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Journal of Zhejiang University SCIENCE A 2010 Vol.11 No.1 P.18-24

10.1631/jzus.A0800855


Dependence patterns associated with the fundamental diagram: a copula function approach


Author(s):  Jia LI, Yue-ping XU

Affiliation(s):  Department of Civil and Environmental Engineering, University of Massachusetts Amherst, Amherst, MA 01002, USA; more

Corresponding email(s):   yuepingxu@zju.edu.cn

Key Words:  Nonparametric copula, Dependence patterns, Traffic flow, Loop detector


Jia LI, Yue-ping XU. Dependence patterns associated with the fundamental diagram: a copula function approach[J]. Journal of Zhejiang University Science A, 2010, 11(1): 18-24.

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author="Jia LI, Yue-ping XU",
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DOI - 10.1631/jzus.A0800855


Abstract: 
Randomness plays a major role in the interpretation of many interesting traffic flow phenomena, such as hysteresis, capacity drop and spontaneous breakdown. The analysis of the uncertainty and reliability of traffic systems is directly associated with their random characteristics. Therefore, it is beneficial to understand the distributional properties of traffic variables. This paper focuses on the dependence relation between traffic flow density and traffic speed, which constitute the fundamental diagram (FD). The traditional model of the FD is obtained essentially through curve fitting. We use the copula function as the basic toolkit and provide a novel approach for identifying the distributional patterns associated with the FD. In particular, we construct a rule-of-thumb nonparametric copula function, which in general avoids the mis-specification risk of parametric approaches and is more efficient in practice. By applying our construction to loop detector data on a freeway, we identify the dependence patterns existing in traffic data. We find that similar modes exist among traffic states of low, moderate or high traffic densities. Our findings also suggest that highway traffic speed and traffic flow density as a bivariate distribution is skewed and highly heterogeneous.

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Reference

[1] Brilon, W., Geistefeldt, J., Regler, M., 2005. Reliability of Freeway Traffic Flow: A Stochastic Concept of Capacity. Proceedings of the 16th International Symposium on Transportation and Traffic Theory (ISTTT), Woods Hole, MA, USA.

[2] Cassidy, M.J., Bertini, R.L., 1999. Some traffic features at freeway bottlenecks. Transportation Research Part B: Methodological, 33(1):25-42.

[3] Cassidy, M.J., Mauch, M., 2001. An observed traffic pattern in long freeway queues. Transportation Research Part A: Policy and Practice, 35(2):143-156.

[4] Chavez-Demoulin, V., Embrechts, P., Nešlehová., 2006. Quantitative models for operational risk: extremes, dependence and aggregation. Journal of Banking & Finance, 30(10):2635-2658.

[5] Chen, S.X., Huang, T., 2007. Nonparametric estimation of copula functions for dependence modeling. Canadian Journal of Statistics, 35(2):265-282.

[6] Clemen, R.T., Reilly, T., 1999. Correlations and copulas for decision and risk analysis. Management Science, 45(2):208-224.

[7] Devroye, L., 1982. A note on approximations in random variate generation. Journal of Statistical Computation and Simulation, 14(2):149-158.

[8] Favre, A.C., El-Adlouni, S., Perreault, L., Thiemonge, N., Bobee, B., 2004. Multivariate hydrological frequency analysis using copulas. Water Resources Research, 40(1):W01101.

[9] Genest, C., Favre, A.C., 2007. Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering, 12(4):347-368.

[10] Hoogendoorn, S.P., van Lint, H., Knoop, V.A., 2008. Stochastic Macroscopic Modeling Framework to Interpret the Fundamental Diagram. Symposium on the Fundamental Diagram: 75 Years, Woods Hole, MA, USA.

[11] Hörmann, W., Leydold, J., Derflinger, J., 2004. Automatic Nonuniform Random Variate Generation. Springer, p.63-68.

[12] Junker, M., May, A., 2005. Measurement of aggregate risk with copulas. The Econometrics Journal, 8(3):428-454.

[13] Kühne, R., Lubashevsky, I., Mahnke, R., Kaupush, J., 2004. Probabilistic Description of Traffic Breakdowns Caused by On-ramp Flow. arXiv:cond-mat/0405163v1.

[14] Li, J., Chen, Q.Y., Wang, H., Ni, D., 2008. Investigation of LWR Model with Flux Function Driven by Random Free Flow Speed. Symposium on the Fundamental Diagram: 75 Years, Woods Hole, MA, USA.

[15] Mahnke, R., Kaupužs, J., 2001. Probabilistic description of traffic flow. Networks and Spatial Economics, 1(1/2): 103-136.

[16] Nagel, K., Wagner, P., Woesler, R., 2003. Still flowing: approaches to traffic flow and traffic jam modeling. Operations Research, 51(5):681-710.

[17] Nelsen, R.B., 1999. An Introduction to Copulas. Springer, p.54-79.

[18] Silverman, B.W., 1986. Kernel Density Estimation for Statistics and Data Analysis. Chapman and Hall, p.100-150.

[19] Sklar, A., 1959. Fonctions de Répartition à n-Dimensions et Leurs Marges. Publications de l’Institut Statistique de l’Université de Paris, 8:229-231.

[20] Trivedi, P.K., Zimmer, D.M., 2007. Copula Modeling: An Introduction for Practitioners. Now Publishers Inc., p.230-240.

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