Queuing delay models for single-lane roundabouts

This article presents an analytical model for a few important operational characteristics of single-lane roundabouts in the United States. In particular, we obtain renewal-based analytical expressions for the mean and variance of the time required for entry into the circulating stream for an arbitrary vehicle occupying the first position of the approach, regardless of the distribution of time headways for the circulating stream. These analytical models are subsequently applied in a M/G/1 queuing model to compute the steady-state average delay and length of the queue at the approach under stable conditions. The analytical models are validated by comparing numerical results for average delay with field observations obtained at six single-lane roundabout sites in the United States. The models are shown to perform well under a range of circulating stream flow rates. †The views expressed in this paper are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense or the US Government.

[1]  R. J. Troutbeck,et al.  Average Delay at an Unsignalized Intersection with Two Major Streams Each Having a Dichotomized Headway Distribution , 1986, Transp. Sci..

[2]  Dirk Heidemann,et al.  QUEUEING AT UNSIGNALIZED INTERSECTIONS , 1997 .

[3]  G. M. Davis.  The Department of Transportation , 1970 .

[4]  Rod Troutbeck.  AVERAGE DELAY AT AN UNSIGNALISED INTERSECTION WITH TWO MAJOR STREAMS EACH HAVING A DICHOTOMISED HEADWAY DISTRIBUTION , 1987 .

[5]  R J Troutbeck.  CURRENT AND FUTURE AUSTRALIAN PRACTICES FOR THE DESIGN OF UNSIGNALIZED INTERSECTIONS. INTERSECTIONS WITHOUT TRAFFIC SIGNALS, PROCEEDINGS OF AN INTERNATIONAL WORKSHOP, 16-18 MARCH 1988, BOCHUM, WEST GERMANY , 1988 .

[6]  I. Summersgill,et al.  DELAY PROCESSES AT UNSIGNALISED JUNCTIONS : THE INTERRELATION BETWEEN GEOMETRIC AND QUEUEING DELAY , 1986 .

[7]  W F Adams,et al.  ROAD TRAFFIC CONSIDERED AS A RANDOM SERIES. (INCLUDES PLATES). , 1936 .

[8]  W. F. Adams.  Road Traffic Considered as a Random Series , 1950 .

[9]  C. S. Fisk.  Traffic performance analysis at roundabouts , 1991 .

[10]  R. J. Troutbeck,et al.  Current and Future Australian Practices for the Design of Unsignalized Intersections , 1988 .

[11]  R M Kimber,et al.  A TRACK EXPERIMENT ON THE ENTRY CAPACITIES OF OFFSIDE PRIORITY ROUNDABOUTS , 1977 .

[12]  E J Myers.  MODERN ROUNDABOUTS FOR MARYLAND , 1994 .

[13]  J. Tanner,et al.  The capacity of uncontrolled intersection. , 1967, Biometrika.

[14]  Michael Kyte,et al.  EMPIRICAL MODELS FOR ESTIMATING CAPACITY AND DELAY AT STOP- CONTROLLED INTERSECTIONS IN THE UNITED STATES , 1991 .

[15]  Carl M. Harris,et al.  Fundamentals of queueing theory , 1975 .

[16]  Richard Cowan,et al.  Useful headway models , 1975 .