A study on delay of single-lane roundabout

Abstract

Roundabouts are widely used in Europe, Australia and other countries. They work better than traffic signals at intersections with low and medium traffic volume and reduce the overall delay, better handle intersections with high volume of left turns. The purpose of this research is to validate Troutbeck's theoretic model by using field data in China. Circulating volume, entry volume, and entry delay are measured during peak and off-peak periods using video survey. Data on geometric design elements including circulating lane width, entry width, and roundabout diameter are measured through field survey. After surveying the actual traffic status of Fuming Square roundabout in Dalian, China, the theoretic delays of all approaches based on gap-accepted theory are calculated. We also calculate the mean delay of whole roundabout and compare it with the actual mean delay. The analytical results for traffic delays are validated via field data obtained from the single-lane roundabout. Finally the level of service of the roundabout is analyzed.

Full text

A Study on Delay of Single-lane Roundabout
Rui-Jun Guo1,2 , Wan-Xiang Wang 2
1.School of Traffic and Transportation Engineering, Dalian Jiaotong University, Dalian, China.
2.School of Traffic and Transportation, Beijing Jiaotong University, Dalian, China.
Abstract: Roundabouts are widely used in Europe, Australia and other countries. They work better than traffic
signals at intersections with low to medium traffic volumes. The overall delay is reduced and high volumes of left
turns are better handled. Based on this research, the theoretic model was validated by use of field data in China.
Circulating volume, entry volume, and entry delay were measured during peak and off-peak periods using video
survey. The geometric parameters including circulating width, entry width and roundabout diameter were measured.
By surveying the actual traffic status of Fuming Square roundabout in Dalian, China, the theoretic delays of all
approaches are calculated based on gap accentance theory. The mean delay of whole roundabout was calculated
and compared with the actual mean delay. The calculated results of traffic delays in the single-lane roundabout are
validated via field data.
Keywords: Roundabout; Gap acceptance Theory; Delay; Level of Service
1. Introduction
Delay is the increase in running time as vehicles speed
is less than the free speed when they run through the road
or across the intersections. The delay of roundabouts can
be divided into geometric delay and traffic delay (or
queuing delay). The geometric delay is the additional
running time caused by the roundabout geometry,
including the delay caused by vehicle acceleration and
deceleration in the process of turning orientation. The
geometric delay of roundabouts with a certain shape is
constant. Traffic delay is the additional running time in
the process of slowing, waiting, speeding up when
vehicles enter the intersection.
By surveying the operation characteristics of
roundabouts,which include geometry, flow rate of
turning orientation, ideal speed of vehicles, minimum
headway of major stream and follow-up headway, the
theoretic delays were calculated and compared with field
delays based on gap acceptance theory. The validation of
the delay model was test and the level of service (LOS)
was determined for the roundabout.
2 Delay model of roundabouts
2.1 Delay model of entry vehicles Geometric delay
is mainly related to the diameter of roundabouts. Based
on gap acceptance theory, when the entering vehicles are
under the steady-conditions, the mean traffic delay (DT)
can be expressed as follow
x
D
DT 
1min
(1)
Where
min
D
is Adams delay (Troutbeck, 1986),
x
is
the saturated degree of approach stream. If the queue
length of approach stream follows geometric distribution,
min
D
is denoted as follow.
)(2 22
12
)(
min








m
mmm
c
tt
tttt
t
q
e
Dmc
(2)
where

is decay variable (1/s) ,
)1/( m
qtq

;
c
t
is critical gap(s);
m
t
is minimum headway of approach
stream(s)；

is ratio of unbunched vehicles;
q
is flow
rate of circulating vehicles (pcu/s).
2.2 Calculation of entry capacity For single-lane
roundabouts, the capacity can be calculated as follow
provided that headway of circulating vehicles follows
M3 distribution (Cowan, 1975).
f
mc
t
tt
e
qe
C






1
3600 )(
(3)
Where
f
t
is the follow-up headway of approach
stream(s)；
f
t
and
m
t
can be obtained by field survey.
2.3 Critical gap The critical gap can be calculated
using Ashworth’s method (1970) based on the headway
of circulating stream follows exponential distribution and
the acceptance gap and critical gap follow normal
distribution.
2
aac sqtt 

(4)
Where
a
t
is the mean headway of circulating stream
which were accepted by approach vehicles (s);
2
a
S
is
the variance of acceptance gaps (s2).
3 Survey and calculation of theoretic delay
3.1 Survey and statistics Fuming Square is an
unsignalized single-lane roundabout located in Dalian,
China. Fuming Road and Tianbao Street cross here. The
diameter of the roundabout is 23.5m. After rush-hour
video survey on June 11, 2009, the distance and field
running time of vehicles passed through roundabout can be
Corresponding author: R.J. Guo Dalian Jiaotong
University, email: rjguo@163.com

derived, and the flow rate table is showed as follow.
Table 1. Flow rate of different turning orientation (pcu/h)
Entry
Turn left
Straight
Turn right
Total
East
25
1144
28
1197
South
19
4
29
52
West
26
1152
23
1201
North
20
4
26
50
3.2 Calculation of theoretic delay Values of
theoretic delay can be calculated by use of equation (1)
and (2) as follow.
Table 2. Values of theoretic delay(s)
Entry
Traffic delay
Geometric delay
Entry delay
East
0.13
8
8.13
South
11.60
8
19.60
West
0.13
8
8.13
North
11.29
8
19.29
4 Compare of theoretic delay and field delay
4.1 Compare of entry delays The entry delay is
contributed by vehicle delay of each turning orientation.
It can be calculated as the sum of products of
turn-orientation proportion and field delay of relevant
orientation for each entry.
The ideal running velocity is 40.4km/h which is
derived by measured the average velocity on Fuming
Road before the roundabout. So the ideal running times
of vehicles passing through roundabout can be derived.
The field delay is the difference of field running time
and ideal running time. The result values are as follow.
Table 3. Field delay(s)
Entry
Turn left
Straight
Turn right
East
17.79
8.98
5.99
South
25.10
20.79
8.82
West
14.99
7.08
5.53
North
24.29
22.79
6.27
Compare of field delay and theoretic delay is
showed as follow.
Table 4. Compare of field delay and theoretic delay(s)
Entry
Field
delay
Theoretic
delay
Absolute
error
Relative
error
East
9.10
8.59
-0.51
5.6%
South
15.69
21.63
5.94
37.9%
West
7.22
8.60
1.37
19.0%
North
14.80
21.13
6.34
42.8%
From table 4, the delays in east and west entry are
smaller than the ones in south and north entry. The
theoretic delay is well matched with field delay for east
and west entry. The delay errors between the theoretic
delay and field delay are larger for south and north entry
vehicles.
3.2 Mean delay and LOS The mean delay
D
of
roundabouts can be calculated based on all entry delay. It
can be as reference for LOS of roundabouts.




n
iiVD
V
D1i
*
1
(5)
Where
i
V
is the flow rate of
i
th entry (pcu/h);
V
is
the sum of all entry flow rates (pcu/h);
i
D
is the delay
of
i
th entry(s).
The mean field delay is 8.45s and the mean theoretic
delay is 9.12s in Fuming square. The relative error is
7.92%. LOS of Fuming Square is class 1 based on the
LOS criteria of roundabouts which demonstrates that
vehicles run smoothly and are subjected a slight
resistance.
5 Conclusions
By comparing theoretic delay and field delay of
Fuming Square roundabout, the east entry, west entry
and the mean delay of roundabout were well predicted,
while south and north entry had larger error. Some
conclusions can be derived as follows.
(1) The flow rates are large and the proportion of running
straight is the largest for east and west entry. The flow
rates of south and north entry are small and have only
slight influence to Fuming Road. So the theoretic delay
is well matched with field delay for east and west entry.
(2) The conflicting flow rates are large for south and
north entry vehicles, so the delay values and errors
between the theoretic delay and field delay are larger.
(3) The field delay is smaller than theoretic delay
because there are much operations of forcing approach.
(4) The good prediction effect can be obtained by use of
equation (1) and (2). While the further research are
needed to revise the equation based on a large size
sample of roundabouts with small flow rate.
Reference:
[1].Jonathan Bunker, Rod Troutbeck. Prediction of minor
stream delays at a limited priority freeway merge.
Transportation Research Part B. Vol.37, pp719–735(2003).
[2].Cowan, R. J. Useful headway models. Transportation Res.
Vol.9, pp 371–375(1975).
[3].Ashworth, R. The analysis and interpretation of gap
acceptance data. Transportation Science, Vol.4,
pp270-280( 1970).