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Traffic Dynamics-Aware Probe Selection for Fault Detection in Networks

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A Correction to this article was published on 26 March 2020

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Abstract

Fault detection in modern networks is done with a set of specially instrumented nodes which send probes to find faults. These probes generate additional traffic in network and compete with other regular traffic for bandwidth. In this paper we consider the problem of dynamically adapting the probes based on traffic dynamics experienced by nodes. We propose to profile the links and nodes to get aggregate I/O statistics in a time window and use it as an instantaneous measure of congestion. We consider the network with I/O statistics to generate a weighted graph and formulate an optimization problem to find a set of probes covering whole network with minimum weight. By showing that finding minimum weight probes maps to a known NP complete problem, we propose three greedy algorithms for selecting probes. With both simulation and real graphs of Internet Service Provider (ISP) networks, we perform five sets of experiments and show that proposed algorithms can dynamically adapt to changes in traffic dynamics and also can select probes in large networks in reasonable time.

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Change history

  • 26 March 2020

    The original version of the article unfortunately contained a typo error in the first author name in the author group.

Notes

  1. A preliminary version of this paper appeared in COMSNETS 2018 [2].

  2. Congestion can be measured with other parameters also.

  3. This inherently limit usage of our probe selection algorithms within an autonomous system.

  4. Assuming the graph is connected.

  5. We further assume that the situation where K needs to be \(n-1\) does not occur in practical networks with atleast two probe-stations.

  6. Although Dijkstra’s algorithm is used with link state routing algorithms, in practice some policy based decisions may also be involved. Our model can be tweaked to work with other routing algorithms to identify Candidate Probe Set.

  7. This is a random choice among the two equal weight probes \(CP_6= \{(5,1,4,7),399\}\) and \(CP_{12}= \{(7,4,1,5),399\}\)

  8. The threshold for our experiments is set to 50% which is a heuristic selection, however a system administrator can change this to any value.

  9. We can use other metrics like number of bytes transmitted, etc.

  10. Dikjstra’s algorithm is used here to reduce the number of candidate probes available for selection and to be consistent with other two approaches.

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Acknowledgements

First author would like to thank Vaishali Sadaphal for the discussions she had when she was interning at TRDDC Pune. She would also like to thank for the financial assistance given to her by Department of IT under Visvesvaraya Ph.D. Scheme.

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Authors and Affiliations

  1. Discipline of Computer Science and Engineering, Indian Institute of Technology Indore, Indore, India

    Anuja Tayal, Neha Sharma & Neminath Hubballi

  2. Tata Research Development and Design Centre Pune, Pune, India

    Maitreya Natu

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  1. Anuja Tayal
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  2. Neha Sharma
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  3. Neminath Hubballi
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  4. Maitreya Natu
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Correspondence to Neminath Hubballi.

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The original version of this article was revised: The first author name was incorrectly published as ‘Anjua Tayal’ and the corrected name is ‘Anuja Tayal’.

Probe Selection is a NP–Complete Problem

Probe Selection is a NP–Complete Problem

In this Appendix, we show that probe-selection optimization problem of selecting minimum weight probes from the set of candidate probes is a known NP-Complete problem as it can be mapped to weighted set cover problem. Weighted set cover problem is defined as follows [43]

Definition 2

Given a finite universe \(U = \{e_{1,} e_{2}, ..., e_{n}\}\) of n members, \(S = \{s_{1}, s_{2}, ..., s_{m}\} \bigwedge , \forall i \; s_{i} \subseteq U\) a collection of subsets of U and a weight function \(w : s \rightarrow {\mathbb {R}}^{+}\) that assigns a positive real weight to each subset of U, the goal is to find the minimum weight subcollection of S whose union is U or a minimum weight set cover.

We define the problem of selecting probes from given set of candidate probes as follows

Definition 3

Given set of nodes to be covered in a graph \(V = \{v_{1}, v_{2}, ..., v_{n}\}\) of n nodes and Candidate Probe Set \(CP = \{CP_{1}, CP_{2}, ..., CP_{cp}\} \bigwedge , \forall i \; CP_{i} \subseteq V\) a collection of subsets of V and a weight function \(W : CP \rightarrow {\mathbb {R}}^{+}\) that assigns a positive real weight to each subset of V, the goal is to find the minimum weight subcollection of CP whose union is V or a minimum weight probes.

The set of finite universe U in weighted set cover problem is analogous to the set of nodes V to be covered in a graph G, while set S is equivalent to set of candidate probes. Each candidate probe \(CP_{i}\) consists of set of nodes \(\subseteq V\) covered by that probe. There exists a weight function W which assigns weight to each candidate probe which is the cost of selecting that probe. Our goal is to find minimum weight probes \(PS \subseteq CP\) which covers all the nodes of the graph or the union is V.

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Tayal, A., Sharma, N., Hubballi, N. et al. Traffic Dynamics-Aware Probe Selection for Fault Detection in Networks. J Netw Syst Manage 28, 1055–1084 (2020). https://doi.org/10.1007/s10922-020-09514-3

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