintain a consistent coordinate
  space

128
Virtual Polar Coordinate Space

• Each node is assigned a label
• label is number of hops to root and virtual angle
  range

Discussion how to do routing?
129
Build the Tree

• Root node
• starts as root
• broadcasts level 0
• A non-root node
• receives message level n marks parent
• broadcasts message saying level n1
• All subtrees report size back to parent.
• Root does assignment of virtual angles.

Question what about the issues of the described
algorithm?
130
Motivation for a Better Metric
131
Implementation and such

• Modify DSDV or DSR
• Example evaluation
• in DSDV w/ ETX, route table is a snapshot taken
  at end of 90 second warm-up period
• in DSR w/ ETX, source waits additional 15 sec
  before initiating the route request

132
ETX Performance
DSDV
DSR