Journal of Network and Systems Management

, Volume 27, Issue 2, pp 409–429 | Cite as

Identify Congested Links with Network Tomography Under Multipath Routing

  • Shengli Pan
  • Yingjie ZhouEmail author
  • Zhiyong Zhang
  • Song Yang
  • Feng Qian
  • Guangmin Hu


Identifying congested links accurately to ensure the Service Level Agreements is an important but challenging task, since it is costly or even practically unfeasible to monitor massive interior links directly for large networks. Network tomography has been proposed to overcome this problem by using end-to-end (path) measurements. However, most of existing tomographic methods only focus on the loss performance degradation, while paying much less attention the fact that network congestion will also greatly worsen the delay performance. Nevertheless, most of them normally work under single-path routing, which may also get violated in today’s Internet as multipath routing is increasingly common. In this paper, we consider the problem of using end-to-end measurements to identify congested links when multipath routing is employed in a non-tree network. Firstly, we use both link delay variances and link loss rates to model the system constraints between end- to-end paths and the interior links, and transfer the issue of congested link identification as an optimization problem. By theoretically demonstrating that the link delay variances are identifiable from the end-to-end delay measurements with certain topology conditions, we further prove that the above optimization problem is a Non-deterministic Polynomial-time hard (NP-hard) problem. Then in order to solve such an NP-hard problem, two greedy algorithms based on bool and additive congestion statuses are proposed. Lastly, simulation studies show that with extra delay constraints, our proposed algorithms are able to achieve better identification performances than existing methods under multipath routing.


Network measurements Boolean tomography Congested link identification End-to-end measurement Multipath routing NP-hard 



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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computer ScienceChina University of Geosciences (Wuhan)WuhanPeople’s Republic of China
  2. 2.College of Computer ScienceSichuan UniversityChengduPeople’s Republic of China
  3. 3.Cyberspace Security Technology Laboratory of CETC, Cyberspace Security Key Laboratory of Sichuan ProvinceChina Electronic Technology Cyber Security Co. LTD.ChengduPeople’s Republic of China
  4. 4.School of Communication and Information EngineeringUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China
  5. 5.School of Resources and EnvironmentUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China

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