Published in IET Communications
Received on 24th October 2011
Revised on 25th July 2012
doi: 10.1049/iet-com.2011.0779
ISSN 1751-8628
Accurate and effective inference of network link loss
from unicast end-to-end measurements
G. Fei G. Hu
Key Laboratory of Optical Fiber Sensing and Communication, Ministry of Education, University of Electronic Science and
Technology of China, Chengdu 611731, People’s Republic of China
E-mail: fgl@uestc.edu.cn
Abstract: Understanding the network link loss is particularly important for optimising delay-sensitive applications. This study
addresses the issue of estimating temporal dependence characteristic of link loss by using network tomography. Different
from existing works of network loss tomography, the authors use a kth order Markov Chain (k-MC for short, k . 1) to model
the packet loss process, and propose a constrained optimisation-based method to estimate the state transmission probabilities
of the k-MC link loss model. The authors also propose a top–down algorithm in order to ensure that our method can be
applied to large networks. Compared with existing loss tomography methods, our method is capable of obtaining more
accurate packet loss probability estimates. The ns-2 simulation results show the good performance of our method.
1 Introduction
In order to design, control and manage the networks
successfully, it is essential to understand the network
internal performance parameters such as the link loss and
the link delay. Usually, one can measure these parameters
directly based on the cooperation between the internal
nodes. However, some internal nodes may refuse to
cooperate because sharing the link loss or the link delay
information may have negative impact on network security.
As the size of Internet grows rapidly, it becomes
increasingly difficult to measure the network internal
performance parameters directly.
Quite different from the internal cooperation-based
methods, network tomography [1, 2] infers the internal
performance parameters from end-to-end measurements
without the cooperation between the internal nodes. This
technology can also be extended to infer network topology
and traffic matrix (e.g. [3, 4]). Since it is more practical and
scalable than the internal cooperation-based methods,
network tomography has attracted many studies since it has
been proposed.
Network link loss inference (also called loss tomography) is
an important component of network tomography because
understanding network link loss is particularly important for
optimising the delay-sensitive applications (such as VoIP [5,
6]) and improving the reliability of networks [7]. For the
issue of loss tomography, selecting an appropriate model to
describe the packet loss process is critical for obtaining
accurate link loss estimates. However, most existing works
use the Bernoulli model or the Gilbert model to describe the
packet loss process, which may prevent the temporal
dependence characteristic of link loss from being accurately
captured, and the estimated results may have significant errors.
In this paper, we investigate the issue of the temporal
dependence network link loss inference based on unicast
end-to-end measurement. Different from existing works of
network loss tomography, we use a kth-order Markov Chain
(k-MC for short, k . 1) to model the packet loss process.
The k-MC link loss model considers the dependence of
k + 1 concussive packets, and the state transition
probabilities of the model represent the conditional loss or
transmission probability of a packet if the loss or
transmission states of its previous k packets are known. It
has been demonstrated in [8] that k-MC is more accurate
than the Bernoulli model and the Gilbert model in
describing the packet loss process [8]. However, literature
[8] only focuses on analysing the property of end-to-end
loss in actual networks, and did not address the problem of
obtaining the loss behaviour of each link.
In order to obtain the parameters of the k-MC link loss
model, we propose a constrained optimisation-based method
to estimate the state transmission probabilities of the k-MC
link loss model from the data set obtained through unicast
end-to-end measurement. There are two reasons that
motivate us to develop the constrained optimisation-based
method. First, the constrained optimisation-based method
is capable of overcoming the computational complexity
problem raised by the traditional methods used in network
tomography, such as the expectation-maximisation (EM)
algorithm. Second, solving the constrained optimisation
problem has been deeply studied, and there are many
sophisticated methods that can be used to solve the problem.
A large network usually contains many links, and there are
a large number of parameters that need to be estimated.
However, most existing tools to solve the constrained
optimisation problem usually fail to return an appropriate
solution in a reasonable time if the number of unknown
IET Commun., pp. 1 –9 1
doi: 10.1049/iet-com.2011.0779
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