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.
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This work was partly supported by the National Natural Science Foundation of China (Grant Nos. 61701074, 61171091, 6130217, 61201127), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) under Grant No. G1323541861, and the Sichuan Science and Technology Program. Also it was revised according to our previous work , which has appeared in the proceedings of the 2016 IEEE Symposium on Computers and Communications, ©2016 IEEE.
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Pan, S., Zhou, Y., Zhang, Z. et al. Identify Congested Links with Network Tomography Under Multipath Routing. J Netw Syst Manage 27, 409–429 (2019). https://doi.org/10.1007/s10922-018-9471-2
- Network measurements
- Boolean tomography
- Congested link identification
- End-to-end measurement
- Multipath routing