The observability problem in traffic models: Algebraic and topological methods

IEEE Transactions on Intelligent Transportation Systems

Volumn 9, Issue 2, 2008, Pages 275-287

  Castillo, Enrique ^a,b   Jiménez, Pilar ^a,c   Menéndez, José María ^a,c   Conejo, Antonio J ^a,c  

^a IEEE

^b UNIVERSITY OF CANTABRIA   (Spain)

^c UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

Author keywords

Algebraic and topological methods; Link flow estimation; Origin desination (OD) flow estimation; Traffic model

Indexed keywords

BOOLEAN ALGEBRA; ERROR ANALYSIS; MATRIX ALGEBRA; METROPOLITAN AREA NETWORKS; NETWORK PROTOCOLS; TOPOLOGY;

ALGEBRAIC METHOD (AM); LINK FLOW; ORIGIN-DESTINATION (OD); ROUNDING ERRORS; STEP-BY-STEP; TOPOLOGICAL METHODS; TRAFFIC MODELLING; TRAFFIC NETWORKS; ZERO TEST;

COMPUTER NETWORKS;

EID: 45249094079     PISSN: 15249050     EISSN: None     Source Type: Journal    
DOI: 10.1109/TITS.2008.922929     Document Type: Article

References (52)

1. A. Abur and A. Gómez Expósito, Power System State Estimation-Theory and Implementations. New York: Marcel Dekker, 2004.
2. G. Alessandretti, A. Broggi, and P. Cerri, "Vehicle and guard rail detection using radar and vision data fusion," IEEE Trans. Intell. Transp. Syst., vol. 8, no. 1, pp. 95-105, Mar. 2007.
3. C. N. E. Anagnostopoulos, I. E. Anagnostopoulos, V. Loumos, and E. Kayafas, "A license plate-recognition algorithm for intelligent transportation system applications," IEEE Trans. Intell. Transp. Syst., vol. 7, no. 3, pp. 377-392, Sep. 2007.
4. K. Ashok and M. Ben-Akiva, "Alternative approaches for real-time estimation and prediction of time-dependent origin - Destination flows," Transp. Sci., vol. 34, no. 1, pp. 21-36, Feb. 2000.
5. O. Axelsson, Iterative Solution Methods. Cambridge, U.K.: Cambridge Univ. Press, 1996.
6. M. Ben-Akiva and S. R. Lerman, Discrete Choice Analysis: Theory and Application to Travel Demand. Cambridge, MA: MIT Press, 1985.
7. E. Cascetta, "Estimation of trip matrices from traffic counts and survey data: A generalized least squares estimator," Transp. Res., Part B, vol. 18, no. 4/5, pp. 289-299, Aug./Oct. 1984.
8. E. Cascetta and S. Nguyen, "A unified framework for estimating or updating origin/destination matrices from traffic counts," Transp. Res., Part B, vol. 22, no. 6, pp. 437-455, Dec. 1988.
9. E. Castillo, A. Cobo, F. Jubete, and R. E. Pruneda, Orthogonal Sets and Polar Methods in Linear Algebra: Applications to Matrix Calculations, Systems of Equations and Inequalities, and Linear Programming. New York: Wiley, 1999.
10. E. Castillo, A. Cobo, F. Jubete, R. E. Pruneda, and C. Castillo, "An orthogonally based pivoting transformation of matrices and some applications," SIAM J. Matrix Anal. Appl., vol. 22, no. 3, pp. 666-681, 2000.
11. E. Castillo, A. J. Conejo, P. Pedregal, R. García, and N. Alguacil, "Building and solving mathematical programming models in engineering and science," in Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts. New York: Wiley, 2001.
12. E. Castillo, A. J. Conejo, R. E. Pruneda, and C. Solares, "State estimation observability based on the null space of the measurement Jacobian matrix," IEEE Trans. Power Syst., vol. 20, no. 3, pp. 1656-1658, Aug. 2005.
13. E. Castillo, A. J. Conejo, R. E. Pruneda, and C. Solares, "Observability analysis in state estimation: A unified numerical approach," IEEE Trans. Power Syst., vol. 21, no. 2, pp. 877-886, May 2006.
14. E. Castillo, A. J. Conejo, R. E. Pruneda, and C. Solares, "Observability in linear systems of equations and inequalities: Applications," Comput. Oper. Res., vol. 34, no. 6, pp. 1708-1720, Jun. 2007.
15. E. Castillo, F. Jubete, E. Pruneda, and C. Solares, "Obtaining simultaneous solutions of linear subsystems of inequalities and duals," Linear Algebra Appl., vol. 346, no. 1-3, pp. 131-154, May 2002.
16. E. Castillo and F. Jubete, "The T-algorithm and some applications," Int. J. Math. Educ Sci. Technol., vol. 35, no. 3, pp. 369-389, May/Jun. 2004.
17. E. Castillo, J. M. Menéndez, and S. Sánchez-Cambronero, "Predicting traffic flow using Bayesian networks," Transp. Res., Pt. B, vol. 42, no. 5, pp. 482-509, Jun. 2008.
18. E. Castillo, A. J. Conejo, J. M. Menéndez, and P. Jiménez, "The observability problem in traffic models," Comput.-Aided Civil Infrastruct. Eng., vol. 23, no. 3, pp. 208-222, Apr. 2008.
19. E. Castillo, J. M. Menéndez, and P. Jiménez, "Trip matrix and path flow reconstruction and estimation based on plate scanning and link observations," Transp. Res., Part B, vol. 42, no. 5, pp. 455-481, Jun. 2008.
20. E. Castillo, J. M. Menéndez, P. Jiménez, and A. Rivas, "Closed form expressions for choice probabilities in the Weibull case," Transp. Res., Pt. B, vol. 42, no. 4, pp. 373-380, May 2008.
21. E. Castillo, J. M. Menéndez, and S. Sánchez-Cambronero, "Traffic estimation and optimal counting location without path enumeration using Bayesian networks," Comput.-Aided Civil Infrastruct. Eng., vol. 23, no. 3, pp. 189-207, Apr. 2008.
22. K. A. Clements and B. F. Wollenberg, "An algorithm for observability determination in power system state estimation," presented at the IEEE PES Summer Meeting, San Francisco, CA, Jul. 1975, Paper A75 447-3.
23. C. Daganzo and Y. Sheffi, "On stochastic models of traffic assignment," Transp. Sci., vol. 11, no. 3, pp. 253-274, 1977.
24. J. Doblas and F. G. Benitez, "An approach to estimating and updating origin-destination matrices based upon traffic counts preserving the prior structure of a survey matrix," Transp. Res., Pt. B, vol. 39, no. 7, pp. 565-591, Aug. 2005.
25. I. S. Duff and G. A. Watson, Eds., The State of the Art in Numerical Analysis. Oxford, U.K.: Oxford Univ. Press, 1997.
26. A. Ehlert, M. G. H. Bell, and S. Grosso, "The optimisation of traffic count locations in road networks," Transp. Res., Pt. B, vol. 40, no. 6, pp. 460-479, Jul. 2006.
27. A. G. Exposito and A. Abur, "Generalized observability analysis and measurement classification," IEEE Trans. Power Syst., vol. 13, no. 3, pp. 1090-1095, Aug. 1998.
28. C. Fisk, "Some developments in equilibrium traffic assignment," Transp. Res., Pt. B, vol. 14, no. 3, pp. 243-255, Sep. 1980.
29. G. H. Golub and C. F. van Loan, Matrix Computations. London, U.K.: Johns Hopkins Univ. Press, 1996.
30. M. L. Hazelton, "Estimation of origin-destination matrices from link flows on uncongested networks," Transp. Res., Pt. B, vol. 34, no. 7, pp. 549-566, Sep. 2000.
31. B. Gou and A. Abur, "A direct numerical method for observability analysis," IEEE Trans. Power Syst., vol. 15, no. 2, pp. 625-630, May 2000.
32. B. Gou and A. Abur, "An improved measurement placement algorithm for network observability," IEEE Trans. Power Syst., vol. 16, no. 4, pp. 819-824, Nov. 2001.
33. C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations. Philadelphia, PA: SIAM, 1995.
34. G. N. Korres, P. J. Katsikas, K. A. Clements, and P. W Davis, "Numerical observability analysis based on network graph theory," IEEE Trans. Power Syst., vol. 18, no. 3, pp. 1035-1045, Aug. 2003.
35. G. R. Krumpholz, K. A. Clements, and P. D. Davis, "Power system observability - A practical algorithm using network topology," IEEE Trans. Power App. Syst., vol. PAS-99, no. 4, pp. 1534-1542, Jul. 1980.
36. B. Li and B. De Moor, "Dynamic identification of origin-destination matrices in the presence of incomplete observations," Transp. Res., Pt. B, vol. 36, no. 1, pp. 37-57, Jan. 2002.
37. H. P. Lo, N. Zhang, and W H. K. Lam, "Estimation of an origin-destination matrix with random link choice proportions: A statistical approach," Transp. Res., Pt. B, vol. 30, no. 4, pp. 309-324, Aug. 1996.
38. M. Maher, "A stochastic assignment model," in Mathematica in Transport Planning and Control. Oxford, U.K.: Oxford Univ. Press, 1992, pp. 121-132.
39. A. Monticelli, "Electric power system state estimation," Proc. IEEE, vol. 88, no. 2, pp. 262-282, Feb. 2000.
40. A. Monticelli and F. F. Wu, "Network observability-Identification of observable islands and measurement placement," IEEE Trans. Power App. Syst., vol. PAS-104, no. 5, pp. 1035-1041, May 1985.
41. A. Monticelli and F. F. Wu, "Network observability-Theory," IEEE Trans. Power App. Syst., vol. PAS-104, no. 5, pp. 1042-1048, May 1985.
42. R. R. Nucera and M. L. Gilles, "Observability analysis: A new topological algorithm," IEEE Trans. Power Syst., vol. 6, no. 2, pp. 466-475, May 1991.
43. C. C. C. Pang, W W L. Lam, and N. H. C. Yung, "A method for vehicle count in the presence of multiple-vehicle occlusions in traffic images," IEEE Trans. Intell. Transp. Syst., vol. 8, no. 3, pp. 441-459, Sep. 2007.
44. W B. Powell and Y Sheffi, "The convergence of equilibrium algorithms with predetermined step sizes," Transp. Sci., vol. 16, no. 1, pp. 45-55, Feb. 1982.
45. J. N. Praskher and S. Bekhor, "Some observations on stochastic user equilibrium and system optimum of traffic assignment," Transp. Res., Pt. B, vol. 34, no. 4, pp. 277-291, May 2000.
46. J. N. Praskher and S. Bekhor, "Route choice models used in the stochastic user equilibrium problem: A review," Transp. Rev., vol. 24, no. 4, pp. 437-463, Jul. 2004.
47. Y Sheffi, Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods. Englewood Cliffs, NJ: Prentice-Hall, 1985.
48. S. Sun, C. Zhang, and G. Yu, "A Bayesian network approach to traffic flow forecasting," IEEE Trans. Intell. Transp. Syst., vol. 7, no. 1, pp. 441-459, Mar. 2007.
49. R. L. Tobin and T. L. Friesz, "Sensitivity analysis for equilibrium network flows," Transp. Sci., vol. 22, pp. 242-250, 1988.
50. Y Vardi, "Network tomography: Estimating source-destination traffic intensities from link data," J. Amer. Stat. Assoc., vol. 91, no. 433, pp. 365-377, Mar. 1996.
51. H. Yang, T. Sasaki, Y. Iida, and Y. Asakura, "Estimation of origindestination matrices from link traffic counts on congested networks," Transp. Res., Pt. B, vol. 26, no. 6, pp. 417-434, Dec. 1992.
52. H. Yang and J. Zhou, "Optimal traffic counting locations for origindestination matrix estimation," Transp. Res., Pt. B, vol. 32, no. 2, pp. 109-126, Feb. 1998.