DCE: A NOVEL DELAY CORRELATION MEASUREMENT FOR TOMOGRAPHY WITH PASSIVE REALIZATION

International Journal of Distributed and Parallel Systems (IJDPS) Vol.6, No.2/3, May 2015
DOI:10.5121/ijdps.2015.6301 1
DCE: A NOVEL DELAY CORRELATION
MEASUREMENT FOR TOMOGRAPHY WITH PASSIVE
REALIZATION
Peng Qin1,2
, Bin Dai1
, Benxiong Huang1
and Guan Xu1
1
Department of Electronics and Information Engineering, Huazhong University of
Science and Technology, Wuhan, China
2
China Academy of Electronics and Information Technology, Beijing, China
ABSTRACT
Tomography is important for network design and routing optimization. Prior approaches require either
precise time synchronization or complex cooperation. Furthermore, active tomography consumes explicit
probing resulting in limited scalability. To address the first issue we propose a novel Delay Correlation
Estimation methodology named DCE with no need of synchronization and special cooperation. For the
second issue we develop a passive realization mechanism merely using regular data flow without explicit
bandwidth consumption. Extensive simulations in OMNeT++ are made to evaluate its accuracy where we
show that DCE measurement is highly identical with the true value. Also from test result we find that
mechanism of passive realization is able to achieve both regular data transmission and purpose of
tomography with excellent robustness versus different background traffic and package size.
KEYWORDS
Network Tomography, Delay Correlation Measurement, Passive Realization.
1. INTRODUCTION
Network tomography [1] studies internal characteristics of Internet using information derived
from end nodes. One advantage is that it requires no participation from network elements other
than the usual forwarding of packets while traditional traceroute method needs response to ICMP
messages facing challenge of anonymous routers [2,3].
Many literatures choose delay to calculate correlation between end hosts for tomography.
However, they require either precise time synchronization or complex cooperation. Moreover,
active tomography consumes quantities of explicit probing bandwidth which results in limited
scalability.
In this paper we propose a novel Delay Correlation Estimation approach named DCE with no
need of cooperation and synchronization between end nodes. The greatest property is that we only
need to measure the packet arriving time at receivers. To further reduce bandwidth consumption a
passive mechanism using regular data flow is developed.
We do extensive simulations in OMNeT++ to evaluate its accuracy. Results show that the
correlation of delays 2
, b
a d
d
σ measured by DCE is highly identical with the true value 2
s
σ on
shared path. By altering background traffic and package size we see that passive mechanism has

2
excellent robustness and is able to achieve regular data transmission as well as purpose of
tomography.
1.1. Contributions
• We propose DCE to estimate delay correlation. This method needs no special cooperation or
synchronization and avoids issues using RTT, making it largely different from prior
tomography tools [4] and [5].
• We develop a passive mechanism for realization, which is efficient for bandwidth saving.
• Extensive simulations in OMNeT++ demonstrates its accuracy and robustness.
2. RELATED WORK
Y. Vardi was one of the first to study network tomography [6] that can be implemented in either
an active or passive way. Active network tomography [7,8,9,10] needs to explicitly send out
probing messages to estimate the end-to-end path characteristics, while passive network
tomography [11,12,13,14] infers network topology without sending any explicit probing
messages.
Article [4]describes delay tomography which however, needs synchronization and cooperation
between sender and receiver. In [5] authors develop Network Radar based on RTT trying to solve
these issues. However, two reasons distort the measurement accuracy. One is due to the variable
processing delay at destination nodes and the other is its violation of a significant assumption that
return paths of packet are uncorrelated while actually they overlaps.
In addition, delay correlation can be further used for topology recovery [15,16], which is
important to improve network performance.
In [17], the concept of DCE was briefly introduced without detailed analysis and evaluation. This
paper includes the full-fledged version of the DEC method together with a comprehensive
analysis of practical cases and experiment results.
3. DELAY CORRELATION ESTIMATION
Figure 1. The tree structure: a sender f and two receivers a,b

3
A simple model we use in this paper is shown in Fig.1. The routing structure from sender f to
receivers a,b is a tree rooted at f. Otherwise, there is routing loop which must be corrected.
Assume that router s is the ancestor node of both a and b. Assume that the sender uses unicast to
send messages to receivers, and assume that packets are sent in a back-to-back pair. For the k-th
pair of back-to-back packets, denoted as a and b, sent from f to a and b, respectively, we use the
following notations:
• ta(k): the time when a receive ak
in the k-th pair.
• tb(k): the time when b receive bk
in the k-th pair.
• da(k): the latency of ak
along the path from f to a.
• da(k): the latency of bk
along the path from f to b.
• tf(k): the time when f sends the k-th pair of packets.
Using network model of Fig.1 we obtain Eq.(1) for a0
(we start the index with 0 for convenience):
ta(0) = tf(0) + da(0). (1)
Similarly, for ak
, we have
ta(k) = tf(k) + da(k). (2)
Let Eq.(2) − Eq.(1) and δa(k) ≡ta(k) − ta(0). We can obtain Eq. (3) :
δa(k) = (tf(k) − tf(0)) + (da(k) − da(0)). (3)
Denote the time interval between two consecutive pairs of packets as δ. We assume that δ is a
constant for simplicity at this moment, and relax this assumption later. In this case we use
δ
k
kδ ⋅
≡ to replace tf(k)-tf(0) in Eq.3. We then have:
da(k) = δa(k) − kδ + da(0). (4)
Let δ´a(k) ≡δa(k) − kδ. Eq. (4) can be transformed into Eq. (5) :
da(k) =δ´a(k) + da(0). (5)
We can achieve similar result at receiver b as in Eq.(6):
db(k) =δ´b(k) + db(0). (6)
where δ´b(k) ≡ δb(k) − k·δ.
To estimate the correlation between da(k) and db(k), we introduce the following lemma.
Lemma 1. Assume that ζ, η are two random variables, and χ = aζ + b, γ = cη + d, where a,b,c,d are
constants and a,c have the same symbol, thus we have σ2
ζ,η= σ2
χ,γ.
Proof.
γ
χ
γ
γ
χ
χ
σ γ
χ
D
D
E
E
E )
)(
(
2
,
−
−
=
(7)

4
2
,
2
2
)
)(
(
|
||
|
)
)(
(
)
)(
(
η
ζ
σ
η
ζ
η
η
ζ
ζ
η
ζ
η
η
ζ
ζ
η
ζ
η
η
ζ
ζ
=
−
−
=
−
−
=
−
−
+
−
−
+
=
D
D
E
E
E
D
D
c
a
E
E
acE
D
c
D
a
d
cE
d
c
b
aE
b
a
E
Since da(0) and db(0) can both be regarded as constants in one serial of probing packets, based on
Lemma 1, we have the following theorem:
Theorem 1. The correlation between delay variables da(k) and db(k) is equal to the correlation
between variables δ´a (k) and δ´b(k), which means,
2
)
(
),
(
2
)
(
),
( k
k
k
d
k
d b
a
b
a δ
δ
σ
σ ′
′
= . (8)
Based on the measurements of δ´a (k) and δ´b(k), we can calculate the correlation of delays along
the path from f to a and along the path from f to b, denoted as 2
, b
a δ
δ
σ ′
′ ., using Eq.(9):
∑
=
′
′ ′
−
′
′
−
′
−
=
n
k
b
b
a
a k
k
n
b
a
1
2
, ]
)
(
][
)
(
[
1
1
δ
δ
δ
δ
σ δ
δ . (9)
where δ´a is the sample mean of n
a k 1
k
)
( =
′
δ for i=a,b.
Theorem 2. 2
, b
a δ
δ
σ ′
′ in Eq.(9) is an unbiased estimator of the correlation on shared path.
Proof. First of all we show that 2
,
ˆ b
a d
d
σ (not 2
,
ˆ b
a δ
δ
σ ′
′ ) is an unbiased estimator of the correlation on
shared path (f,s). Let λa λb denote the mean time latency of patha, pathb and let a
d , b
d denote the
sample mean correspondingly; true correlation )]
)
(
)(
)
(
[(
2
, b
b
a
a
d
d k
d
k
d
E
b
a
λ
λ
σ −
−
= To prove
that 2
,
2
, ]
ˆ
[ b
a
b
a d
d
d
d
E σ
σ = we analyze the expectation of )]
)
(
)(
)
(
[( b
b
a
a d
k
d
d
k
d
E −
− :
∑∑
∑
∑
= =
=
=
+
−
−
=
−
−
n
i
n
j
b
a
n
i
b
a
n
i
b
a
b
a
b
b
a
a
j
d
i
d
E
n
k
d
i
d
E
n
i
d
k
d
E
n
k
d
k
d
E
d
k
d
d
k
d
E
1 1
2
1
1
)]
(
)
(
[(
1
)]
(
)
(
[(
1
)]
(
)
(
[(
1
)]
(
)
(
[(
)]
)
(
)(
)
(
[(
(10)
Since delays of the ith
and kth
pair are independent and
b
a
b
a
b
b
a
a
d
d k
d
k
d
E
k
d
k
d
E
b
a
λ
λ
λ
λ
σ −
=
−
−
= )]
(
)
(
[
)]
)
(
)(
)
(
[(
2
,
We obtain Eq. (11)

5



=
+
≠
=
i
k
i
k
i
d
k
d
E
b
a d
d
b
a
b
a
b
a 2
,
)]
(
)
(
[
σ
λ
λ
λ
λ
(11)
Substituting Eq.(11) into Eq.(10) we obtain
2
,
)
1
(
)]
)
(
)(
)
(
[( b
a d
d
b
b
a
a
n
n
d
k
d
d
k
d
E σ
−
=
−
−
Therefore, 2
,
ˆ b
a d
d
σ is an unbiased estimator of the correlation on shared path as is shown in Eq.(12)
2
,
2
,
1
2
, )
1
(
1
1
)
)
(
)(
)
(
[(
1
1
]
ˆ
[ b
a
b
a
b
a d
d
d
d
n
k
b
b
a
a
d
d
n
n
n
n
d
k
d
d
k
d
E
n
E σ
σ
σ =
−
−
=
−
−
−
= ∑
=
(12)
According to 2
,
2
, b
a
b
a d
d δ
δ
σ
σ ′
′
= in Theorem 1 we prove it.
3.1. Discussion of δ
3.1.1. δ is a constant
A complete delay correlation estimation algorithm (DCE) is summarized in Algorithm 1 if the
time interval δ is a constant.
Algorithm 1 Delay Correlation Estimation Algorithm
Require:
Given the time interval δ
Ensure:
1: for k = 0 : n do
2: Use Eq. (1) to Eq. (3) to measure δa(k) in the k-th transmission;
3: Use δ´a(k) = δa(k)−kδ to calculate δ′a(k) in the k-th loop;
4: Similarly, measure δb(k) and calculate δ´b(k) =δb(k) − kδ;
5: end for
6: With all the values of δ´a(k) and δ´b(k), use Eq.(9) toobtain the correlation 2
, b
a δ
δ
σ ′
′ , which is
equivalent to 2
, b
a d
d
σ between hosts a and b according to Theorem 1.
3.1.2 δ is not a constant
If the time interval δ is not a constant then tf(k) - tf(0) ≠ kδ. In this case using kδ to replace tf(k) -
tf(0) is inappropriate and we choose δf(k) to denote tf(k) - tf(0) in Eq.(3), then Eq.(4) can be
rewritten to Eq.(13).
)
0
(
)
(
)
(
)
( a
f
a
a d
k
k
k
d +
−
= δ
δ . (13)
Correspondingly, Eq.(5) and Eq.(6) can be replaced with δ´a(k) ≡δa(k) − δf(k) and δ´b(k) ≡δb(k)
− δf(k) respectively.
Note that tf(k) is a timestamp contained in the packet, and thus δf(k) = tf(k) − tf(0) is readily
available in practice.

6
3.2. A mechanism for passive realization
To reduce explicit probing we propose a mechanism for passive realization of Algorithm 1 in real
networks.
Figure 2: The mechanism for passive tomography with source and N end hosts.
As Fig.2 shows passive mechanism works as follows. In practical networks (for example, P2P
networks) if N end hosts request common contents from a source, it will distribute packets. In this
situation source first chooses the No.1 requested data block which is duplicated into packet serial
1 and sent out to all N hosts simultaneously guaranteeing that there exist two successive packets
in a back-to-back manner. An indicator (IR) is needed to tell if the received packet at each host
belongs to the back-to-back pair. If serial of No.1 is sent completely source repeats to the next
until all requested contents are received by N hosts. As regular data flow proceeds transmitting
we change destination address of the current two successive packets when delay correlation
between the corresponding host pair has been measured (if number of packets sent to them with
indicator IR reaches τ, where τis a tunable threshold).
One may naturally raise two questions: first is which two successive packets in one serial are
chosen to add an IR? while the other is how to guarantee that in each transmission the two
successive packets are in a back-to-back manner? A simple solution can address both of them.
The basic idea is that we divide packets into small size. This can satisfy both the need of back-to-
back and regular data transmission. In fact our experiment results show that any two successive
packets in a serial distributed to N hosts can be chosen to add IR as long as the time interval δ is
appropriate.
3.3. Arrangement of IR
Based on above argument that each successive pair of packets can be regarded as back-to-back, in
one transmitting serial at most N-1 delay correlations are measured (shown on top of Fig.3). After
N-1 times switching of destination addresses and IRs all delay correlations between N hosts can
be obtained.

7
In this way the complexity is only O(N) compared with O(N2) to measure N(N−1)/2 correlations.
Figure 3: Arrangement of IR. IRi,j in each serial indicates blocks destined to i, j should be successive.
4. SIMULATION RESULTS
4.1. Dynamic Network Tomography
We use OMNeT++ for simulations [18] to demonstrate the correctness and robustness of passive
DCE tomography. We generate a network shown in Fig.4. Nodes of BG are randomly and
dynamically selected for producing background traffic while others are the source and client
nodes. When two client nodes a, b request contents from source node f, it sends regular data in a
back-to-back manner. In this case route algorithm determines a multicast tree with root f and
leaves a, b.
Figure 4: Structure for DCE test
We set packet size hundreds of bytes to satisfy both regular transmission and back-to-back
property. One advantage is that since it is smaller than Maximum Transmission Unit (MTU) we
avoid delay for package segmentation. We set bandwidth of each link value of 100Mbps; the

8
background traffic pattern conforms to the Poisson distribution, whose expectation value could be
set from 1MBps to 12MBps. We also change the size of packet from 100 bytes to MTU to see its
influence on DCE measurement.
4.2. Results
Using DCE methodology we set τto be 1550 and observe over 1500 timing samples for receiver
pair.
Figure 5: One way trip time latency on patha, pathband shared path (f,s)
Fig.5 depicts the one way trip latency in our environment. One example of the average delay on
patha, pathb and shared path are 0.6526ms, 0.5478ms and 0.4317ms respectively. In some case
errors may happen to the timestamp as the variation of background traffic. Therefore, we ignore
packets beyond twice the average delay on each path.
Figure 6: DCE measurement covariance
2
, b
a δ
δ
σ ′
′ versus the directly measured delay variance on the shared
path (f,s)

9
Fig.6 shows the DCE covariance 2
, b
a δ
δ
σ ′
′ versus true value 2
s
σ on shared path (f,s) with different
packet size. Value 2
, b
a δ
δ
σ ′
′ is calculated using the arriving time of package at a,b while 2
s
σ is
calculated directly from delay on (f,s). According to Theorem 1 we know that 2
, b
a d
d
σ is equal to
2
, b
a δ
δ
σ ′
′ thus, ideally 2
, b
a δ
δ
σ ′
′ and 2
s
σ should be identical and fall onto the 45 degree line. Taking
test result with package size of 800 Bytes for example we see the estimated value is always
locating nearby the true value with slight difference which demonstrates the correctness of DCE
tomography. If we change size of data packet from 100 bytes to MTU, delay correlations
measured by DCE are always desired. This demonstrates that passive mechanism is able to
achieve both data transmission and tomography.
Figure 7: 2
2
2
,
s
s
b
a
σ
σ
σ δ
δ −
′
′
: DCE measurement error versus different background traffic
To see its robustness with different background traffic, in Fig.7 packet size is fixed to be MTU. In
this case performance of DCE tomography is perfect with the percentage error below 4% when
the expectation value of background traffic is within the region [1.25MBps,7.5MBps]. However,
when it increases to 8MBps, error percentage increases sharply. This is because in this situation
network's performance becomes worse and some shared paths between higher level routers are
congested heavily, which destroys the back-to-back property of packets. Note that when the
expectation value of background traffic is relatively small (below 1MBps) delay correlation
caused by queuing on routers will not be significant thus the performance also degrades.
5. CONCLUSIONS AND FUTURE WORK
In this paper we propose a novel tomography method named DCE to estimate delay correlation
with no need of synchronization and cooperation between end hosts. We also develop the passive
mechanism to further save bandwidth. Extensive simulations demonstrate the correctness of DCE.
Moreover, passive realization is able to achieve both purpose of tomography and data
transmission with excellent robustness versus different background traffic and package size.
In future, we plan to utilize the DCE measure for topology inference and implement it in practical
network environment.

10
ACKNOWLEDGEMENTS
This work was supported by the National Key Technology Research and Development Program
of the Ministry of Science and Technology of China under Grant no.2012BAH93F01, the
Innovation Research Fund of Huazhong University of Science and Technology, no. 2014TS095
and the National Sciece Foundation of China under Grant no. 60803005.
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link data, Journal of the American statistical association 95 (2000) 1063–1075.
[12] V. N. Padmanabhan, L. Qiu, H. J. Wang, Passive network tomography using bayesian inference,
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Authors
Peng Qin received the B. S. Degree in Electronics and Information Engineering from
Huazhong University of Science and Technology, Wuhan, P. R. China, in 2009. His
research interests are in the areas of network tomography, network measurement, p2p
network and applications of network coding.

11
Bin Dai received the B. Eng, the M. Eng degrees and the PhD degree from Huazhong
University of Science and Technology of China, P. R. China in 2000, 2002 and 2006,
respectively. From 2007 to 2008, he was a Research Fellow at the City University of Hong
Kong. He is currently an associate professor at Department of Electronics and Information
Engineering, Huazhong University of Science and Technology, P. R. China. His research
interests include p2p network, wireless network, network coding, and multicast routing.
Benxiong Huang received the B. S. degree in 1987 and PhD degree in 2003 from
Huazhong University of Science and Technology, Wuhan, P. R. China. He is currently a
professor in the Department of Electronics and Information Engineering, Huazhong
University of Science and Technology, P. R. China. His research interests include next
generation communication system and communication signal processing.
Guan Xu received the B.S. degree in Electronics and Information Engineering from
Huazhong University of science and technology, Wuhan, P. R. China, in 2008. He is
currently a PhD Candidate in the Department of Electronics and Information Engineering
at the Huazhong University of science and technology. His research interests are in the
areas of practical network coding in P2P network, IP switch networks and SDN networks
with emphasis on routing algorithms and rate control algorithms.

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