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Location-aware routing for Delay Tolerant Networks

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This paper designed a location aware routing scheme for Delay Tolerant Networks that can deliver more messages within shorter delays, therefore improves the network intensively and compares with other representative DTN routing schemes.
Abstract
In this paper, we sought to understand the reasons causing failures and delays of message delivery in Delay Tolerant Networks (DTN), and to use this understanding for improving the network. By studying two real-world datasets, we found that node isolation is prevalent, which largely accounts for the inefficiencies in DTN's message delivery. In addition, by analyzing nodes' contact-location relationship, we found that individual and system-wide key locations exist and their existence suggests potential improvements. Motivated by our observations, we designed a location aware routing scheme for DTN networks. With simulation-based experiments, we compared our proposal with other representative DTN routing schemes, and showed that with the awareness of the location information, our solution can deliver more messages within shorter delays, therefore improves the network intensively.

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Location-aware Routing for
Delay Tolerant Networks
Ye Tian
Anhui Province Key Laboratory on High Performance Computing
School of Computer Science and Technology
University of Science and Technology of China
Hefei, Anhui 230027, China
Email: yetian@ustc.edu.cn
Jiang Li
Department of Systems and Computer Science
Howard University
Washington DC 20059, USA
Email: lij@scs.howard.edu
Abstract—In this paper, we sought to understand the reasons
causing failures and delays of message delivery in Delay Tolerant
Networks (DTN), and to use this understanding for improving
the network. By studying two real-world datasets, we found
that node isolation is prevalent, which largely accounts for
the inefficiencies in DTN’s message delivery. In addition, by
analyzing nodes’ contact-location relationship, we found that
individual and system-wide key locations exist and their existence
suggests potential improvements. Motivated by our observations,
we designed a location aware routing scheme for DTN networks.
With simulation-based experiments, we compared our proposal
with other representative DTN routing schemes, and showed that
with the awareness of the location information, our solution can
deliver more messages within shorter delays, therefore improves
the network intensively.
I. INTRODUCTION
With advance of wireless technologies and prevalent usage
of portable wireless devices, in recent years, the idea of
Delay Tolerant Networks (DTN[1]) has been proposed. Simply
speaking, a DTN network is an ad-hoc network formed by
portable devices such as cell phones or PDAs, and in such
a network, device-to-device communication is enabled using
the store-and-forward paradigm. As the only communication
opportunity in a DTN network is the device contact caused by
uncontrollable human mobility, it is essential to understand
and exploit the human contacts in designing a DTN routing
scheme.
Many routing schemes have been proposed for DTN net-
works in recent years. However, for most of them (e.g.
[2][3][4][5][6]), a “flat” network was assumed, where each
node plays an equal role. In these schemes, decisions on
message forwarding are based on some destination dependent
quality metrics, and the message is forwarded towards the
nodes with better qualities. On the other hand, a recent
study[7] shows that social structure of the network exist and
should be labeled and exploited. In our work, we also labeled
the inherited structure of the network explicitly, but unlike the
previous work, we labeled the nodes based on their location
This work is funded by the Specialized Research Fund for the Doctoral
Program of Higher Education of China 20093402120020, and was funded
in part by US NSF grant CNS-0832000 and the Mordecai Wyatt Johnson
Program at Howard University.
visiting information as well as their contact information to
make forwarding decisions.
Two contributions were made in this paper: first of all, we
conducted an insightful analysis on the contact and location
information of nodes in DTN networks. By examining two
real-world datasets, we found that the phenomenon of node
isolation is prevalent and is the major reason for the inef-
ficiencies in DTN’s message delivery. We also found that
there exist special locations for individual node and some
of them are of system-wide importance. Motivated by these
observations, we proposed a location aware routing scheme for
DTN networks. In addition, we demonstrated the superiority
of the proposed scheme over other representative schemes via
extensive simulation experiments using the contact trace from
real-world dataset.
The remainder part of this paper is organized as follows:
related works are surveyed in Section II; we introduce and
analyze the real-world datasets in Section III; in Section IV,
we propose the location aware routing scheme for DTN net-
works; performance evaluation and comparison are presented
in Section V; finally, Section VI concludes this paper.
II. RELATED WORK
Early works on the DTN routing problem were focused
on deploying and using dedicated nodes, such as static
throwboxes[8] and controllable mobile ferries[9]. In recent
years, DTN networks composed of portable devices carried
by human beings have received great attentions. For message
routing in such a network, although the epidemic scheme[10]
based on flooding makes use of every device contact, it is
regarded as impractical due to the large volume of message
duplicates generated. The Spray and Wait routing[11] made an
effort on reducing the duplicates by assigning limitations on
message copies. Besides the epidemic-style ones, for majority
of the DTN routing schemes, messages are forwarded towards
the nodes which are considered as better candidates for de-
livery. Examples include MED[2], FRESH[3], PRoPHET[4],
MobySpace[5], SimBet[6], and delegation forwarding[12].
These schemes vary on their criteria in evaluating the next
hop, and for most of them, the criteria is destination dependent.
Besides simply comparing destination dependent metrics and
CHINACOM 2010, August 25-27, Beijing, China
Copyright © 2011 ICST 973-963-9799-97-4
DOI 10.4108/chinacom.2010.4

forwarding messages on a “flat” network, inherited social
structure of the network is also exploited. In the recent pro-
posed BUBBLE Rap routing scheme[7], communities among
the nodes are detected and explicitly labeled, and different
forwarding strategies are applied in different routing phases
based on the community structure.
III. ANALYSIS OF REAL-WORLD DATASETS
A. Datasets under study
To investigate the device contacts in DTN networks, we
selected two real-world datasets which contain long-time
mobility and contact information from a large number of
participating nodes for our study. The two datasets are from the
MIT Reality Mining project[13] and from the UCSD Wireless
Topology Discover project[14] in respective. For details of the
datasets, please refer to our technical report[15]. In particular,
in the UCSD dataset, we considered a contact between two
devices happened if they were associated with a same AP
simultaneously, as in the previous works [16][17]. In the
remainder part of this paper, we refer to the two datasets as
Reality and UCSD for simplicity.
B. Connectivity and isolation
TABLE I
COMPONENTS AND ISOLATION IN CONTACT GRAPH
Contact Num. of Num. of Largest 2
nd
largest
graph
comp. isolated nodes comp. comp.
G(Reality, 25) 13 12 84 1
G(Reality, 35)
15 14 82 1
G(Reality, 45)
23 21 73 2
G(UCSD, 10) 89 86 155 2
G(UCSD, 15)
108 106 137 2
G(UCSD, 20)
128 125 58 54
35 45 55
0
0.5
1
1.5
2
2.5
Threshold
Delay (days)
Reality
15 20 25
0
5
10
15
20
25
30
UCSD
Threshold
Delay (days)
Intra−component
Inter−component
Fig. 1. Comparison of intra- and inter-component delays for Reality and
UCSD
For DTN networks, how to avoid the message delivery
failure and reduce the delay is the major concern. In this
section, we sought to find the fundamental reasons causing
these inefficiencies by studying contact graph of the datasets
above introduced.
Given a dataset d, a contact graph G(d, t) = (V, E) is
defined as an undirected graph, with V as the vertex set where
each node in the dataset corresponds to a vertex. For any two
vertexes v
i
and v
j
, there is an edge (v
i
, v
j
) in the edge set E
if the number of the contacts between the two corresponding
nodes in d is no smaller than a threshold number t. By
varying contact thresholds, we obtained a number of contact
graphs from Reality and UCSD, that is, G(Reality, t) with
t = 25, 35, 45 and G(UCSD, t) with t = 10, 15, 20 in
respective. The summaries of the contact graphs are listed
in Table I. From the table one can see that nodes are het-
erogeneous regarding their connectivity. In Reality, one giant
component containing more than half of the nodes exists, and
nearly all the other nodes are either isolated or form tiny
components (a component contains very few nodes). When
the threshold gets increased, more nodes are isolated from
the giant component but the giant component still exists.
For UCSD, similar observations could be made except that
with the increase of the threshold, one giant component splits
into two giant components of approximately the same size.
In the following part of this paper, we refer to a dataset’s
giant component as component, and refer to the isolated nodes
and the nodes in tiny components together as isolated nodes.
Clearly for any node in the dataset, it is either in a component
or be isolated.
1st 2nd 3rd 4th
0
0.2
0.4
0.6
0.8
1
Ratio of time
Component I
Component II
Isolated
(a)
0
5
10
15
20
AP index
Num. of nodes
Component I
(b)
0
5
10
15
20
AP index
Num. of nodes
Component II
(c)
0
5
10
15
20
AP index
Num. of nodes
Isolated
(d)
Fig. 2. (a) Comparison of APs in ratio of time a node stayed; (b-d)
Histograms of times an AP became home location of nodes in Component I,
of nodes in component II, and of isolated nodes
With node isolation widely observed, to investigate its im-
plication on the DTN routing problem, we studied two metrics
of a contact graph, namely the intra-component delay and the
inter-component delay. To define the metrics, we modified the
contact graph into a weighted contact graph G
w
(d), where
for each edge on the graph, its weight is defined as the
averaged inter-contact time between the two corresponding
nodes. With the weighted contact graph, the intra-component
delay is defined as the mean distance between any two nodes in
a same component using the MED algorithm[2], and the inter-
component delay is defined as the mean distance between one
component and one isolated node.
We show the calculated intra- and the inter-component
delays under different thresholds in Fig. 1. From the figure,
one can see that for both datasets, the inter-component delays
are much longer than the intra-component ones. In fact in
practical DTN routing, failures are more likely to be expected
than the long delays due to timeout. The observation suggests

that node isolation is the major reason for the latency and the
failure in DTN’s message delivery, and should be our focus
in designing the routing scheme.
C. Contact-location relationship
In this section, we studied the locations where nodes make
their contacts. As location information is not available in
Reality, we only used the UCSD dataset. We set a threshold
of 20 contacts for detecting the components, and as listed in
Table I, we had 58 nodes in one component (referred to as
Component I), and 54 nodes in the other component (referred
to as Component II), and all the other 133 nodes were regarded
as isolated.
1) Home location: To find a specific node, the most direct
way is to identify the location where it is most likely to stay.
Therefore we considered the location (i.e., AP) each node
stayed for the longest time accumulatively in UCSD. Fig. 2(a)
shows the ratios of the time nodes in different groups spent at
their most favorite locations. We also identified the 2nd, 3rd,
and 4th favorite locations of the nodes and plotted the ratios
on the figure. It is surprising to see that a node spends more
than 90% of its time at just one location, regardless whether
it is in a component or isolated. We refer to this location as
the node’s home location.
With each node’s home location identified, we also counted
how many times an AP becomes a node’s home location and
plotted the histograms over all the APs for each group in
Fig. 2(b-d) respectively. One can see from the histograms that
although some nodes share their home locations, nodes are
in general not having a common home location, especially
for the isolated ones. Our observation suggests that although
nodes tend to stay at their home locations, none of them is of
a system-wide importance.
1st 2nd 3rd 4th
0
0.2
0.4
0.6
0.8
Ratio of total nodes met
Component I
Component II
Isolated
(a)
0
20
40
60
AP index
Num. of nodes
Component I
AP 173
(b)
0
20
40
60
AP index
Num. of nodes
Component II
AP 173
(c)
0
20
40
60
AP index
Num. of nodes
Isolated
AP 173
(d)
Fig. 3. (a) Comparison of APs in ratio of nodes a node could meet; (b-d)
Histograms of times an AP became pub location of nodes in Component I,
of nodes in Component II, and of isolated nodes
2) Pub location: Meanwhile, we also considered the lo-
cation where a node could encounter many other nodes. For
each node in UCSD, we identified the AP where it could meet
the largest number of distinct nodes, as well as its 2nd, 3rd,
and 4th popular APs for comparison. The ratios of the nodes
a node in different group could meet at these locations are
calculated and plotted in Fig. 3(a). From the figure one can
see that a node could encounter over 70% of the total nodes
it could ever meet at just one location, regardless whether it
is in a component or isolated. We refer to this location as the
node’s individual pub location.
We also counted the times an AP is chosen as the indi-
vidual pub location by nodes in different groups and plot the
histograms in Fig. 3(b-d). It is surprising to see that overall
there are nearly half of the nodes having one location, i.e. AP
173, as their pub location, and AP 173 is the most and the
only popular pub location candidate for both component nodes
and isolated nodes. For such a location which is the individual
pub location of a large population, such as AP 173 in UCSD,
we name it as a system-wide pub location
1
as it is system-
wide important. Meanwhile, we also found that in general a
node is not likely to have a same location as its home and pub
locations.
As many nodes were observed to go to the system-wide
pub locations, we investigated their visiting patterns to this
location. By analyzing the nodes in UCSD with AP 173 as
their pub locations, we found that 1) there is only a limited
number of nodes which visited AP 173 frequently; 2) a node
did not meet many other nodes in its one single visit to AP
173; 3) most pairs of nodes did not meet at AP 173 repeatedly.
We omit the detailed statistical results here for space reason,
interested readers can refer to our technical report [15]. Finally,
our observation show that although pub locations of system-
wide importance exist, they are not hot locations for each
single node’s activity in DTN networks, therefore to exploit
them, a well designed routing scheme is required.
IV. ROUTING SCHEME
Motivated by the observations made in the previous section,
we propose a message routing scheme for DTN networks to
avoid the failures and reduce the delays in message delivery.
In our scheme, we assume that the network area is divided
into cells called locations, components among the nodes are
identified and nodes’ pub location information as well as their
belongings to the components are available. For the concept
of component in our routing scheme, other definitions (such
as the “community” defined in [18]) can be used as long as
frequently contacting nodes are grouped together.
We proposed a location aware routing scheme (referred to
as Location) under the DTN networking environment. In the
Location routing, we differentiate the operations of forwarding
a message and replicating a message. As in many message
forwarding algorithms (e.g., [7], [19]), a node holding a
message can forward the message to a non-destination node
only once, after that, the node becomes forwarding inactive
and can only pass the message to the destination. On the other
hand, a node holding the message can replicate it to other
nodes without such constraint.
1
We will use the term “pub location” for the individual and system-wide
pub location depending on the context.

Location Assisted Routing
PhaseIRoute (Current)
1 foreach Encountered do
2 if (Encountered.Comp = Dest.Comp)
3 Forward(Encountered)
4 PhaseIIRoute(Encountered)
5 if (Current = Source && Is_New(Encountered.PubLoc) =
true)
6 Replicate(Encountered)
7 PhaseIRoute(Encountered)
8 if (Encountered.PubLoc = Current.PubLoc &&
Encountered.NodesMetAtPub > Current.NodesMetAtPub)
9 Forward(Encountered)
10 PhaseIRoute(Encountered)
PhaseIIRoute (Current)
1 foreach Encountered do
2 if Encountered.Metrcs > Current.Metrics
3 Forward(Encountered)
4 PhaseIIRoute(Encountered)
Fig. 4. Location aware routing scheme
The message routing procedure in Location is divided into
two phases: the first phase happens when the forwarding
active node is outside the component of the destination or the
destination node is isolated; the second phase happens when
the forwarding active node is in the same component of the
destination. A brief description of the scheme can be found in
Fig. 4.
In the second phase, many message routing strategies such
as the ones used in MED[2], FRESH[3], PRoPHET[4], and
MobySpace[5] can be applied. The basic idea is to compare
certain destination dependent quality metrics and forward the
message to a node with better quality. For our experimental
evaluation, we chose the Greedy strategy used in [19]. We
stress that our focus here is not on comparing the metrics
based routing strategies in the second routing phase, but is on
the first routing phase (i.e., routing outside the destination’s
component).
In the Location routing scheme, we exploited the location
information as well as the social network structure (i.e. com-
ponents) in the first routing phase. In detail, if a forwarding
active node outside the destination’s component encounters a
node, it examines whether the encountered node is in the same
component of the destination, and adopts different strategies
as described in line 2-4 and line 8-10 respectively. In addition,
for the source node, if it encounters a node with a pub location
it has not seen before, it replicates the message on it, and the
replicated node starts to forward the message among the nodes
with the same pub location as described in line 5-7.
V. PERFORMANCE EVALUATION
In this section, we evaluated the performance of the pro-
posed location-aware approach, and compared it with other
four representative DTN routing schemes, which are named
Epidemic, Wait, Greedy and Social. In particular, the So-
cial routing scheme applies exactly the same strategy used
in BUBBLE Rap[7] when routing messages outside of the
destination’s component. For details of these schemes, please
refer to our technical report[15].
For each routing scheme under study, given a message
delivery task between a source and a destination node within a
delay constraint, we are interested in 1) whether the message
can be successfully delivered within the constraint; 2) how
many times the message is copied and transferred during the
routing procedure. The former metric regards the effectiveness
of the routing scheme while the latter indicates the cost of
bandwidths and storages paid for delivering the message.
A. Overall comparison
TABLE II
COMPARISON OF ROUTING SCHEMES USING UCSD TRACE
Message delivered Message copies
Epidemic 76.0±8.2 104.6±5.92
Wait
25.2±2.0 1.0±0.0
Greedy
52.6±3.3 3.0±0.25
Social
63.0±5.5 6.7±0.4
Location
67.0±5.1 12.1±1.2
We evaluated and compared performances of the ve
schemes above mentioned using the contact trace from the
UCSD dataset. An event-driven simulator is developed. In
our first experiment, for each routing scheme, we randomly
selected one hundred source/destination pairs for message
delivery, and we did not restrict the delay constraint. The
averaged number of successfully delivered messages and the
averaged number of message copies are listed in Table II.
From the table one can see that Epidemic can deliver the
largest number of messages, while Wait delivers the fewest.
For the three forwarding-style schemes, i.e., Greedy, Social,
and Location, Location delivers more messages, suggesting
its superiority over the other two schemes. For the message
copies, Epidemic duplicates and transfers much more copies
than the other schemes, making it impractical under the context
of DTN networks. Among the three forwarding-style schemes,
Location has more copies than the other two. However, the
message copies generated by Location are much fewer than
by Epidemic, and under moderate conditions, Location could
be considered as real-world practical. As Social and Location
perform much better than Greedy, in our following study, we
only focus on comparing the two schemes. In addition, as both
schemes just incur moderate costs, in the following study we
only focus on their effectiveness (i.e. messages successfully
delivered).
B. Detailed study
In Section III, we point out that node isolation is the main
reason for message delivery failures and delays, we testify this
argument in this experiment. Instead of randomly selection,
four cases of source/destination pairs are considered: in the
“Component Component” case, the source and destination
nodes are in different components; in the “Component
Isolated” case, we select the source node from a component,
and select an isolated node as the destination; the third and the
fourth cases are referred to as “Isolated Component” and
“Isolated Isolated”, with denotations of the same meanings.

In addition, for each case we only select the infrequent visitors
to its pub location.
0 5 10 15 20 25
40
50
60
70
80
90
Delay constraint (days)
Messages successfully delivered
Component −−> Component
Social
Location
(a)
0 5 10 15 20 25
0
10
20
30
40
50
Delay constraint (days)
Messages successfully delivered
Component −−> Isolated
Social
Location
(b)
0 5 10 15 20 25
20
30
40
50
60
70
80
Delay constraint (days)
Messages successfully delivered
Isolated −−> Component
Social
Location
(c)
0 5 10 15 20 25
0
10
20
30
40
Delay constraint (days)
Messages successfully delivered
Isolated −−> Isolated
Social
Location
(d)
Fig. 5. Number of successfully delivered messages by Social and Location
with varying delay constraint under different source/destination cases using
UCSD trace
We randomly chose one hundred source/destination pairs
for each case for simulation. In this experiment, a delay
constraint was imposed as messages must be delivered within
this delay. For Social and Location routing schemes under
each source/destination case, we varied the delay constraint
and plotted the successfully delivered messages in Fig. 5.
From the figure, first of all one can see that performances
of the two routing schemes under different source/destination
cases differ greatly: for both schemes, they have the best
performance under the “Component Component” case,
but in cases where isolated nodes are involved, either as
source or as destination, fewer messages could be delivered,
especially when the destination is isolated. The observation
here confirms our argument that node isolation is the major
reason for failures and delays in DTN’s message delivery.
Moreover, by comparing the two routing schemes, one can
see that although the Location scheme suffers node isolation
as well, it outperforms Social all the time. In particular, under
“Component Component”, “Component Isolated”, and
“Isolated Isolated”, when the delay constraint is stringent,
say, 5 days, Location delivers much more messages than
Social. Apparently, this feature makes Location an attractive
solution under environments where message deliveries are not
so “delay tolerant”. Finally, for all the four cases, it is observed
that Location consistently delivers more messages than Social.
We believe this is because by the replicating operation in the
Location scheme, the source node has more chances to forward
the message into the destination node’s component.
VI. CONCLUSION
In this paper, we considered the message routing problem
under Delay Tolerant Networks (DTN). By analyzing real-
world datasets , we found that node isolation is prevalent,
and it is the major reason for message delivery failures and
long delays in DTN networks. We also investigated the nodes’
contact-location relationship, and found that there exist pub
locations which are of system-wide importance.
Motivated by these observations, we considered incorporat-
ing the location information of nodes as well as their contact
information in routing messages by designing a location
aware routing scheme for DTN networks. We demonstrated
the scheme’s effectiveness by comparing it with a number
of representative solutions via simulation-based experiments,
where real-world contact traces is used to drive the simulator.
In particular, we show that with the awareness of contact-
location relationship, message delivery jobs involved with
isolated nodes could be better accomplished, comparing with
the schemes without such concern (e.g., Bubble Rap[7]).
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Book ChapterDOI

Routing Protocols in Delay Tolerant Networks

TL;DR: This paper surveys the state-of-the-art routing protocols and gives a comparison of them with respect to the important challenging issues in DTNs and separates them into flooding families and forwarding families.

Human Dynamic Networks in Opportunistic Routing and Epidemiology

TL;DR: This paper is intended to serve as a “roadmap” for future generations of scientists and historians to consider the search for extraterrestrial intelligence during the period of World War II.
References
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Epidemic routing for partially-connected ad hoc networks

TL;DR: This work introduces Epidemic Routing, where random pair-wise exchanges of messages among mobile hosts ensure eventual message delivery and achieves eventual delivery of 100% of messages with reasonable aggregate resource consumption in a number of interesting scenarios.
Proceedings ArticleDOI

Spray and wait: an efficient routing scheme for intermittently connected mobile networks

TL;DR: A new routing scheme, called Spray and Wait, that "sprays" a number of copies into the network, and then "waits" till one of these nodes meets the destination, which outperforms all existing schemes with respect to both average message delivery delay and number of transmissions per message delivered.
Proceedings ArticleDOI

Routing in a delay tolerant network

TL;DR: This work forms the delay-tolerant networking routing problem, where messages are to be moved end-to-end across a connectivity graph that is time-varying but whose dynamics may be known in advance, and proposes a framework for evaluating routing algorithms in such environments.
Book ChapterDOI

Probabilistic Routing in intermittently connected networks

TL;DR: This paper proposes PRoPHET, a probabilistic routing protocol for intermittently connected networks and shows that it is able to deliver more messages than Epidemic Routing with a lower communication overhead.
Proceedings ArticleDOI

Bubble rap: social-based forwarding in delay tolerant networks

TL;DR: BUBBLE is designed and evaluated, a novel social-based forwarding algorithm that utilizes the aforementioned metrics to enhance delivery performance and empirically shows that BUBBLE can substantially improve forwarding performance compared to a number of previously proposed algorithms including the benchmarking history-based PROPHET algorithm, and social- based forwarding SimBet algorithm.
Related Papers (5)
Frequently Asked Questions (8)
Q1. What are the contributions mentioned in the paper "Location-aware routing for delay tolerant networks" ?

In this paper, the authors sought to understand the reasons causing failures and delays of message delivery in Delay Tolerant Networks ( DTN ), and to use this understanding for improving the network. In addition, by analyzing nodes ’ contact-location relationship, the authors found that individual and system-wide key locations exist and their existence suggests potential improvements. With simulation-based experiments, the authors compared their proposal with other representative DTN routing schemes, and showed that with the awareness of the location information, their solution can deliver more messages within shorter delays, therefore improves the network intensively. 

Given a dataset d, a contact graph G(d, t) = (V,E) is defined as an undirected graph, with V as the vertex set where each node in the dataset corresponds to a vertex. 

With the weighted contact graph, the intra-component delay is defined as the mean distance between any two nodes in a same component using the MED algorithm[2], and the intercomponent delay is defined as the mean distance between one component and one isolated node. 

With node isolation widely observed, to investigate its implication on the DTN routing problem, the authors studied two metrics of a contact graph, namely the intra-component delay and the inter-component delay. 

The authors believe this is because by the replicating operation in the Location scheme, the source node has more chances to forward the message into the destination node’s component. 

The observation suggeststhat node isolation is the major reason for the latency and the failure in DTN’s message delivery, and should be their focus in designing the routing scheme. 

In their first experiment, for each routing scheme, the authors randomly selected one hundred source/destination pairs for message delivery, and the authors did not restrict the delay constraint. 

To define the metrics, the authors modified the contact graph into a weighted contact graph Gw(d), where for each edge on the graph, its weight is defined as the averaged inter-contact time between the two corresponding nodes.