American Institute of Mathematical Sciences

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September  2013, 8(3): 783-802. doi: 10.3934/nhm.2013.8.783

Spoofing cyber attack detection in probe-based traffic monitoring systems using mixed integer linear programming

Edward S. Canepa 1, , Alexandre M. Bayen 2, and  Christian G. Claudel 1,

1. 

King Abdullah University of Science and Technology, Electrical Engineering Department, Thuwal, Makkah 23955, KSA, Saudi Arabia, Saudi Arabia
2. 

University of California at Berkely, Electrical Engineering and Computer Sciences, Berkeley CA 94720-170

Received  September 2012 Revised  March 2013 Published  October 2013

Traffic sensing systems rely more and more on user generated (insecure) data, which can pose a security risk whenever the data is used for traffic flow control. In this article, we propose a new formulation for detecting malicious data injection in traffic flow monitoring systems by using the underlying traffic flow model. The state of traffic is modeled by the Lighthill-Whitham-Richards traffic flow model, which is a first order scalar conservation law with concave flux function. Given a set of traffic flow data generated by multiple sensors of different types, we show that the constraints resulting from this partial differential equation are mixed integer linear inequalities for a specific decision variable. We use this fact to pose the problem of detecting spoofing cyber attacks in probe-based traffic flow information systems as mixed integer linear feasibility problem. The resulting framework can be used to detect spoofing attacks in real time, or to evaluate the worst-case effects of an attack offline. A numerical implementation is performed on a cyber attack scenario involving experimental data from the Mobile Century experiment and the Mobile Millennium system currently operational in Northern California.
Keywords: hyperbolic partial differential equations, cybersecurity., Mixed integer linear programming.
Mathematics Subject Classification: 68U35, 90C11, 90C9.
Citation: Edward S. Canepa, Alexandre M. Bayen, Christian G. Claudel. Spoofing cyber attack detection in probe-based traffic monitoring systems using mixed integer linear programming. Networks & Heterogeneous Media, 2013, 8 (3) : 783-802. doi: 10.3934/nhm.2013.8.783
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References:
[1]

in "Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control," Springer-Verlag, (2009), 31-45. doi: 10.1007/978-3-642-00602-9_3.  Google Scholar

[2]

In "Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control," ACM, (2010),161-170. doi: 10.1145/1755952.1755976.  Google Scholar

[3]

Systems and Control: Foundations and Applications, Birkhäuser, Boston, MA, 1991.  Google Scholar

[4]

SIAM Journal on Control and Optimization, 47 (2008), 2348-2380. doi: 10.1137/060659569.  Google Scholar

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Birkhäuser, Boston, MA, 1997. doi: 10.1007/978-0-8176-4755-1.  Google Scholar

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Communications in Partial Differential Equations, 15 (1990), 1713-1742. doi: 10.1080/03605309908820745.  Google Scholar

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In "Proceedings of the 15th International IEEE Conference on Intelligent Transportation Systems", (2012), 832-839. Google Scholar

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Birkhäuser, Boston, MA, 2001. doi: 10.1007/978-1-4612-0185-4.  Google Scholar

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IEEE Transactions on Automatic Control, 55 (2010), 1142-1157. doi: 10.1109/TAC.2010.2041976.  Google Scholar

[10]

IEEE Transactions on Automatic Control, 55 (2010), 1158-1174. doi: 10.1109/TAC.2010.2045439.  Google Scholar

[11]

SIAM Journal on Control and Optimization, 49 (2011), 383-402. doi: 10.1137/090778754.  Google Scholar

[12]

Transactions of the American Mathematical Society, 277 (1983), 1-42. doi: 10.1090/S0002-9947-1983-0690039-8.  Google Scholar

[13]

Transportation Research, 28B (1994), 269-287. doi: 10.1016/0191-2615(94)90002-7.  Google Scholar

[14]

Transportation Research B, 39B (2005), 187-196. doi: 10.1016/j.trb.2004.04.003.  Google Scholar

[15]

Networks and Heterogeneous Media, 1 (2006), 601-619. doi: 10.3934/nhm.2006.1.601.  Google Scholar

[16]

SIAM Journal of Control and Optimization, 31 (1993), 257-272. doi: 10.1137/0331016.  Google Scholar

[17]

Transportation Research Part C: Emerging Technologies, 18 (2010), 568-583. doi: 10.1016/j.trc.2009.10.006.  Google Scholar

[18]

in "Proceedings of the 6th International Conference on Mobile Systems, Applications, and Services," ACM, (2008), 15-28. doi: 10.1145/1378600.1378604.  Google Scholar

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[20]

Transportation Research Part B: Methodological, 45 (2011), 1727-1748. doi: 10.1016/j.trb.2011.07.004.  Google Scholar

[21]

Highway Research Record, 99 (1965), 43-44. Google Scholar

[22]

Transporation Research B, 27B (1993), 281-313. Google Scholar

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SIAM, Philadelphia, PA, 2000. doi: 10.1137/1.9780898717525.  Google Scholar

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