Delay‐Tolerant Routing in Opportunistic Delay‐Tolerant Routing in Opportunistic and Intermittent Networks and Intermittent Networks

Delay‐Tolerant Routing in Opportunistic
and Intermittent Networks
Delay‐Tolerant Routing in Opportunistic
and Intermittent Networks
Chih‐Lin Hu（胡誌麟）
Department of Communication Engineering
National Central University
Taiwan
clhu@ieee.org
2013‐3‐11
Chih‐Lin Hu（胡誌麟）
Department of Communication Engineering
National Central University
Taiwan
clhu@ieee.org
2013‐3‐11

Outline
● A Brief to Delay‐Tolerant Networking
 Opportunistic and Intermittent Networks
 Routing Requirements
● Our Ideas and Some Proposals
 Density‐Aware Routing
 Coding‐Based Routing to Multiple Receivers
● Concluding Remarks
2

8
Source: http://www.spaceref.com/focuson/ipn/

Environments & Applications
 Interplanetary Internet, which
focused primarily on deep‐space
communications in high delay
environments
 Sensor‐based networks, using
scheduled intermittent
connectivity
 Terrestrial wireless networks
cannot ordinarily maintain end‐to‐
end connectivity
 Satellite networks with moderate
delays and periodic connectivity
 Underwater acoustic networks
with moderate delays and frequent
interruptions due to
environmental factors
 Interplanetary space
 Natural disasters
 Agricultural lands
 Fishery grounds
 Forest parks
 Grazing areas
 Wilderness
[RFC 4838, by Vint Cerf, et al (April 2007 )]
9

History of Delay‐Tolerant Networking [Wiki]
● In the 1980s, while the field of ad‐hoc routing was inactive …
● In the 1990s, the widespread use of wireless protocols
reinvigorated the field as mobile ad‐hoc networking (MANET)
and vehicular ad‐hoc networking (VANET) became areas of
increasing interest.
● In the 2002, the term delay‐tolerant networking and the DTN
acronym were coined. [Kevin Fall, Vint Cerf, et al.]
● The mid‐2000s brought about increased interest in DTNs, as well
as growing interest in combining work from sensor networks
and MANETs with the work on DTNs.
11

Delay‐Tolerant Networking (DTN)
● Delay‐tolerant networking (DTN) is an approach to computer
network architecture that seeks to address technical issues in
heterogeneous networks that are characterized by tight
resource constraints on intermittent connectivity, available
storage, and internode bandwidth throughput.
 Delay/Disruptions may happen because of the limited wireless radio
range, sparsity of mobile nodes, energy resources, attack, and
communication noise.
 Classical examples of such networks are those operating in mobile or
extreme terrestrial environments, or planned networks in space.
 Recent works on DTNs bring growing interest in combining works from
Sensor Networks and MANETs.
12
In 2002, the term delay‐tolerant networking (DTN ) was coined.
[Kevin Fall, Vint Cerf, et al.]
Classical examples of such networks are those operating in mobile or
extreme terrestrial environments, or planned networks in space.
Recent works on DTNs bring growing interest in combining works from
Sensor Networks and MANETs.

Delay‐Tolerant Routing: Why
● Existing Internet routing and messaging mechanisms do not
work well for DTNs due to several fundamental assumptions:
 An end‐to‐end path between source and destination exists for the
duration of a communication session. [y/n?]
 Retransmissions based on timely and stable feedback from data receivers
is an effective means for repairing transmission errors. [y/n?]
 End‐to‐end loss is relatively small. [y/n?]
 All routers and end stations support the TCP/IP protocols. [y/n?]
 Selecting a single route between sender and receiver is sufficient. [y/n?]
● Did you ever get false answers in mind?
 Delay‐tolerant networking may be one of many alternatives to resolve
the issues.
13
Did you ever get false answers in mind?
Delay‐tolerant routing may be one of important alternatives to resolve the issues.

DTN Architecture: How
● The DTN architecture provides a common method for
interconnecting heterogeneous gateways or proxies that
employ store‐and‐forward message routing to overcome
communication disruptions. [Classical Definition in RFC 4838]
● The use of the bundle layer is guided not only by its own design
principles, but also by a few application design principles:
 Applications should minimize the number of round‐trip exchanges
 Applications should cope with restarts after failure while network
transactions remain pending
 Applications should inform the network of the useful life and relative
importance of data to be delivered
 [RFC 5050] Bundle Protocol Specification
14

DTN Architecture: Reference [RFC 4838]
15
Source: Kevin Fall, A Delay-Tolerant Network Architecture for Challenged Internets, SIGCOMM’03.

Delay‐Tolerant Routing in DTNs
● In DTNs, instantaneous end‐to‐end paths are difficult or
impossible to be established and guaranteed
 Lack of network connectivity by many realistic constraints:
► intervening objects, sparse node densities, limited radio range, limited
energy resource, and node mobility
● Popular ad hoc routing protocols, such as ad‐hoc on‐demand
distance vector (AODV) and dynamic source routing (DSR), may
fail to establish routes in these challenging environments.
 These protocols try to first establish a complete route and then, after the
route has been established, forward the data.
16

● Routing protocols can take to a store, carry and forward
approach.
 Data are sent to intermediate (relay) nodes where store and send data
later over multiple paths to final destinations or to other relay nodes.
17

● Two major performance problems in DTNs
 Long transfer delay time
 Low message delivery ratio
● Replicating many copies of the message is a common technique
used to maximize the probability of a message being
successfully received.
 It’s feasible only on networks with large local storage and internode
bandwidth relative to the expected traffic.
● A more discriminating algorithm is required, however, when
available storage and internode throughput opportunities are
more tightly constrained.
18

Existing DTN Routing Protocols
● Replica‐based protocols are feasible only when the networks can provide
large amounts of local storage and internode bandwidth relative to expected
message traffic and resource waste.
● History‐based protocols require nodes to extra maintain a history of
frequency with ever‐encountered nodes, complicating the forwarding
decision and inducing considerable computation and maintenance costs
when node population is large.
● Location‐based protocols were based on a weak premise that all nodes have
special localization abilities, e.g., GPS.
● Coding‐based protocols much concentrate on special coding technologies,
e.g., erasion coding and network coding, rather than developing any routing
algorithm itself in DTNs.
19
delivery ratio / delivery time / message traffic

Existing Delay‐Tolerant Routing Protocols
20
Sourec: T. Spyropoulos, et al., Routing for disruption tolerant networks: taxonomy and design, Wireless Networks,
16:2349–2370, 2010.

Our Ideas and Proposals
‐ Density‐Aware Routing with Node Density
‐ Coding‐based routing to Multiple Receivers
21

Literature Review on Density‐Aware
Routing
● Using different concepts of “density”
 Node density [a]
 Replication density [b]
 Map‐based density [c]
 Information density [d]
22

Density‐Aware Routing with Node Density
● This work traced real message traffic produced by people
wearing in‐line skates during city tour activities.
● This work analyzed the accordion phenomenon of node
distribution in DTNs.
● This paper proposed a modified SnW protocol where the
number of distributed messages is proportional to the number
of neighboring nodes in the vicinity.
23
P.-U. Tournoux, J. Leguay, F. Benbadis, V. Conan, V. Conan, and J. Whitbeck, “The accordion
phenomenon: Analysis, characterization, and impact on DTN routing,” in Proceedings of IEEE INFOCOM,
April 2009, pp. 1116–1124.

Density‐Aware Routing with Replication
Density
● Replication density indicates that a ratio of a number of
encountered nodes that already have the particular message by
a total of encountered nodes within a time period.
● This work changed the replication policy in the epidemic routing
protocol.
 When a node determines that the current replication density is higher
than a threshold, it will lower the probability of copying messages to
neighboring nodes to reduce traffic load in the same area.
24
X. Wang, Y. Shu, Z. Jin, Q. Pan, and B. S. Lee, “Adaptive randomized epidemic routing for disruption
tolerant networks,” in Proceedings of the 5th International Conference on Mobile Ad-hoc and Sensor
Networks, December 2009, pp. 424–429.

Density‐Aware Routing with Map‐based
Density
● This work assumed that all nodes have GPS facilities and use
location‐aided knowledge to route messages in DTNs.
● Mobile nodes can mark the dense areas on the geographic map,
and then forward query messages towards dense areas to
receive fast responses.
25
J. Li and P. Mohapatra, “Laker: location aided knowledge extraction routing for mobile ad hoc networks,”
in Proceedings of IEEE Wireless Communications and Networking Conference, March 2003, pp. 1180–
1184.

Density‐Aware Routing with Info. Density
● This work addressed the content retrieval based on information
density in semantic DTN environments.
● Each node can overhear the content of any passing messages to
learn semantic distances to the source and destination nodes in
DTNs.
● Accordingly, a node can direct query message towards the area
with higher information density to reduce the traffic by query
messages.
26
M. Fiore, C. Casetti, and C.-F. Chiasserini, “Information density estimation for content retrieval in
manets,” IEEE Transactions on Mobile Computing, vol. 8, no. 3, pp. 289–303, 2009.

Density‐Aware Routing in DTNs
Chih‐Lin Hu and Bing‐Jung Hsieh, “A Density‐Aware Routing Scheme in Delay
Tolerant Networks,” Proceedings of the 27th ACM Symposium on Applied
Computing (ACM SAC'12), Riva del Garda (Trento), Italy, March 25‐29, 2012.
27

Density‐Aware Routing Protocol
● The distribution of node population is non‐uniform
(sparse/dense) in the geographic scale, and time scale.
● In DTNs, ideally, nodes should move or copy messages to
encountered nodes that are going into dense areas.
 The inter‐meeting time between two consecutive encounters in dense
areas is shorter than that in sparse areas
 Nodes may distribute messages rapidly in DTNs, hopefully reducing
transfer delay and increasing message delivery ratio.
28
…
…
…
…
…
…
…
…
…
…
…
…

Our idea stems from …
● Keeping messages in the dense area
 Considering non‐uniform node distributions, it has higher probability to
encounter target nodes with lower delay time.
● Generating a small, fixed number of message copies
 Avoiding congestion and resource waste, where available storage and
inter‐node throughput opportunities are more tightly constrained
● Without auxiliary equipment (e.g. GPS)
● Exploiting the tendency of Inter‐Meeting‐Time
 Good scalability (The factor is independent of node population)
 Low complexity
29

DTN Context
● Two general assumptions
 Nodes can be aware of their motion speeds in
 Each node can keep track of its Inter‐Meeting‐Time (I) with any
encountered nodes.r to normalize I
30

Density‐Aware Routing Scheme
● Four design phases
(1) Inter‐meeting time normalization
(2) Density estimation
(3) Boundary detection
(4) Message forwarding
31

(1) Inter‐Meeting Time Formulation
● Design Properties：
 Each node Nn estimates its local density with
 With respect to any encountered nods N1, N2 , N3 at time t1, t2,
each node can have a sequence of I = , , …
● Node Nn estimates its local density with .
 At t1, Nn encounters a node and updates
where α is the number of the preceding Is.
 At t0 and , Nn immediately updates
32



)
(
1



k
k
n
n I
I



)
(
1
0




k
k
n
n I
I

i
n
I
i
n
I
n
n I

0
I
1
n
I 2
n
I 3
n
I

Normalized Inter‐Meeting Time
● In the Random WayPoint (RWP) mobility model, the expectation
of I is in inverse proportion to a node’s motion speed v [8].
A : size of network area
R : transmission range
: expected epoch distance
: expected epoch duration
: average pause time after an epoch
: normalized relative speed
33
)
(
2
)
1
(
2
ˆ
1
]
[ stop
m
rwp
m
rwp T
T
L
R
A
p
v
p
I
E 



L
stop
T
rwp
v̂
T

Normalized Inter‐Meeting Time
● With the simple simulation, the expectation of I is in inverse
proportion to a node’s motion speed v.
● Normalized I:
34
v
v
I
I 
 

(2) Line‐Based Density Estimation (1/3)
● Considering the factor of mobile trajectory,
it could be beneficial to develop an incremental density
estimation to enhance the estimation measure.
● Estimation incorporation
 to obtain more estimation
information from encountered
nodes in the surrounding area
to enhance its estimation of
node density in the current area.
35

Line‐Based Density Estimation (2/3)
● Define the density estimation Dn(t) in [0 ~ 0.5 ~1]
36
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
I
I
and
I
I
I
I
and
I
I
I
I
and
I
I
I
I
and
I
I
I
I
I
I
t
D


















0
0
0
0
2
,
2
,
2
,
2
,
2
1
0
2
1
0
)
(










Line‐Based Density Estimation (3/3)
● Two encountered nodes exchange their values of
density estimate, i.e., Dn(t) and De(t)
● For simplification, a node Nn defines the real density
estimate ௡ in [0,1], given as
37
2
))
(
)
(
(
)
( t
D
t
D
t
D e
n
n 

similar Dn(t) different Dn(t)

1
n
I
2
n
I 0
n
I
3
n
I
1
n
I
2
n
I
1
2
I
0
n
I
3
n
I
1
1
I
2
1
I
1
9
I
Tree‐Based Density Estimation (1/4)
● Keep track of I instead of only considering α I.
● Two encountered nodes exchange their values of
density estimate, i.e., SDn(t) and SDe(t)
38



1
2
i
i

● Building the tree based on the history table.
39
2
e
I
1
9
I
1
e
I
1
n
I
1
2
I
2
n
I
1
n
I
2
n
I
1
2
I
2
e
I 1
e
I
2
2
I
1
n
I
2
n
I
1
2
I
1
e
I
2
e
I 1
9
I
1
9
I
1
3
I
3
n
I
1
8
I
n
e
V
V

e
n
V
V


● Weighting local density estimation:
40
1
n
I
2
n
I
1
2
I
2
e
I 1
e
I
1
n
I
2
n
I 1
2
I
2
e
I
1
e
I
)
1
(
2 
 i
-1
2
-2
2
1
2
2
I
1
9
I
2
2
I
1
9
I
1
3
I
3
n
I
1
8
I 1
8
I



)
(
1



k
k
n
n I
I 




)
2
(
1
,
2
1
)
1
(
1

 




k
j
k
n
j
n I
I

● Considering the encountered angle.
 We try to know the quantity of information from the
encountered node.
41
)
2
sin
1
(
))
(
2
sin
)
(
(
)
(





 t
SD
t
SD
t
D node
encounter
n
n
 


(3) Boundary Detection
● Two nodes determine that they should locate in a dense area
boundary as Dn(t)>0.5 and De(t)<0.5
● Four cases as two nodes encounter in a dense area boundary:
42

(4) Forwarding Strategy
● Quota‐based routing scheme (Spray‐and‐Wait [7])
 There are a fixed number of M message copies distributed in
the network.
 Binary spray delivery
 Forwarding phase
● Packet forwarding priority
 Destination > Spray phase > Forwarding phase
43

Forwarding Strategy
● Binary spray phase:
 The source node of a message initially starts with a replication quota of
M message copies.
 When any node (source or relay node) has more than one message
copies and encounters another node with no copies, it hands over half of
its message copies to the other.
● Wait  Forwarding phase:
 When a node is left with only one copy, it switches to the wait phase.
 Whenever such a node meets another node, it performs a proactive
forwarding decision according to density estimation in proximity and
boundary detection.
► The message copy is sent to a node being in or going to a dense area.
44

Simulation Environment
 The ONE Simulator (Opportunistic
Network Environment)
 Simulation area : 2400*2000 m2
 Number of node : 100~1000 (300)
 Transmission rate : 250 KB/s
 Transmission range : 10 m
 Buffer size : 10 MB
 Message generation period : 50
seconds
 Message size : 50 KB
 Time to Live (TTL) : 9000 seconds
 Number of copies per message : 8
 Extended Random WayPoint
Mobility model
 Regarding the center of the map
as a dense area, a parameter P
indicates the probability of a node
moving toward the dense area
 P : 0.1~0.9
 Motion speed : 0.5~2.5 m/sec
 Pause times : 0 second
 Number of preceding inter‐
meeting times: α = 1~6
45
The simulator runs in 345600 seconds and
sends out 5912 original packets in total.

Effective Density Estimation
● P = 0.6
46

Delivery Ratio (Line based)
with Different Values of P and α
47

Delivery Ratio (Tree based)
with Different Values of P and α
48

Delivery Ratio
in Different Number of Dense Areas
49
● P = 0.6

0.65
0.7
0.75
0.8
0.85
0.9
100 200 300 400 500 600 700
Delivery
Ratio
(%)
Number of nodes
SnW Line Based Tree Based
Delivery Ratio
in Different Number of Nodes
50

0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.1 0.25 0.5 1 2 3 4 5 6 7 8 9 10 100
Delivery
Ratio
(%)
Buffer size(MB)
SnW Line Based
Tree Based Epidemic
Delivery Ratio
in Different Buffer size
51

0
100
200
300
400
500
600
700
800
100 200 300 400 500 600 700 800 900 100
Transmission
overhead
Number of nodes
SnW
Line Based
Tree Based
Epidemic
Transmission Overhead
in Different Number of Nodes
52

0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 2 3 4 5 6 7 8 9 10 11 12
Delivery
Ratio
(%)
Number of copies
Delivery Ratio
in Different Number of Copies
53

Delivery Ratio
in Different Speeds
54
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.1 0.2 0.4 0.8 1.6 3.2 6.4 12.8
Delivery
Ratio
(%)
Speed(m/s)
SnW
Line Based
Tree Based

0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1200×1000 2400×2000 3600×3000 4800×4000 6000×5000
Delivery
Ratio
(%)
Map size(m × m)
Delivery Ratio
in Different Map Sizes
55

Summary
● The proposed DARS enables mobile nodes to estimate the local
density and keep messages in dense areas, significantly
increasing the message delivery ratio in DTNs.
● This design generates only a small, fixed number of message
copies to avoid congestion and resource waste.
● DARS is affected by the number of dense areas.
 DARS outperforms the SnW and Epidemic methods with the buffer size of
2‐5 MB,.
 DARS can further improve the delivery ratio of SnW by 8% (as α = 4 and P
= 0.6).
56

Concluding Remarks
● Many natural environments introduce a lot of delay‐tolerant
networks and application domains.
● Traditional routing techniques in computer networks, as well as
in MANETs, may be questionable.
● New routing methodologies will be required to meet realistic
constraints.
● The proposed routing scheme with density‐awareness
 This design is free from egoistic assumptions.
 This design competes with other routing techniques with better
performance.
57

Open Issues Yet
● Unicasting versus Multicasting in DTN
 Most of previous research efforts were dedicated to the
performance regarding how to send one message from the
source to the destination.
● In‐network Intelligence
● The relationship with social community
58

Q&A
Thank you for your listening.
59

Applied Network Domains
[RFC 4838, by Vint Cerf, et al (April 2007 )]
● Interplanetary Internet, which focused primarily on the issue of
deep‐space communication in high delay environments
 NASA researchers quarrel over how to network outer space.
[Joab Jackson, IEEE Spectrum, Aug. 2005 ]
 It would use optical communications using laser beams for their lower
ping rates than radiowaves.
● Sensor‐based networks using scheduled intermittent
connectivity
● Terrestrial wireless networks that cannot ordinarily maintain
end‐to‐end connectivity
● Satellite networks with moderate delays and periodic
connectivity
● Underwater acoustic networks with moderate delays and
frequent interruptions due to environmental factors 60

Application Domains
● Interplanetary space
● Natural disasters
● Agricultural lands
● Fishery grounds
● Forest parks
● Grazing areas
● Wilderness
61

DTN Architecture: Why?
● The existing Internet architectures do not work well for DTN
environments due to some fundamental assumptions:
 An end‐to‐end path between source and destination exists for the
duration of a communication session
 Retransmissions based on timely and stable feedback from data receivers
is an effective means for repairing errors
 End‐to‐end loss is relatively small
 All routers and end stations support the TCP/IP protocols
 Packet switching is the most appropriate abstraction for interoperability
and performance
 Selecting a single route between sender and receiver is sufficient
 Applications need not worry about communication performance
 Endpoint‐based security mechanisms are sufficient for meeting most
security concerns
62

DTN Architecture: What
● The DTN architecture is conceived to relax most of these
assumptions, based on a number of design principles here.
 Use variable‐length messages (possibly long; not streams or limited‐sized
packets) as the communication abstraction to help enhance the ability of
the network to make good scheduling/path selection decisions as possible
 Use a naming syntax that supports a wide range of naming and
addressing conventions to enhance interoperability
 Use storage within the network to support store‐and‐forward operation
over multiple paths, and over potentially long timescales
 Provide security mechanisms that protect the infrastructure from
unauthorized use by discarding traffic as quickly as possible
 Provide coarse‐grained classes of service, delivery options, and a way to
express the useful lifetime of data to allow the network to better deliver
data in serving the needs of applications
63

● Use storage within the network to support store‐and‐
forward operation over multiple paths, and over
potentially long timescales
● Provide coarse‐grained classes of service, delivery
options, and a way to express the useful lifetime of
data to allow the network to better deliver data in
serving the needs of applications
64

Delivery Ratio with Multiple Dense Areas
65

Communication Cost by Node Population
66

Delivery Ratio
 Dense Area =1  Dense Area = 1~9
67
α: the number of the recent Is
p: the probability of a node moving toward the dense area
number of
dense areas
DARS can further improve the delivery ratio of SnW by 8% (as α = 4 and P = 0.6).

Sensitivity to Node Population
 Delivery Ratio  Communication Cost
68
Epidemic: a flooding‐type approach can
induce a huge amount of messages to
attain a high delivery ratio.
DARS is more effective in the case of larger
node population.
DARS can further improve the delivery ratio
of SnW by 8%.

Coding‐Based Routing to Multiple Receivers
in DTNs
Yu‐Feng Hsu and Chih‐Lin Hu*, “Erasure Coding‐Based Routing for Message Multicasting in
Delay‐Tolerant Networks,” Proceedings of the 2012 IET International Conference on
Frontier Computing ‐ Theory, Technologies and Applications (IET FC'12), Xining, China,
August 2012.
Yu‐Feng Hsu, and Chih‐Lin Hu*, “Network Coding with Remix Qualification for Multicasting
in Delay‐Tolerant Networks,” accepted by IEEE Wireless Communications and Networking
Conference 2013 (IEEE WCNC'13), Shanghai, China, April 7‐10, 2013.
69

Introduction
● Premise in many studies of mobile ad hoc networks
(MANETs)
 There exists at least one end‐to‐end path between every pair
of nodes in the network most of the time.
► Short Delay
● Delay Tolerant Network (DTN)
 Intermittent and opportunistic network connectivity
 It is very difficult to guarantee any persistent end‐to‐end
routing path between a source and a destination.
► Intermittent Connectivity
► Long Delay
70

Message Forwarding
● Traditional routing paradigms
 Assume that a route should be first determined before
sending out any messages
● For DTNs, an opportunistic routing approach is
assumed with the way “store‐carry‐and‐forward.”
 A message can be stored and carried by a node when the
node has no opportunity to forward the message.
71

Store, Carry, and Forward
72
Source ‐> Relay node 1 Relay node 1 ‐> Relay node 2 Relay node 2 ‐> Destination
Relay race

Routing in DTNs
● Recent research efforts have proposed a variety of
routing mechanisms, such as replication‐based and
coding‐based routing techniques.
● Replication‐based
 Replicating an original message, and then forwarding copies
to encountered nodes.
● Coding‐based
 Coding an original message into many coded blocks, and
then forwarding coded blocks.
73

Replication v.s. Coding
74
Message r copies Received Message
Relay path
Replicate
Replication factor (r)=2
r relays
n relays

Performance Measurement on DTNs
● Message delivery delay
 The time duration from the moment which a message is sent by a source
till the moment which this message is received by a destination.
 Many research works were dedicated to the average delay.
75

Performance Measurement on DTNs
● Message delivery delay
 The time duration from the moment which a message is sent by a source
till the moment which this message is received by a destination.
 Many research works were dedicated to the average delay.
76
Worst‐case delay

Objective
● According to previous studies, the erasure coding
scheme is able to moderate the worst‐case delay.
● This study aims to exploit the essence of the Erasure‐
Coding (EC) technology for not only message unicasting
but also multicasting in DTN environments.
77

Delay Distribution Analysis
● To derive mathematic formulations of delivery delay
distribution.
 The previous study applied the order statistic to address
theoretical behavior of delivery delay distribution on the
base of the EC‐based model.
 We apply the order statistic to analyze the delay distribution
for message multicasting .
78

Principle of Order Statistics
● Considering n independent and identically distributed (i.i.d.)
random variables x1,…,xn, then sorting these n random variables
by ascending order can generate n new random variables y1,…,yn
as y1=min{x1,…,xn} and yn=max{x1,…,xn}
● The random variable yk is called the kth order statistic.
● Let F(x) be the cdf of xi, and f(x) be the pdf of xi, then the pdf of
yk is
79
- -
!
( ) ( ) ( ) ( - ( ))
( - )!( - )!
n k n k
k
n
y x f x F x F x
k n k
 1
1
1 (1)

Delay of Erasure Coding
● Considering a basic EC approach with a replication factor r and a
split degree k. (n=kr)
● Applying the order statistics, the delivery delay by EC is .
● The delivery delay by simple replication is .
80
n
k
Y
r
Y1
n relays

Delay of Erasure Coding
81
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 2 3 4 5 6 7 8 9
CDF
Delay ( Units )
k=1
k=2
k=4
k=8
k=16
k=32
Given that x is under a Pareto distribution
Delivery delay of erasure coding scheme(k>1) and replication scheme (k=1) as r =2.
( ) ( ) , . ,
f x x
 
   
 
  
1
0 6 1

Multicasting Delay
● Considering there are N destination nodes, the delay for
multicasting is the delay of the N‐th destination node .
● Assuming the delay from a source to a destination is a random
variable with distribution wi .
● Applying the order statistics to obtain the delay distribution of
multicasting with N destination nodes:
82
!
( ) ( ) ( ) ( ( ))
( )!( )!
( )* * ( )
N N N N
N
N
N
Z w f w F w F w
N N N
f w N F w
 

 
 

1
1
1
1 (2)

0
0.2
0.4
0.6
0.8
1
1 3 5 7 9 11 13 15 17 19 21
CDF
Delay ( units )
EC(1,2)
EC(2,4)
EC(4,8)
0
0.2
0.4
0.6
0.8
1
1 3 5 7 9 11 13 15 17 19 21
CDF
Delay ( units )
EC(1,2)
EC(2,4)
EC(4,8)
Reducing Delivery Delay by EC
83
( ) ( ) , . ,
f x x
 
   
 
  
1
0 6 1
Assume that the delay of coded block is under Pareto distribution
EC (k, k  r)
1 destination 16 destinations

Simulation Environment
● Using the Opportunistic Network Environment
Simulator.
● The mobility model follows the Self‐similar Least‐Action
Human Walk (SLAW) mobility with default values.
● Comparisons:
 Erasure coding with r and k ：EC(k, k  r)
 Simple replication with r ：EC(1, r)
84

Sensitivity to the Number of Destination
Nodes ( N )
85
1 destination 16 destinations
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50000 100000 150000 200000 250000
CDF
Delay time (seconds)
EC(1,2)
EC(2,4)
EC(4,8)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50000 100000 150000 200000 250000
CDF
EC(1,2)
EC(2,4)
EC(4,8)

Upper Bound for the Number of Divided
Blocks (k)
86
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20000 40000 60000 80000 100000 120000 140000
CDF
EC(1,2)
EC(2,4)
EC(4,8)
EC(8,16)
EC(16,32)
EC(32,64)
EC(8,16)
16 destinations , replication factor r = 2
Kmax=8

Sensitivity to the replication factor (r)
87
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50000 100000 150000
CDF
EC(1,2)
EC(2,4)
EC(4,8)
EC(8,16)
EC(16,32)
EC(32,64)
EC(8,16)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20000 40000 60000 80000
CDF
EC(1,8)
EC(2,16)
EC(4,32)
EC(8,64)
EC(2,16)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50000 100000 150000
CDF
EC(1,4)
EC(2,8)
EC(4,16)
EC(8,32)
EC(16,64)
EC(4,16)
Kmax  r = 16
100 nodes
16 destinations
Replication factor = 2 Replication factor = 4
Replication factor = 8

Sensitivity to Node Population and
Density
88
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50000 100000 150000 200000
CDF
EC(1,2)
EC(2,4)
EC(4,8)
EC(8,16)
EC(16,32)
EC(32,64)
EC(16,32)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50000 100000 150000
CDF
EC(1,4)
EC(2,8)
EC(4,16)
EC(8,32)
EC(16,64)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20000 40000 60000 80000 100000
CDF
EC(1,8)
EC(2,16)
EC(4,32)
EC(8,64)
EC(8,32)
EC(4,32)
Replication factor = 2 Replication factor = 4
Replication factor = 16
Kmax  r = 32
200 nodes
16 destinations

Summary
● The delivery delay distribution is much affected by the
number of divided blocks.
● As the number of destination nodes increases, the
performance gain by EC can become better in terms of
either overall delay or worst case delay.
● There should be an upper bound for the number of
coded blocks under a fixed value of replication factor.
● This upper bound is sensitive to the replication factor
and node density in DTNs.
89

Q&A
Thank you for your listening.
90

Delay‐Tolerant Routing in Opportunistic Delay‐Tolerant Routing in Opportunistic and Intermittent Networks and Intermittent Networks

More Related Content

Similar to Delay‐Tolerant Routing in Opportunistic Delay‐Tolerant Routing in Opportunistic and Intermittent Networks and Intermittent Networks (20)

Recently uploaded (20)

Delay‐Tolerant Routing in Opportunistic Delay‐Tolerant Routing in Opportunistic and Intermittent Networks and Intermittent Networks