网络诊断技术研究综述

doi:10.11959/j.issn.2096-6652.202316

Abstract

Abstract:

Network tomography is an efficient and convenient tool to infer the internal state of a network through end-toend path measurement.It has been widely used in link measurement and fault location of wired and wireless networks.This paper summarized and analyzed the model foundation of four basic models of network tomography, boolean network tomography technology, additive network tomography technology, bandwidth network tomography technology and the stochastic network tomography technology.This paper systematically combed the key problems in network tomography technology, including monitor placement, beacon and service placement, path construction and data analysis, the problem of identifiability, and attack in network tomography when identification was not guaranteed.At the same time, the new research and new problems in the field of network tomography such as network tomography with network coding, neural network tomography and node fault location method in NFV were sorted out.Finally, based on the development status of network tomography technology, the future development trend of network tomography was analyzed and discussed.

Key words: network tomography, network measurement, monitor placement, path construction, identifiability, rank deficiency problem

CLC Number:

TP393

Xiaojia XU,Yongcai WANG,Deying LI. A survey on network tomography technology[J]. Chinese Journal of Intelligent Science and Technology, 2023, 5(2): 163-179.

Figures/Tables 13

类型	测量路径	网络类型	研究问题	算法复杂度
MMP^[10]	无环路径	静态	放置最少数量的监视器，以识别所有链路度量	$O (\| V \| + \| L \|)$
GMMP^[6]	无环路径	静态	放置给定数量的监视器，以识别最大数量的链路度量	$O ({\| V \|}^{4} + {\| V \|}^{3} \| L \|)$
Scalpel^[40]	无环路径	静态	分配监视器，以识别所有感兴趣的链路	$O (\| V \| + \| L \|)$
OMA^[41]	无环路径	静态	分配最小数量的监视器，以识别所有感兴趣的链路	$O (\| V \| + \| L \|)$
MPK^[42]	无环路径	静态	放置监视器，使k-可识别链路的数量最大化	$O ({\| V \|}^{6})$
FMP^[43]	无环路径	动态	在拓扑变化的网络中放置最少监视器，识别链路度量	$O ({\| V \|}^{2})$

类型	测量路径	网络类型	研究问题	算法复杂度
CLIC^[51]	有环路径	静态	使用一个监视器和使用监控环路来识别链路度量的问题	$O ({\| V \|}^{2})$
CLR^[52]	有环路径	静态	使用测量节点识别链路度量并在它们之间建立路径的问题	$O ({\| V \|}^{2})$
STPC^[11]	无环路径	静态	构建可识别测量路径中单个链路度量的测量路径的问题	$O (\| V \| \| L \|)$
RoMe^[21]	无环路径	静态	在成本约束下最大化对已知故障的健壮性的路径选择问题	$O (2^{\| L \|} \| L \| {\| P \|}^{4})$
PC^[53]	无环路径	静态	选择能对网络全面监控覆盖的最小端到端测量路径的问题	$O (\| V \| (\| L \| + \| V \| \log (\| V \|)))$

References 90

[1]	PRASAD R , DOVROLIS C , MURRAY M ,et al. Bandwidth estimation:metrics,measurement techniques,and tools[J]. IEEE Network, 2003,17(6): 27-35.
[2]	周爱平, 程光, 郭晓军 . 高速网络流量测量方法[J]. 软件学报, 2014,25(1): 135-153.
	ZHOU A P , CHENG G , GUO X J . High-speed network traffic measurement method[J]. Journal of Software, 2014,25(1): 135-153.
[3]	VARDI Y . Network tomography:estimating source-destination traffic intensities from link data[J]. Journal of the American Statistical Association, 1996,91(433): 365-377.
[4]	BU T , DUFFIELD N , PRESTI F L ,et al. Network tomography on general topologies[C]// Proceedings of the 2002 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems. New York:ACM, 2002: 21-30.
[5]	ZHAO J , GOVINDAN R , ESTRIN D . Sensor network tomography[J]. ACM SIGCOMM Computer Communication Review, 2002,32(1): 64.
[6]	MA L , HE T , LEUNG K K ,et al. Monitor placement for maximal identifiability in network tomography[C]// Proceedings of IEEE INFOCOM 2014 - IEEE Conference on Computer Communications. Piscataway:IEEE Press, 2014: 1447-1455.
[7]	DUFFIELD N , LO PRESTI F , PAXSON V ,et al. Network loss tomography using striped unicast probes[J]. IEEE/ACM Transactions on Networking, 2006,14(4): 697-710.
[8]	CHEN A , CAO J , BU T . Network tomography:identifiability and Fourier domain estimation[C]// Proceedings of IEEE INFOCOM 2007 26th IEEE International Conference on Computer Communications. Piscataway:IEEE Press, 2007: 1875-1883.
[9]	AHUJA S S , RAMASUBRAMANIAN S , KRUNZ M . SRLG failure localization in all-optical networks using monitoring cycles and paths[C]// Proceedings of IEEE INFOCOM 2008 - The 27th Conference on Computer Communications. Piscataway:IEEE Press, 2008: 700-708.
[10]	MA L , HE T , LEUNG K K ,et al. Identifiability of link metrics based on end-to-end path measurements[C]// Proceedings of the 2013 conference on Internet measurement conference. New York:ACM, 2013: 391-404.
[11]	MA L , HE T , LEUNG K K ,et al. Efficient identification of additive link metrics via network tomography[C]// Proceedings of 2013 IEEE 33rd International Conference on Distributed Computing Systems. Piscataway:IEEE Press, 2013: 581-590.
[12]	SHIH M F , HERO A . Unicast inference of network link delay distributions from edge measurements[C]// Proceedings of 2001 IEEE International Conference on Acoustics,Speech,and Signal Processing.Proceedings (Cat.No.01CH37221). Piscataway:IEEE Press, 2002: 3421-3424.
[13]	ADAMS A , BU T , FRIEDMAN T ,et al. The use of end-to-end multicast measurements for characterizing internal network behavior[J]. IEEE Communications Magazine, 2000,38(5): 152-159.
[14]	XI B W , MICHAILIDIS G , NAIR V N . Estimating network loss rates using active tomography[J]. Journal of the American Statistical Association, 2006,101(476): 1430-1448.
[15]	钱峰, 胡光岷 . 网络层析成像研究综述[J]. 计算机科学, 2006,33(9): 12-17.
	QIAN F , HU G M . A survey of network tomography technologies[J]. Computer Science, 2006,33(9): 12-17.
[16]	潘胜利, 张志勇, 费高雷 ,等. 网络链路性能参数估计的层析成像方法综述[J]. 软件学报, 2015,26(9): 2356-2372.
	PAN S L , ZHANG Z Y , FEI G L ,et al. Survey on network tomography for link performance parameter evaluation[J]. Journal of Software, 2015,26(9): 2356-2372.
[17]	李惠康, 高艺, 董玮 ,等. 网络断层扫描:理论与算法[J]. 软件学报, 2021,32(2): 475-495.
	LI H K , GAO Y , DONG W ,et al. Network tomography:theory and algorithm[J]. Journal of Software, 2021,32(2): 475-495.
[18]	MA L , HE T , SWAMI A ,et al. Node failure localization via network tomography[C]// Proceedings of the 2014 Conference on Internet Measurement Conference. New York:ACM, 2014: 195-208.
[19]	FENG C Y , AN J W , WU K ,et al. Bound inference and reinforcement learning-based path construction in bandwidth tomography[J]. IEEE/ACM Transactions on Networking, 2022,30(2): 501-514.
[20]	HE T , LIU C , SWAMI A ,et al. Fisher information-based experiment design for network tomography[J]. ACM SIGMETRICS Performance Evaluation Review, 2015,43(1): 389-402.
[21]	TATI S , SILVESTRI S , HE T ,et al. Robust network tomography in the presence of failures[C]// Proceedings of 2014 IEEE 34th International Conference on Distributed Computing Systems. Piscataway:IEEE Press, 2014: 481-492.
[22]	QIAO Y , JIAO J , RAO Y ,et al. Adaptive path selection for link loss inference in network tomography applications[J]. PLoS One, 2016,11(10): e0163706.
[23]	GU Y , JIANG G F , SINGH V ,et al. Optimal probing for unicast network delay tomography[C]// 2010 Proceedings IEEE INFOCOM. Piscataway:IEEE Press, 2010: 1-9.
[24]	MA L , HE T , SWAMI A ,et al. On optimal monitor placement for localizing node failures via network tomography[J]. Performance Evaluation, 2015,91: 16-37.
[25]	ZHAO S Q , LU Z , WANG C . When seeing isn't believing:on feasibility and detectability of scapegoating in network tomography[C]// Proceedings of 2017 IEEE 37th International Conference on Distributed Computing Systems (ICDCS). Piscataway:IEEE Press, 2017: 172-182.
[26]	CHIU C C , HE T . Stealthy DGoS attack:degrading of service under the watch of network tomography[C]// Proceedings of IEEE INFOCOM 2020 - IEEE Conference on Computer Communications. Piscataway:IEEE Press, 2020: 367-376.
[27]	李贵山, 蔡皖东 . 网络断层扫描技术的研究与发展[J]. 测控技术, 2008,27(2): 1-4.
	LI G S , CAI W D . Research and development of network tomography[J]. Measurement ＆ Control Technology, 2008,27(2): 1-4.
[28]	COATES M J , NOWAK R D . Network tomography for internal delay estimation[C]// Proceedings of 2001 IEEE International Conference on Acoustics,Speech,and Signal Processing.Proceedings (Cat.No.01CH37221). Piscataway:IEEE Press, 2002: 3409-3412.
[29]	SHIH M F , HERO A O . Unicast-based inference of network link delay distributions with finite mixture models[J]. IEEE Transactions on Signal Processing, 2003,51(8): 2219-2228.
[30]	GUO D , WANG X D . Bayesian inference of network loss characteristics with applications to TCP performance prediction[C]// Proceedings of IEEE Workshop on Statistical Signal Processing. Piscataway:IEEE Press, 2004: 530-533.
[31]	GUO D , WANG X D . Bayesian network loss inference[C]// Proceedings of 2003 IEEE International Conference on Acoustics,Speech,and Signal Processing,2003.Proceedings.(ICASSP '03). Piscataway:IEEE Press, 2003:VI-33.
[32]	ZHANG J Z . Origin-destination network tomography with Bayesian inversion approach[C]// Proceedings of 2006 IEEE/WIC/ACM International Conference on Web Intelligence (WI 2006 Main Conference Proceedings)(WI'06). Piscataway:IEEE Press, 2007: 38-44.
[33]	CACERES R , DUFFIELD N G , HOROWITZ J ,et al. Multicast-based inference of network-internal loss characteristics[J]. IEEE Transactions on Information Theory, 1999,45(7): 2462-2480.
[34]	COATES M , CASTRO R , NOWAK R ,et al. Maximum likelihood network topology identification from edge-based unicast measurements[C]// Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems. New York:ACM, 2002: 11-20.
[35]	LIANG G , YU B . Maximum pseudo likelihood estimation in network tomography[J]. IEEE Transactions on Signal Processing, 2003,51(8): 2043-2053.
[36]	TSANG Y , COATES M , NOWAK R D . Network delay tomography[J]. IEEE Transactions on Signal Processing, 2003,51(8): 2125-2136.
[37]	李勇军, 蔡皖东, 王伟 . 网络断层扫描技术综述[J]. 计算机工程, 2006,32(13): 91-93.
	LI Y J , CAI W D , WANG W . A survey on network tomography[J]. Computer Engineering, 2006,32(13): 91-93.
[38]	CHO S , RAMASUBRAMANIAN S . Localizing link failures in all-optical networks using monitoring tours[J]. Computer Networks, 2014,58: 2-12.
[39]	MA L , HE T , LEUNG K K ,et al. Inferring link metrics from end-toend path measurements:identifiability and monitor placement[J]. IEEE/ACM Transactions on Networking, 2014,22(4): 1351-1368.
[40]	GAO Y , WU W B , DONG W ,et al. Preferential link tomography:monitor assignment for inferring interesting link metrics[C]// Proceedings of 2014 IEEE 22nd International Conference on Network Protocols. Piscataway:IEEE Press, 2014: 167-178.
[41]	DONG W , GAO Y , WU W B ,et al. Optimal monitor assignment for preferential link tomography in communication networks[J]. IEEE/ACM Transactions on Networking, 2017,25(1): 210-223.
[42]	REN W , DONG W . Robust network tomography:K-Identifiability and monitor assignment[C]// Proceedings of IEEE INFOCOM 2016 - The 35th Annual IEEE International Conference on Computer Communications. Piscataway:IEEE Press, 2016: 1-9.
[43]	HE T , MA L , GKELIAS A ,et al. Robust monitor placement for network tomography in dynamic networks[C]// Proceedings of IEEE INFOCOM 2016 - The 35th Annual IEEE International Conference on Computer Communications. Piscataway:IEEE Press, 2016: 1-9.
[44]	HE T , GKELIAS A , MA L ,et al. Robust and efficient monitor placement for network tomography in dynamic networks[J]. IEEE/ACM Transactions on Networking, 2017,25(3): 1732-1745.
[45]	BULUSU N , HEIDEMANN J , ESTRIN D . Adaptive beacon placement[C]// Proceedings of 21st International Conference on Distributed Computing Systems. New York:ACM, 2001: 489-498.
[46]	KUMAR R , KAUR J . Practical beacon placement for link monitoring using network tomography[J]. IEEE Journal on Selected Areas in Communications, 2006,24(12): 2196-2209.
[47]	BEJERANO Y , RASTOGI R . Robust monitoring of link delays and faults in IP networks[J]. IEEE/ACM Transactions on Networking, 2006,14(5): 1092-1103.
[48]	NGUYEN H , THIRAN P . Active measurement for multiple link failures diagnosis in ip networks[C]// Proceedings of Passive and Active Network Measurement:5th International Workshop. Berlin:Springer, 2004: 185-194.
[49]	HE T , BARTOLINI N , KHAMFROUSH H ,et al. Service placement for detecting and localizing failures using end-to-end observations[C]// Proceedings of 2016 IEEE 36th International Conference on Distributed Computing Systems (ICDCS). Piscataway:IEEE Press, 2016: 560-569.
[50]	STANIC S , SUBRAMANIAM S , SAHIN G ,et al. Active monitoring and alarm management for fault localization in transparent all-optical networks[J]. IEEE Transactions on Network and Service Management, 2010,7(2): 118-131.
[51]	GOPALAN A , RAMASUBRAMANIAN S . On identifying additive link metrics using linearly independent cycles and paths[J]. IEEE/ACM Transactions on Networking, 2012,20(3): 906-916.
[52]	GOPALAN A , RAMASUBRAMANIAN S . On the maximum number of linearly independent cycles and paths in a network[J]. IEEE/ACM Transactions on Networking, 2014,22(5): 1373-1388.
[53]	PEPE T , PULERI M . Network Tomography:a novel algorithm for probing path selection[C]// Proceedings of 2015 IEEE International Conference on Communications (ICC). Piscataway:IEEE Press, 2015: 5337-5341.
[54]	DUFFIELD N G , LO PRESTI F , PAXSON V ,et al. Inferring link loss using striped unicast probes[C]// Proceedings of Proceedings IEEE INFOCOM 2001.Conference on Computer Communications.Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat.No.01CH37213). Piscataway:IEEE Press, 2002: 915-923.
[55]	LO PRESTI F , DUFFIELD N G , HOROWITZ J ,et al. Multicast-based inference of network-internal delay distributions[J]. IEEE/ACM Transactions on Networking, 2002,10(6): 761-775.
[56]	DUFFIELD N G , LO PRESTI F . Multicast inference of packet delay variance at interior network links[C]// Proceedings of Proceedings IEEE INFOCOM 2000.Conference on Computer Communications.Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat.No.00CH37064). Piscataway:IEEE Press, 2002 1351-1360.
[57]	CACERES R , DUFFIELD N G , HOROWITZ J ,et al. Loss-based inference of multicast network topology[C]// Proceedings of the 38th IEEE Conference on Decision and Control (Cat.No.99CH36304). Piscataway:IEEE Press, 2002: 3065-3070.
[58]	LUCIAN C . Attackers slip rogue,backdoored firmware onto Cisco routers \| PCWorld
[59]	TAGUE P , POOVENDRAN R . Modeling node capture attacks in wireless sensor networks[C]// Proceedings of 2008 46th Annual Allerton Conference on Communication,Control,and Computing. Piscataway:IEEE Press, 2009: 1221-1224.
[60]	MA L , HE T , SWAMI A ,et al. Network capability in localizing node failures via end-to-end path measurements[J]. IEEE/ACM Transactions on Networking, 2017,25(1): 434-450.
[61]	BARTOLINI N , HE T , ARRIGONI V ,et al. On fundamental bounds on failure identifiability by Boolean network tomography[J]. IEEE/ACM Transactions on Networking, 2020,28(2): 588-601.
[62]	GALESI N , RANJBAR F . Tight bounds for maximal identifiability of failure nodes in Boolean network tomography[C]// Proceedings of 2018 IEEE 38th International Conference on Distributed Computing Systems (ICDCS). Piscataway:IEEE Press, 2018: 212-222.
[63]	NGUYEN H X , THIRAN P . The Boolean solution to the congested IP link location problem:theory and practice[C]// Proceedings of IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications. Piscataway:IEEE Press, 2007: 2117-2125.
[64]	XIA Y , TSE D . Inference of link delay in communication networks[J]. IEEE Journal on Selected Areas in Communications, 2006,24(12): 2235-2248.
[65]	ALON N , EMEK Y , FELDMAN M ,et al. Economical graph discovery[J]. Operations Research, 2014,62(6): 1236-1246.
[66]	FENG C Y , WANG L N , WU K ,et al. Bound-based network tomography with additive metrics[C]// Proceedings of IEEE INFOCOM 2019 IEEE Conference on Computer Communications. Piscataway:IEEE Press, 2019: 316-324.
[67]	LI H K , GAO Y , DONG W ,et al. Bound-based network tomography for inferring interesting link metrics[C]// Proceedings of IEEE INFOCOM 2020 - IEEE Conference on Computer Communications. Piscataway:IEEE Press, 2020: 1588-1597.
[68]	ZARIFZADEH S , GOWDAGERE M , DOVROLIS C . Range tomography:combining the practicality of Boolean tomography with the resolution of analog tomography[C]// Proceedings of the 2012 Internet Measurement Conference. New York:ACM, 2012: 385-398.
[69]	ZHAO S Q , LU Z , WANG C . Measurement integrity attacks against network tomography:feasibility and defense[J]. IEEE Transactions on Dependable and Secure Computing, 2021,18(6): 2617-2630.
[70]	SEN J , KOILAKONDA S , UKIL A . A mechanism for detection of cooperative black hole attack in mobile ad hoc networks[C]// Proceedings of 2011 Second International Conference on Intelligent Systems,Modelling and Simulation. Piscataway:IEEE Press, 2011: 338-343.
[71]	SHARMA B . A distributed cooperative approach to detect gray hole attack in MANETs[C]// Proceedings of the Third International Symposium on Women in Computing and Informatics. New York:ACM, 2015: 560-563.
[72]	YAAR A , PERRIG A , SONG D . Pi:a path identification mechanism to defend against DDoS attacks[C]// Proceedings of 2003 Symposium on Security and Privacy. Piscataway:IEEE Press, 2003: 93-107.
[73]	YAO G , BI J , VASILAKOS A V . Passive IP traceback:disclosing the locations of IP spoofers from path backscatter[J]. IEEE Transactions on Information Forensics and Security, 2014,10(3): 471-484.
[74]	MIZRAK A T , SAVAGE S , MARZULLO K . Detecting compromised routers via packet forwarding behavior[J]. IEEE Network, 2008,22(2): 34-39.
[75]	HUGHES J R , AURA T , BISHOP M . Using conservation of flow as a security mechanism in network protocols[C]// Proceedings of Proceeding 2000 IEEE Symposium on Security and Privacy.S＆P. Piscataway:IEEE Press, 2002: 132-141.
[76]	CHIU C C , HE T . Stealthy DGoS attack against network tomography:the role of active measurements[J]. IEEE Transactions on Network Science and Engineering, 2021,8(2): 1745-1758.
[77]	FRAGOULI C , SOLJANIN E . Network coding fundamentals[J]. Foundations and Trends? in Networking, 2006,2(1): 1-133.
[78]	QIN P , DAI B , HUANG B X ,et al. A survey on network tomography with network coding[J]. IEEE Communications Surveys ＆ Tutorials, 2014,16(4): 1981-1995.
[79]	CZAP L , FRAGOULI C , PRABHAKARAN V M ,et al. Secure network coding with erasures and feedback[C]// Proceedings of 2013 51st Annual Allerton Conference on Communication,Control,and Computing (Allerton). Piscataway:IEEE Press, 2014: 1517-1524.
[80]	HO T , LEONG B , CHANG Y H ,et al. Network monitoring in multicast networks using network coding[C]// Proceedings of International Symposium on Information Theory,2005.ISIT. Piscataway:IEEE Press, 2005: 1977-1981.
[81]	FRAGOULI C , MARKOPOULOU A . A network coding approach to overlay network monitoring[J]. 43rd Annual Allerton Conference on Communication,Control and Computing 2005, 2005,2: 774-783.
[82]	GUI J , SHAH-MANSOURI V , WONG V W S . A linear algebraic approach for loss tomography in mesh topologies using network coding[C]// Proceedings of 2010 IEEE International Conference on Communications. Piscataway:IEEE Press, 2010: 1-6.
[83]	QIN P , DAI B , HUANG B X ,et al. DCE:a novel delay correlation measurement for tomography with passive realization[J]. International Journal of Distributed and Parallel Systems, 2015,6(2/3): 1-11.
[84]	JAFARISIAVOSHANI M , FRAGOULI C , DIGGAVI S ,et al. Bottleneck discovery and overlay management in network coded peer-topeer systems[C]// Proceedings of the 2007 SIGCOMM workshop on Internet network management. New York:ACM, 2007: 293-298.
[85]	JAFARI SIAVOSHANI M , FRAGOULI C , DIGGAVI S N . Subspace properties of network coding and their applications[J]. IEEE Transactions on Information Theory, 2012,58(5): 2599-2619.
[86]	MA L , ZHANG Z , SRIVATSA M . Neural network tomography"[EB/OL]. 2020:arXiv:2001.02942.https://arxiv.org/abs/200.02942".
[87]	SARTZETAKIS I , VARVARIGOS E . Machine Learning Network Tomography with partial topology knowledge and dynamic routing[C]// Proceedings of GLOBECOM 2022 - 2022 IEEE Global Communications Conference. Piscataway:IEEE Press, 2023: 4922-4927.
[88]	IBRAHEEM A , SHENG Z G , PARISIS G ,et al. Neural network based partial tomography for In-vehicle network monitoring[C]// Proceedings of 2021 IEEE International Conference on Communications Workshops (ICC Workshops). Piscataway:IEEE Press, 2021: 1-6.
[89]	IBRAHEEM A , SHENG Z G , PARISIS G ,et al. Internal network monitoring with DNN and network tomography for In-vehicle networks[C]// Proceedings of 2022 IEEE International Conference on Unmanned Systems (ICUS). Piscataway:IEEE Press, 2022: 928-933.
[90]	LIN Y L , HE T , WANG S Q ,et al. Looking glass of NFV:inferring the structure and state of NFV network from external observations[J]. IEEE/ACM Transactions on Networking, 2020,28(4): 1477-1490.

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类型	性能度量	适用问题
布尔网络诊断^[18]	将链路或节点故障指标等内部性能度量建模为未知的布尔常数	部分网络系统不需要精确掌握具体数值，只需要掌握设备状态，从端到端布尔测量中推断未知参数的二进制状态。
可加网络诊断^[11]	将平均链路延迟等可加的内部性能度量建模为未知常数	每个端到端测量等于对应测量路径上的链路度量的总和，从端到端的路径测量推断出单个链路的度量。
带宽网络诊断^[19]	将带宽这一内部性能度量建模为未知的常数	每个端到端测量等于对应测量路径上的链路的最小带宽，从端到端的路径测量推断出单个链路的带宽。
随机网络诊断^[20]	将瞬时链路延迟等内部性能度量建模为有未知分布的随机变量	每个端到端测量是从相应路径性能度量的分布中提取的随机实现。

A survey on network tomography technology

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