Opportunistic Routing in Wireless Mesh Networks
Amir Darehshoorzadeh
amir@ac.upc.edu
Llorenç Cerdá-Alabern
llorenc@ac.upc.edu
Vicent Pla
vpla@dcom.upv.es
August 31, 2012
Opportunistic Routing in Wireless Mesh Networks
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Outline
1
Introduction to Opportunistic Routing (OR).
2
Research directions in OR.
3
Routing metrics in OR.
4
Coordination methods in OR.
5
Candidate selection algorithms.
6
Performance evaluation.
7
Conclusions.
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Introduction to Opportunistic Routing (OR).
Traditional Uni-path Routing
10%
30%
S
90%
A
90%
B
90%
D
Node
S
A
B
Next Hop for D
A
B
D
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Introduction to Opportunistic Routing (OR).
Traditional Uni-path Routing
10%
30%
S
90%
A
90%
B
90%
D
Node
S
A
B
Next Hop for D
A
B
D
For each destination selects a single next-hop forwarder.
End-to-End delivery probability: 0.9 × 0.9 × 0.9 ≈ 0.72
Opportunistic Routing in Wireless Mesh Networks
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Introduction to Opportunistic Routing (OR).
Traditional Uni-path Routing
10%
30%
S
90%
A
90%
B
90%
D
Node
S
A
B
Next Hop for D
A
B
D
For each destination selects a single next-hop forwarder.
End-to-End delivery probability: 0.9 × 0.9 × 0.9 ≈ 0.72
Lot of retransmissions.
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Introduction to Opportunistic Routing (OR).
Traditional Uni-path Routing
10%
30%
S
90%
A
90%
B
90%
D
Node
S
A
B
Next Hop for D
A
B
D
For each destination selects a single next-hop forwarder.
End-to-End delivery probability: 0.9 × 0.9 × 0.9 ≈ 0.72
Lot of retransmissions.
Waste of network resources.
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Introduction to Opportunistic Routing (OR).
What is Opportunistic Routing (OR)?
For each destination selects an ordered set of nodes
(Candidate Set). CandSet(S)={D, B, A}
10%
30%
S
90%
A
90%
B
90%
Opportunistic Routing in Wireless Mesh Networks
D
4 / 37
Introduction to Opportunistic Routing (OR).
What is Opportunistic Routing (OR)?
For each destination selects an ordered set of nodes
(Candidate Set). CandSet(S)={D, B, A}
10%
30%
S
90%
A
90%
B
90%
Opportunistic Routing in Wireless Mesh Networks
D
4 / 37
Introduction to Opportunistic Routing (OR).
What is Opportunistic Routing (OR)?
For each destination selects an ordered set of nodes
(Candidate Set). CandSet(S)={D, B, A}
10%
30%
S
90%
A
90%
B
90%
Opportunistic Routing in Wireless Mesh Networks
D
4 / 37
Introduction to Opportunistic Routing (OR).
What is Opportunistic Routing (OR)?
For each destination selects an ordered set of nodes
(Candidate Set). CandSet(S)={D, B, A}
The candidates that receive the packet will coordinate to determine
the best one to actually forward the packet.
10%
30%
S
90%
A
90%
B
90%
Opportunistic Routing in Wireless Mesh Networks
D
4 / 37
Introduction to Opportunistic Routing (OR).
What is Opportunistic Routing (OR)?
For each destination selects an ordered set of nodes
(Candidate Set). CandSet(S)={D, B, A}
The candidates that receive the packet will coordinate to determine
the best one to actually forward the packet.
10%
30%
S
90%
A
90%
B
90%
Opportunistic Routing in Wireless Mesh Networks
D
4 / 37
Introduction to Opportunistic Routing (OR).
What is Opportunistic Routing?
C1
10
0%
C2
10
C3
100%
0%
D
Uni-path Routing
End-to-End
Delivery Probability
20%
%
0%
%
20
C4
0
10
10
S
%
20
20 %
20%
20
%
C5
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Introduction to Opportunistic Routing (OR).
What is Opportunistic Routing?
C1
10
0%
C2
10
C3
100%
0%
%
D
Uni-path Routing
OR
10
%
20
C4
0
10
End-to-End
Delivery Probability
20%
1 − (1 − 20%)5 ≈ 67%
0%
S
%
20
20 %
20%
20
%
C5
OR Combines weak physical links into one stronger virtual link.
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Issues in Opportunistic Routing
Issues in Opportunistic Routing
Candidate selection in OR.
OR metric.
Candidate coordination in OR.
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Research Directions in Opportunistic Routing
Research Directions in Opportunistic Routing
Protocol
Year Type Topic
Metric
Coord.
Cand. Sel.
SDF
GeRaF
ExOR ver-1
ExOR ver-2
NA
COPE
OAPF
LCOR
MORE
GOR
NA
NA
NA
CORE
MTS
2001
S
Candid. Coord
2003 A/S Cand. Coord
2004
S
Cand. Sel
2005 E Cand. Coord
2005 A/S Sensor networks
2005 E Network coding
2006
S
Cand. Sel
2007
S
Cand. Sel
2007 E Network coding
2007
S
Cand. Sel
2008 A Analytical
2008 A/S Analytical
2008 E Cand. Sel
2008
S
Network coding
2009
S
Cand. Sel
ETX
Geo.
ETX
ETX
Geo.
ETX
ETX/EAX
EAX
ETX
Geo.
Geo.
Geo.
ETX
Geo.
EAX
Ack
RTS-CTS
Ack
Timer
RTS-CTS
Net. coding
Ack
NA
Net. coding
Timer
NA
NA
Ack
Timer
Timer
Topology
Location
Topology
Topology
Location
Topology
Topology
Topology
Topology
Location
Location
Location
Topology
Location
Topology
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Research Directions in Opportunistic Routing
Research Directions in Opportunistic Routing
Protocol Year Type Topic
Metric
Coord.
POR
SOAR
Pacifier
NA
Geo.
ETX
ETX
EAX
Timer
Location
Timer
Topology
Net. coding Topology
NA
Location
MSTOR
MORP
NA
2009
S
Cand. Sel
2009 S/E Cand. Sel
2009
S
Multicast
2010 A Maximum performance
2010
S
Multicast
2011
S
Multicast
2011 A Analytical/Cand.
Sel
EAX/ETX Ack
ETX
Ack
ETX/EAX NA
Opportunistic Routing in Wireless Mesh Networks
Cand. Sel.
Topology
Topology
Topology
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Routing metrics in OR.
Usual routing metric in OR
Hop Count
geographic-distance (Geo-Distance)
Expected Transmission Count ETX [Douglas 2003]: The average number of transmissions required to reliably send a packet across a link or
route including retransmissions.
Ï
pij is the delivery probability between nodes i and j then ETX=
Ï
Using the ETX does not give an accurate metric for OR.
1
pij
Expected Any-path Transmission EAX: [Zhong 2006]: is an extension of
ETX and can capture the expected number of transmissions taking into
account the multiple paths that can be used under OR.
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Routing metrics in OR.
What is EAX?
source
1
q12 = 0.7
q13 = 0.3
2
destination
3
q23 = 0.7
node candidates to 3
1
2
3, 2
3
qij is the delivery probabilities from node i to node j
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Routing metrics in OR.
What is EAX?
source
1
q12 = 0.7
q13 = 0.3
2
destination
3
q23 = 0.7
node candidates to 3
1
2
3, 2
3
qij is the delivery probabilities from node i to node j
What is the expected number of transmissions from node 1 to the
destination using OR (E1OR )?
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Routing metrics in OR.
What is EAX?
source
q13 = 0.3
1
q12 = 0.7
2
destination
3
q23 = 0.7
node candidates to 3
1
2
3, 2
3
qij is the delivery probabilities from node i to node j
What is the expected number of transmissions from node 1 to the
destination using OR (E1OR )?
P
E1OR = 1 + 3i=1 pi Ei
Ï
Ï
pi is the probability of node i being the next forwarder.
Ei is the expected number of transmissions from node i to the
destination.
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Routing metrics in OR.
What is EAX?
source
q13 = 0.3
1
q12 = 0.7
2
destination
3
q23 = 0.7
node candidates to 3
1
2
3, 2
3
qij is the delivery probabilities from node i to node j
What is the expected number of transmissions from node 1 to the
destination using OR (E1OR )?
P
E1OR = 1 + 3i=1 pi Ei
Ï
Ï
pi is the probability of node i being the next forwarder.
Ei is the expected number of transmissions from node i to the
destination.
E1 = (1 + p2 × E2 )/(p2 + p3 ) =
(1 + (1 − q13 ) q12 × 1/q23 )/((1 − q13 ) q12 + q13 ) ≈ 2.15
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Coordination methods in OR.
Coordination methods in OR.
Acknowledgment-based coordination
Timer-based coordination
Network coding coordination (NC)
RTS-CTS coordination
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Coordination methods in OR.
Acknowledgment-based coordination [Biswas 2004]
Propose modifying 802.11 for OR coordination.
S
(source)
C
data frame
A
D
(destination)
B
Node
S
A
B
C
Candidates
for D
A, B, C
D
D, A
D, A
source S A B C Data frame
candidate C
candidate B
candidate A
destination D
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Coordination methods in OR.
Acknowledgment-based coordination [Biswas 2004]
Propose modifying 802.11 for OR coordination.
S
(source)
C
ack
A
D
(destination)
B
Node
S
A
B
C
Candidates
for D
A, B, C
D
D, A
D, A
source S A B C Data frame
candidate C
candidate B
candidate A
destination D
ack A
SIFS
Opportunistic Routing in Wireless Mesh Networks
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Coordination methods in OR.
Acknowledgment-based coordination [Biswas 2004]
Propose modifying 802.11 for OR coordination.
S
(source)
C
D
(destination)
A
ack
B
Node
S
A
B
C
Candidates
for D
A, B, C
D
D, A
D, A
source S A B C Data frame
candidate C
ack B
candidate B
candidate A
destination D
ack A
SIFS
SIFS
Opportunistic Routing in Wireless Mesh Networks
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Coordination methods in OR.
Acknowledgment-based coordination [Biswas 2004]
Propose modifying 802.11 for OR coordination.
S
ack
(source)
C
D
(destination)
A
B
Node
S
A
B
C
Candidates
for D
A, B, C
D
D, A
D, A
source S A B C Data frame
ack A
candidate C
ack B
candidate B
candidate A
destination D
ack A
SIFS
SIFS
SIFS
Opportunistic Routing in Wireless Mesh Networks
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Coordination methods in OR.
Acknowledgment-based coordination [Biswas 2004]
Propose modifying 802.11 for OR coordination.
S
(source)
C
data
frame
A
Node
S
A
B
C
D
(destination)
B
Candidates
for D
A, B, C
D
D, A
D, A
source S A B C Data frame
ack A
candidate C
ack B
candidate B
candidate A
destination D
ack A
SIFS
SIFS
SIFS
D Data frame
DIFS+backoff
Opportunistic Routing in Wireless Mesh Networks
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Coordination methods in OR.
Timer-based coordination
{B,A} is the candidate set of S to reach D.
S
A
B
Opportunistic Routing in Wireless Mesh Networks
D
13 / 37
Coordination methods in OR.
Timer-based coordination
{B,A} is the candidate set of S to reach D.
Candidates A and B receive the packet.
S
A
B
Opportunistic Routing in Wireless Mesh Networks
D
13 / 37
Coordination methods in OR.
Timer-based coordination
{B,A} is the candidate set of S to reach D.
Candidates A and B receive the packet.
Candidate B forwards the packet.
S
A
B
Opportunistic Routing in Wireless Mesh Networks
D
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Coordination methods in OR.
Timer-based coordination
{B,A} is the candidate set of S to reach D.
Candidates A and B receive the packet.
Candidate B forwards the packet.
If A hears B’s transmissions, it simply discard the packet.
S
A
B
Opportunistic Routing in Wireless Mesh Networks
D
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Coordination methods in OR.
Network coding coordination (NC) [Michele 2003]
{C1 , C2 } is the candidates set of S to reach D.
C1
a
b
D
S
C2
Opportunistic Routing in Wireless Mesh Networks
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Coordination methods in OR.
Network coding coordination (NC) [Michele 2003]
{C1 , C2 } is the candidates set of S to reach D.
S generates two coded packet.
C1
a
b
S
p1
a+b
p2
a−b
D
C2
Opportunistic Routing in Wireless Mesh Networks
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Coordination methods in OR.
Network coding coordination (NC) [Michele 2003]
{C1 , C2 } is the candidates set of S to reach D.
S generates two coded packet.
C2 receives both packets while C1 receives only one.
a+b
C1
a
b
S
p1
a+b
p2
a−b
D
C2
a+b
a-b
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Coordination methods in OR.
Network coding coordination (NC) [Michele 2003]
{C1 , C2 } is the candidates set of S to reach D.
S generates two coded packet.
C2 receives both packets while C1 receives only one.
Both candidates generate coded packet and broadcast them.
a+b
C1
a
b
S
p1
a+b
p2
a−b
p3 2a+2b
D
p4
2a
C2
a+b
a-b
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Coordination methods in OR.
Network coding coordination (NC) [Michele 2003]
{C1 , C2 } is the candidates set of S to reach D.
S generates two coded packet.
C2 receives both packets while C1 receives only one.
Both candidates generate coded packet and broadcast them.
D can decode and restore the original packets.
a+b
C1
a
b
S
p1
a+b
p2
a−b
p3 2a+2b
D
p4
a
b
2a
C2
a+b
a-b
Opportunistic Routing in Wireless Mesh Networks
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Coordination methods in OR.
RTS-CTS coordination [Szymon 2007]
An explicit control packet(s) exchanged immediately before sending a
data packet.
CandSet={a, b, c}
s
a b c RTS
t
c
b
a
Opportunistic Routing in Wireless Mesh Networks
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Coordination methods in OR.
RTS-CTS coordination [Szymon 2007]
An explicit control packet(s) exchanged immediately before sending a
data packet.
CandSet={a, b, c}
Candidates send CTS in time in order of their priorities.
s
a b c RTS
t
c
b
a
SIFS CTS a
Opportunistic Routing in Wireless Mesh Networks
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Coordination methods in OR.
RTS-CTS coordination [Szymon 2007]
An explicit control packet(s) exchanged immediately before sending a
data packet.
CandSet={a, b, c}
Candidates send CTS in time in order of their priorities.
s
a b c RTS
t
c
2*SIFS CTS b
b
a
SIFS CTS a
Opportunistic Routing in Wireless Mesh Networks
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Coordination methods in OR.
RTS-CTS coordination [Szymon 2007]
An explicit control packet(s) exchanged immediately before sending a
data packet.
CandSet={a, b, c}
Candidates send CTS in time in order of their priorities.
Sender sends data to the candidate that sent CTS and is received.
s
SIFS Data
a b c RTS
t
c
2*SIFS CTS b
b
a
SIFS CTS a
Opportunistic Routing in Wireless Mesh Networks
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Coordination methods in OR.
RTS-CTS coordination [Szymon 2007]
An explicit control packet(s) exchanged immediately before sending a
data packet.
CandSet={a, b, c}
Candidates send CTS in time in order of their priorities.
Sender sends data to the candidate that sent CTS and is received.
s
SIFS Data
a b c RTS
t
NAV Data
c
2*SIFS CTS b
b
a
SIFS CTS a
SIFS ACK
NAV Data
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Candidate selection algorithms.
General Aim of OR
To Minimize the expected number of transmissions from the source to the
destination.
Candidate Selection Algorithms
How to select the forwarders from the neighbors?
How to prioritize the selected candidates.
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Candidate selection algorithms.
Extremely Opportunistic Routing (ExOR) [Biswas 2004]
One of the first and most referenced OR protocols.
It uses ETX metric.
Shortest Path First (SPF) algorithm is used.
Simple to implement.
How does ExOR work?
S is the source and D is the destination.
0.85
S
B
0.64
0.67
0.15
A
0.31
0.4
D
Opportunistic Routing in Wireless Mesh Networks
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Candidate selection algorithms.
Extremely Opportunistic Routing (ExOR) [Biswas 2004]
One of the first and most referenced OR protocols.
It uses ETX metric.
Shortest Path First (SPF) algorithm is used.
Simple to implement.
How does ExOR work?
SPF from S to D is S-A-D and A is selected as the candidate.
0.85
S
B
0.64
0.67
0.15
A
0.31
0.4
D
Opportunistic Routing in Wireless Mesh Networks
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Candidate selection algorithms.
Extremely Opportunistic Routing (ExOR) [Biswas 2004]
One of the first and most referenced OR protocols.
It uses ETX metric.
Shortest Path First (SPF) algorithm is used.
Simple to implement.
How does ExOR work?
The edge between S and A is removed.
0.85
B
0.64
A
S
0.15
0.31
0.4
D
Opportunistic Routing in Wireless Mesh Networks
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Candidate selection algorithms.
Extremely Opportunistic Routing (ExOR) [Biswas 2004]
One of the first and most referenced OR protocols.
It uses ETX metric.
Shortest Path First (SPF) algorithm is used.
Simple to implement.
How does ExOR work?
The new SPF is S-B-D and B is selected as the candidate.
0.85
B
0.64
A
S
0.15
0.31
0.4
D
Opportunistic Routing in Wireless Mesh Networks
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Candidate selection algorithms.
Extremely Opportunistic Routing (ExOR) [Biswas 2004]
One of the first and most referenced OR protocols.
It uses ETX metric.
Shortest Path First (SPF) algorithm is used.
Simple to implement.
How does ExOR work?
Prioritization:ETX of each candidate to the destination.
0.85
B
0.64
A
S
0.15
0.31
0.4
D
Opportunistic Routing in Wireless Mesh Networks
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Candidate selection algorithms.
Extremely Opportunistic Routing (ExOR) [Biswas 2004]
One of the first and most referenced OR protocols.
It uses ETX metric.
Shortest Path First (SPF) algorithm is used.
Simple to implement.
How does ExOR work?
CandSet(S)= {A, B}
0.85
S
B
0.64
0.67
0.15
A
0.31
0.4
D
Opportunistic Routing in Wireless Mesh Networks
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Candidate selection algorithms.
Opportunistic Any-Path Forwarding OAPF [Zhong 2006]
It uses EAX.
It does not select the optimum candidate set.
It finds a candidate which improves the EAX of the node.
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Opportunistic Any-Path Forwarding OAPF
How does OAPF work?
InitCandSet(S)={A, B, D}
A and B must select their candidates sets before S
0.85
S
B
0.64
0.67
0.15
A
0.31
0.4
D
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Opportunistic Any-Path Forwarding OAPF
How does OAPF work?
InitCandSet(S)={A, B, D}
A and B must select their candidates sets before S
CandSet(S)={B}
Iteration
1
Selection
EAX ({A}, S, D)=3.99,
EAX ({B}, S, D)=3.97,
0.85
S
B
0.64
0.67
0.15
A
EAX ({D}, S, D)=6.66
0.31
0.4
D
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Opportunistic Any-Path Forwarding OAPF
How does OAPF work?
InitCandSet(S)={A, B, D}
A and B must select their candidates sets before S
CandSet(S)={B}
CandSet(S)={D,A}
Iteration
1
2
Selection
EAX ({A}, S, D)=3.99,
EAX ({A, B}, S, D)= 3.64,
0.85
S
EAX ({B}, S, D)=3.97,
EAX ({D,B}, S, D)= 3.46
B
0.64
0.67
0.15
A
EAX ({D}, S, D)=6.66
0.31
0.4
D
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Candidate selection algorithms.
Least-Cost Opportunistic Routing LCOR [Dubois 2007]
EAX is used.
LCOR is a generalization of the well-known Bellman-Ford algorithm.
It selects the optimum candidates.
Exhaustive search.
CandSet(S)= {D, A}.
0.85
S
B
0.64
0.67
0.15
A
0.31
0.4
D
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Candidate selection algorithms.
Minimum Transmission Selection MTS [Yanhua 2009]
It uses EAX.
Like LCOR, it selects the optimum candidates.
Adding the candidates of the node with smallest EAX to the neighbors
of that node.
It is simpler than LCOR.
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Minimum Transmission Selection (MTS)
How does MTS work?
S = {S, A, B}
Iteration
S
A
B
0
{D}, 6.66
{D}, 2.5
{D}, 3.22
0.85
S
B
0.64
0.67
0.15
A
0.31
0.4
D
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Minimum Transmission Selection (MTS)
How does MTS work?
S = {S, A, B}
A has the minimum EAX
Iteration
S
A
B
0
{D}, 6.66
{D}, 2.5
{D}, 3.22
0.85
S
B
0.64
0.67
0.15
A
0.31
0.4
D
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Minimum Transmission Selection (MTS)
How does MTS work?
S = {S, A, B}
A has the minimum EAX
Iteration
S
A
B
0
1
{D}, 6.66
{D, A}, 3.36
{D}, 2.5
-
{D}, 3.22
{D, A}, 2.79
0.85
S
B
0.64
0.67
0.15
A
0.31
0.4
D
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Minimum Transmission Selection (MTS)
How does MTS work?
S = {S, A, B}
B has the minimum EAX
Iteration
S
A
B
0
1
{D}, 6.66
{D, A}, 3.36
{D}, 2.5
-
{D}, 3.22
{D, A}, 2.79
0.85
S
B
0.64
0.67
0.15
A
0.31
0.4
D
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Minimum Transmission Selection (MTS)
How does MTS work?
S = {S, A, B}
B has the minimum EAX
Iteration
S
A
B
0
1
2
{D}, 6.66
{D, A}, 3.36
{D, A, B}, 3.22
{D}, 2.5
-
{D}, 3.22
{D, A}, 2.79
-
0.85
S
B
0.64
0.67
0.15
A
0.31
0.4
D
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Minimum Transmission Selection (MTS)
How does MTS work?
S = {S, A, B}
Do the exhaustive search over founded candidates sets.
Iteration
S
A
B
0
1
2
{D}, 6.66
{D, A}, 3.36
{D, A, B}, 3.22
{D}, 2.5
-
{D}, 3.22
{D, A}, 2.79
-
0.85
S
B
0.64
0.67
0.15
A
0.31
0.4
D
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Minimum Transmission Selection (MTS)
How does MTS work?
S = {S, A, B}
CandSet(S)= {D, A}.
Iteration
S
A
B
0
1
2
{D}, 6.66
{D, A}, 3.36
{D, A, B}, 3.22
{D}, 2.5
-
{D}, 3.22
{D, A}, 2.79
-
0.85
S
B
0.64
0.67
0.15
A
0.31
0.4
D
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Performance evaluation.
Assumptions
There is only one active connection.
Perfect coordination.
Independent delivery probabilities.
Linear topology with evenly spaced nodes:
d [m]
vs
1
2
3
···
N
vd
D [m]
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Performance evaluation.
Basic Model
Assume that OR is used with a list of 2 candidates.
We can model OR with an absorbing discrete time Markov chain,
where the state is the node forwarding the packet:
p3
p3
p1
p2
vs
1
p3
p1
p2
2
3
p2
4
5
···
p2
p2
p3
p1
1
p1
p3
p1
N
N-1
p0
3
vd
p0
1
Let p(d) be the probability of successfully delivering a packet to a node
located at a distance d. Then:
p1 = p(2 d)
p01 = p(d)
p2 = p(d) (1 − p1 )
p03 = 1 − p01
p3 = 1 − (p1 + p2 )
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Performance evaluation.
Solution of the model
The model yields a discrete phase-type distribution, for which there
exists a simple equation for the distribution and moments of the first
time until absorption.
In our model this is the number of transmissions since the source first
transmits the packet, until it is received by the destination.
Extension of the model
A similar chain can be easily derived for any number of candidates and
arbitrary topology:
Ï
Ï
With 1 candidate is equivalent to uni-path routing. We shall refer to it as
c1 .
We shall refer as infinite candidates, c∞ , to the case when all possible
nodes are candidates.
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Performance evaluation.
Summing up:
The only ingredients needed to build the transition probability matrix
are:
Ï
Ï
The delivery probabilities.
The ordered list of candidates of each node.
Propagation model
We assess the delivery probability at a distance d, p(d), with a
shadowing propagation model, with path loss exponent β and
standard deviation σdB .
We assume that a link exists only if p(d) ≥ min.dp.
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Numerical results.
Evaluation Methodology
Area: A square field with diagonal D = 300 m
Random topology.
Source and destination are placed at the end points of one of the
diagonals.
Number of nodes is equal to 10 ≤ N ≤ 50.
The delivery probabilities o the links are obtained with shadowing
propagation model.
min.dp = 0.1
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Numerical results.
Measures of interest
Expected number of transmissions
Variance of the expected number transmissions.
Probability of the number of transmissions.
Execution Time.
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Numerical results.
Expected number of transmissions and Mean number of candidates
LCOR and MTS have exactly the same results.
OAPF is only slightly larger than optimum algorithms.
EAXOpt(∞) < EAXOpt(3) ¿ EAXUnipath but a large number of candidates are
used.
D=300m, β=2.7, σdB =6, min.dp=0.1
D=300m, β=2.7, σdB =6, min.dp=0.1
25
5.2
ExOR(∞)
OAPF(∞)
Opt(∞)
22
Mean number of candidates
Expected number of transmissions
5.6
4.8
Uni-path
ExOR(3)
OAPF(3)
LCOR(3)
MTS(3)
Opt(∞)
4.4
4
3.6
3.2
19
16
13
10
7
2.8
2.4
4
10
15
20
25
30
35
40
45
50
10
15
20
Number of nodes
Opportunistic Routing in Wireless Mesh Networks
25
30
35
40
45
50
Number of nodes
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Numerical results.
Expected number of transmissions Vs Number of candidates
For ncand=∞ all algorithms have almost the same results.
Limiting the maximum number of candidates makes the selection of the
candidates sets more critical.
D=300m, beta=2.7, sigmadB =6, min.sp=0.1
D=300m, beta=2.7, sigmadB =6, min.sp=0.1
ExOR
OAPF
LCOR
MTS
4.8
4
3.2
2.4
5.6
Expected number of transmissions
Expected number of transmissions
5.6
ExOR
OAPF
LCOR
MTS
4.8
4
3.2
2.4
1
2
3
4
5
∞
1
2
3
ncand
4
5
∞
ncand
Number of Nodes = 10
Number of Nodes = 50
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Numerical results.
Variance of expected number of transmissions
The variance of the expected number of transmissions using OR is
significantly reduced compared with uni-path routing.
D=300m, beta=2.7, sigmadB =6, min.sp=0.1
5.6
ExOR
OAPF
LCOR
MTS
4.8
4
3.2
2.4
1.6
0.8
0
1
2
3
4
5
∞
Variance of the expected number of transmissions
Variance of the expected number of transmissions
2 or 3 is enough to attain a significant part of the potential reduction.
D=300m, beta=2.7, sigmadB =6, min.sp=0.1
5.6
ExOR
OAPF
LCOR
MTS
4.8
4
3.2
2.4
1.6
0.8
0
1
2
3
ncand
4
5
∞
ncand
Number of Nodes = 10
Number of Nodes = 50
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Numerical results.
Probability distribution of the number of transmissions
The number of transmissions needed to reach the destination is
significantly reduced by using OR with respect to the uni-path routing.
D= 300 m, β= 2.7 , σdB = 6 , min.dp= 0.1
D= 300 m, β= 2.7 , σdB = 6 , min.dp= 0.1
0.6
0.6
Uni-path
ExOR(3)
OAPF(3)
LCOR(3)
MTS(3)
Opt(∞)
Probability
0.4
Uni-path
ExOR(3)
OAPF(3)
LCOR(3)
MTS(3)
Opt(∞)
0.5
0.4
Probability
0.5
0.3
0.3
0.2
0.2
0.1
0.1
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
Number of transmissions
Number of Nodes = 10
5
6
7
8
9
10
11
12
13
14
15
Number of transmissions
Number of Nodes = 50
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Numerical results.
Execution Time
The fastest algorithm is ExOR whereas LCOR is the slowest.
OAPF is between the optimal algorithms and ExOR.
MTS outperforms LCOR in terms of the execution time.
D=300m, β=2.7, σdB =6, min.dp=0.1
50
45
40
35
30
25
Execution time in log scale (second)
12000
5000
50
500
ExOR(3)
OAPF(3)
MTS(3)
LCOR(3)
20
100
15
50
10
N=10
50
N=10
N=10
1
N=10
0.1
0.05
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
Expected number of transmissions
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Conclusions and Future Research Directions
Conclusions
We describe the meaning of Opportunistic Routing (OR).
Research directions in OR.
Different metrics in OR.
Coordination in OR.
Candidate selection algorithms in OR.
A discrete time Markov chain to analyze the performance of OR.
We have compared different candidate selection algorithms.
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Conclusions and Future Research Directions
Future Research Directions
An efficient candidate selection algorithm.
A link layer implementation of the candidate coordination.
Ad hoc, sensor, Vehicular ad hoc networks using Opportunistic
Routing.
Using Opportunistic Routing for broadcasting messages.
Using Opportunistic Routing in Multi-channel multi-radio networks .
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