IEEE COMMUNICATIONS LETTERS, VOL. 18, NO. 5, MAY 2014 881
End-to-End Measurements for
Network Tomography under Multipath Routing
Shengli Pan, Student Member, IEEE, Zhiyong Zhang, Student Member, IEEE, Fucai Yu, Member, IEEE,
and Guangmin Hu, Member, IEEE
Abstract—In most works of network tomography, end-to-
end measurements are conducted based on the assumption of
single-path routing. However, multipath routing caused by load
balancing is increasingly common in today’s Internet and makes
it hard to tell which end-to-end path is measured by the current
probing flow. In this letter, we propose a tomographic scheme
able to reveal the corresponding relationship between end-to-
end paths and probing flows. After that, one can explicitly probe
each end-to-end path with a specific five-tuple flow. Simulation
results demonstrate that our proposed scheme could recover the
relationship accurately using around 200 packets per flow.
Index Terms—Network tomography, end-to-end measurement,
multipath routing.
I. INTRODUCTION
N
ETWORK tomography mostly exploits end-to-end mea-
surements to infer link performance parameters of a
network and requires no cooperation of internal elements [1].
It is appealing in scenarios where one needs to monitor the
behavior and performance of a network but without direct
access to it. The conventional network tomography, especially
the tree-based network tomography, implicitly assumes that
any pair of end-hosts has a single routing path during the
measuring period. However, load balancing [2], which leads
to multiple routing paths between a pair of end-hosts, is
widely supported by most commercial routers [3] [4] in
today’s Internet. In this case, the end-to-end measurements
are confronted with the problem of distinguishing which end-
to-end path is measured by the current probing flow.
It is easy to obtain the end-to-end measurements using
unicast probing schemes, such as back-to-back probing [5]
and striped unicast probing (SUP) [6]. All traffic between
two nodes will traverse the same path when only single-path
routing is allowed. However, it is no longer the case in a load-
balancing network where exists multipath routing [7]. When
routers adopt a per-packet load balancing algorithm [4], even
packets within an identical flow will be distributed among all
the active subpaths. Fortunately, B. Augustin et al. [8] find that
per-packet load balancing is rare in the Internet while per-
flow load balancing is much common. Under per-flow load
balancing, a stream of packets with the same five-tuple (IP
source address, IP destination address, source port, destination
port, and protocol) will follow the same route. In addition,
Manuscript received December 25, 2013. The associate editor coordinating
the review of this letter and approving it for publication was G. Lazarou.
The authors are with the School of Communication and Information
Engineering, University of Electronic Science and Technology of China,
Chengdu, 611731 China (e-mail: psl@uestc.edu.cn).
Digital Object Identifier 10.1109/LCOMM.2014.040214.132838
Cunha et al. [9] observe that only about 4% of load-balancing
routers may change routes within a day.
A. Dhamdhere et al. [10] recover a mesh topology with
the help of Paris Traceroute [7], which can trace the routes
under per-flow load balancing. But such route discoveries
could be highly adversely affected by the anonymous routers
in the Internet. There are also some attempts to identify
network topologies under multipath routing scenarios using
tomographic approaches [11] [12]. However, they just recover
one active path for any two end-hosts. Currently, works in
network tomography under multipath routing are greatly rare.
This is mainly because it is hard to explicitly tell which
routing subpath one probing flow traverses before we start
end-to-end measurements for network tomography. Although
the IP-source routing might enable one to specify the path a
packet routes through a network, it is frequently blocked in
the Internet due to security concerns.
In this letter, we propose a tomographic scheme to reveal
the relationships between the subpaths and probing flows
under per-flow load balancing. Given a known logical non-
tree topology [13], we first deploy enough probing flows
between two end-hosts to ensure that any subpath between
them can be covered with a high probability. Then, we cluster
all the probing flows into different groups using their end-to-
end delay measurements, so that the flows in the same group
traverse along the same subpath. After that, we proceed to
identify the subpath corresponding to each group. We prove a
sufficient condition under which it is achievable by comparing
the shared segment between each subpath and some other
end-to-end paths (destined for single-path routing destination
nodes). After that, one can conduct specific-purpose end-to-
end measurements with the knowledge of knowing which path
is going to be measured by a probing flow as [10].
II. S
YSTEM MODEL
A. N-1 Subgraph
We denote a directed acyclic network with a single source
node as G =(V,L),whereV is the set of edge nodes and
L is the set of links. V consists of the source node θ and
the set of destination nodes D. Considering the multipath
routing case, we further define D
s
⊂ D and D
m
= D \ D
s
as
the set of single-path and multipath routing destination nodes
respectively. Moreover, P
θ,r
= {P
k
θ,r
|k =1, ··· ,n; r ∈ D}
represents all the subpaths from the source node θ to a
destination node r,wheren is the total number of active
subpaths to r and P
k
θ,r
is the kth one. If r ∈ D
s
,wehave
|P
θ,r
| =1;Otherwise,|P
θ,r
| > 1. We suppose that there is
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2014 IEEE