Self-Similar Characteristics of Vehicle Arrival Pattern on Highways
Publication: Journal of Transportation Engineering
Volume 135, Issue 11
Abstract
This paper investigates the quantitative characteristics of the vehicle arrival pattern on highways. Inspired from a remarkable finding on data network traffic that most data packet arrival patterns follow the self-similar process as opposed to the classical Poisson process, this paper aims to explore whether the vehicle arrival pattern on highways exhibit the self-similarity property and the corresponding time headway distribution it obeys. By using real highway traffic data provided by the Texas Department of Transportation, United States, this paper examines the existence of self-similarity characteristics on these vehicle arrival data. This is done by estimating the Hurst parameter, which is an index for self-similarity testing. Hypothesis testing for the Hurst parameter estimation shows that the highway vehicle arrival pattern under moderate to heavy traffic conditions exhibit the self-similarity behavior. Then, using the headway data recorded from the Federal Highway situated in Kuala Lumpur of Malaysia, this paper further demonstrates that the time headway of vehicles on the highways follows the heavy-tailed distribution rather than the classical exponential distribution. These two novel findings not only shed some light on the existence of a new distribution to describe the vehicle arrival pattern but also enrich the studies on traffic flow theory.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers thank the Texas Department of Transportation for the real traffic data provided. This study is also supported by Singapore Ministry of Education through an Academic Research Fund of National University of Singapore (Grant No. UNSPECIFIEDR-264-000-200-112).
References
Abdel, W. W. M., Ehm, R., and Mah, M. (1994). “An empirical-study of vehicular headways in urban areas.” Can. J. Civ. Eng., 21(4), 555–563.
Adams, W. F. (1936). “Road traffic considered as a random series.” J. Inst. Civ. Eng., 4, 121–130.
Beran, J. (1994). Statistics for long-memory processes, Chapman & Hall, New York.
Branston, D. (1976). “Models of single lane time headway distributions.” Transp. Sci., 10, 125–148.
Cowan, R. J. (1975). “Useful headway models.” Transp. Res., 9, 371–375.
Crovella, M. E. and Bestavros, A. (1997). “Self-similarity in world wide web traffic: Evidence and possible causes.” IEEE/ACM Trans. Netw., 5, 835–846.
Daou, A. (1966). “On flow within platoons.” Aust. Road Res., 2(7), 4–13.
Fricker, J. D., and Whitford, R. K. (2004). Fundamentals of transportation engineering: Multimodal systems approach, Pearson Prentice Hall, Singapore.
Gerlough, D. L., and Huber, M. J. (1975). Traffic flow theory, Transportation Research Board, National Research Council, Washington, D.C.
Grecco, W. L., and Sword, E. C. (1968). “Prediction of parameters for Schuhl’s headway distribution.” Traffic Eng., 38, 36–38.
Greenberg, I. (1966). “The log-normal distribution of headways.” Aust. Road Res., 2, 14–18.
Griffiths, J. D., and Hunt, J. G. (1991). “Vehicle headways in urban areas.” Traffic Eng. and Control, 32(10), 458–462.
Highway capacity manual (HCM). (2000). Highway capacity manual, Transportation Research Board, National Research Council, Washington, D.C.
Karagiannis, T., and Faloutsos, M. (2002). “SELFIS: A tool for self-similarity and long-range dependence analysis.” The First Workshop on Fractals and Self-Similarity in Data Mining: Issues and Approaches (in KDD), ACM, Edmonton, Canada.
Karagiannis, T., Faloutsos, M., and Molle, M. (2003). “A user-friendly self-similarity analysis tool.” Computer Communication Review, 33, 81–93.
Kyu, B. K., and Elwalid, A. (1996). “The importance of long-range dependence of VBR video traffic in ATM traffic engineering: Myths and realities.” Proc., ACM Sigcomm1996, ACM, New York, 3–14.
Leland, W. E., Taqqu, M. S., Willinger, W., and Wilson, D. V. (1994). “On the self-similar nature of Ethernet traffic (extended version).” IEEE/ACM Trans. Netw., 2, 1–15.
Lieberman, E., and Rath, A. K. (2007). “Traffic simulation.” Traffic Flow Theory: A State-of-Art Special Rep. No. 165, Transportation Research Board, ⟨www.tfhrc.gov/its/tft/tft.htm⟩. (July 24, 2007).
Luttinen, R. T. (1994). “Identification and estimation of headway distributions.” 2nd Int. Symp. on Highway Capacity, R. Akcelik, ed., Australian Road Research Board, Transportation Research Board, Sydney, 427–446.
Luttinen, R. T. (1996). “Statistical analysis of vehicle time headways.” Ph.D. dissertation, Helsinki Univ. of Technology, Finland.
Minitab Web site. (2007). Minitab Inc., ⟨www.minitab.com/⟩ (July 24, 2007).
Montgomery, D. C., and Runger, G. C. (2007). Applied statistics and probability for engineers, 4th Ed., Wiley, New York.
Nagatani, T. (2005). “Self-similar behavior of a single vehicle through periodic traffic lights.” Physica A, 347, 673–682.
Ogden, K. W., and Bennett, D. W. (1984). Traffic engineering practice, Dept. of Civil Engineering, Monash Univ., Victoria.
Park, K., and Willinger, W. (2000). Self-similar network traffic and performance evaluation, Wiley, New York.
Paxson, V., and Floyd, S. (1995). “Wide-area traffic: The failure of Poisson modeling.” IEEE/ACM Trans. Netw., 3, 226–244.
Sainio, H. (1984). “The function of the entrance ramp of an undivided two-lane road for motor traffic only.” MS thesis, Helsinki Univ. of Technology, Espoo.
Schuhl, A. (1955). “The probability theory applied to distribution of vehicles on two-lane highways.” Poisson and traffic, Eno Foundation, Saugatuck, 59–75.
SELFIS Tool. (2007). T. Karagiannis, the researcher, ⟨www.cs.ucr.edu/~tkarag/Selfis/Selfis.html⟩. (July 24, 2007).
Sullivan, D. P., and Troutbeck, R. J. (1994). “The use of Cowan’s M3 headway distribution for modeling urban traffic flow.” Traffic Eng. Control, 35, 445–450.
Taqqu, M. S., Teverovsky, V., and Willinger, W. (1995). “Estimators for long-range dependence: An empirical study.” Fractals, 3, 785–798.
TransGuide Web site. (2007). Texas Department of Transportation, ⟨www.transguide.dot.state.tx.us/⟩ (Nov. 12, 2007).
Willinger, W., Taqqu, M. S., Sherman, R., and Wilson, D. V. (1995). “Self-similarity in high-speed packet traffic: Analysis and modeling of Ethernet traffic measurement.” Stat. Sci., 10, 67–85.
Willinger, W., Taqqu, M. S., Sherman, R., and Wilson, D. V. (1997). “Self-similarity through high variability: Statistical analysis of Ethernet LAN traffic at the source level.” IEEE/ACM Trans. Netw., 5, 71–86.
Information & Authors
Information
Published In
Journal of Transportation Engineering
Volume 135 • Issue 11 • November 2009
Pages: 864 - 872
Copyright
© 2009 ASCE.
History
Received: Nov 20, 2007
Accepted: Jul 15, 2009
Published online: Oct 15, 2009
Published in print: Nov 2009
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.