Estimation of Parameters in Distribution of Headways in Roundabouts
Publication: Journal of Transportation Engineering
Volume 128, Issue 5
Abstract
Estimation of parameters in the distribution of headways in roundabouts is a cumbersome task. Inherent to data employed are temporal variation together with dependence between successive vehicles. This is a consequence of the sampling period and interactions in the roundabouts. The elimination of observations, so as to obtain trend-free samples of independent vehicles, removes too much information from the data. If all the observations are used, the results of the parameter estimations are affected by temporal variation and dependence between headways. In this paper, an analysis of the statistical properties of the headways between major stream vehicles in roundabouts is described. The properties investigated were the existence of temporal variation in the measured headways and independent and identically distributed successive headways, i.e., if the headways were from a random sample. More than 50% of the investigated subsets suffered from trends or other nonrandom variations. The question whether these subsets should be excluded or not is discussed. Three methods for the estimation of parameters in the M3 distribution were tested. For the two-lane subsets, it was possible to demonstrate a linear relationship between the proportion of free vehicles and the volume. For the one-lane subsets, the adjusted was low, and the linear constant was not significant. Nevertheless, the distributions estimated by use of the two-lane subsets did not provide a better fit to the observed data than the distributions estimated by the use of one-lane subsets. The predicted capacity for a minor lane, i.e., the capacity obtained by the fitted distribution, was close to the capacity obtained by the empirical distribution function (the estimated capacity).
Get full access to this article
View all available purchase options and get full access to this article.
References
Akçelik, R., and Chung, E.(1994). “Calibration of the bunched exponential distribution of arrival headways.” Road Transport Res., 3(1), 42–59.
Branston, D.(1976). “Models of single lane time headway distributions.” Transp. Sci., 10(2), 125–148.
Breiman, L., Gafarian, A. V., Lichtenstein, R., and Murthy, V. K. (1969). “An experimental analysis of single-lane time headways in freely flowing traffic.” Beträige zur Theorie des Verkehrsflusses. Referate anläßlich des IV. Internationalen Symposiums über die Theorie des Verkehrsflusses in Karlsruhe im juni 1968, W. Leutzbach and P. Baron, eds., Bonn, Germany (in German).
Brilon, W., and Wu, N.(1990). “Delays at fixed-time traffic signals under time-dependent traffic conditions.” Traffic Eng. Control, 31(12), 623–631.
Cowan, R. J.(1975). “Useful headway models.” Transp. Res., 9(6), 371–375.
Cox, D. R., and Lewis, P. A. W. (1966). The statistical analysis of series of events, Chapman & Hall, London.
Cox, D. R., and Stuart, A.(1955). “Some quick sign tests for trend in location and dispersion.” Biometrika, 42, 80–95.
Drew, D. R. (1968). Traffic flow theory and control, McGraw-Hill, New York.
Hagring, O.(1998). “A further generalisation of Tanners formula.” Transp. Res., 32B(6), 423–429.
Hagring, O.(2000). “Estimation of critical gaps in two major streams.” Transp. Res., 34B(4), 293–313.
Hoogendorn, S. P., Botma, H., and Bovy, P. H. L. (1997). Car headway distribution modelling and estimation, Technische Univ., Delft, The Netherlands.
Kendall, M., and Ord, J. K. (1990). Time-series, Edward Arnold, London.
Kimber, R. M., and Hollis, E. (1979). “Traffic queues and delays at road junctions.” Laboratory Report 909, Transport and Road Research Laboratory, Crowthorne, U.K.
Luttinen, T. (1992). “Statistical properties of vehicle time headways; Highway capacity and traffic flow.” Transportation Research Record. 1365, Transportation Research Board, Washington, D.C.
Luttinen, T. (1996). Statistical analysis of vehicle time headways, Teknillinen korkeakoulu, Otaniemi, Finland.
Miller, A. J.(1961). “A queueing model for road traffic flow.” J. R. Stat. Soc., 23B(1), 64–76.
Plank, A. W.(1982). “The capacity of a priority intersection.” Traffic Eng. Control, 23(2), 88–92.
Siegel, S. (1956). Nonparametric statistics for the behavioural sciences, McGraw-Hill, New York.
Statens Vägverk. (1995). “CAPCAL, model description, four parts: Intersection without traffic signals, signalized intersections, roundabouts, economic costs.” Rep. 1995:007E–1995:010E, Borlänge, Sweden.
Stephens, M. (1986). “Tests based on EDF statistics.” Goodness-of-fit techniques, R. D. Agostino and M. Stephens, eds., Marcel Dekker, New York.
Sullivan, D. P., and Troutbeck, R. J.(1994). “The use of Cowans M3 headway distribution for modelling urban traffic flow.” Traffic Eng. Control, 35(7–8), 445–450.
Troutbeck, J. R. (1989). “Evaluating the performance of a roundabout.” Special Rep. 45, Australian Road Research Board, Vermont, Australia.
Troutbeck, J. R. (1990). “Roundabout capacity and the associated delay.” Transportation and traffic theory, M. Koshi, ed., Elsevier, New York.
Troutbeck, J. R.(1997). “A review of the process to estimate the Cowan M3 headway distribution parameters.” Traffic Eng. Control, 38(11), 600–603.
Wald, A., and Wolfowitz, J.(1940). “On a test whether two samples are from the same population.” Ann. Math. Stat., 2, 147–162.
Information & Authors
Information
Published In
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Mar 20, 2001
Accepted: Sep 25, 2001
Published online: Aug 15, 2002
Published in print: Sep 2002
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.