An approach for the estimation of entry flows on roundabouts

An Approach for the Estimation of Entry Flows on Roundabouts Transportation Research Procedia 17 ( 2016 ) 52 – 62 2352 1465 © 2016 The Authors Published by Elsevier B V This is an open access article[.]

Transportation Research Procedia 17 ( 2016 ) 52 – 62

2352-1465 © 2016 The Authors Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license

( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).

Peer-review under responsibility of the Department of Civil Engineering, Indian Institute of Technology Bombay

doi: 10.1016/j.trpro.2016.11.060

ScienceDirect

11th Transportation Planning and Implementation Methodologies for Developing Countries

TPMDC 2014, 10-12 December 2014, Mumbai, India

An approach for the estimation of entry flows on roundabouts

Srinath Mahesha , AbdullahAhmada, Rajat Rastogia,*

a Department of Civil Engineering, Indian Institute of Technology Roorkee, ROORKEE - 247667 INDIA

Abstract

Roundabouts are commonly used as a means of intersection control for moderate traffic flows and junctions having variations in the intersection geometry It facilitates an orderly movement of traffic in a circular motion around a central island which is generally circular in shape The circulating traffic is considered to be the priority stream and entering traffic waits for a suitable gap in the circulating traffic In this fashion, it reduces the stopped delays as observed on the signalized intersections, as well as reduces the crashes and expenditure required for maintenance of traffic signals This paper examines the entry capacity of a roundabout under different circulating flows by measuring the field entry flows Queue formation in the approach is taken as an indicator that the approach is operating at capacity Relationship between entry flow and circulating flow is found following negative exponential distribution This is compared with the entry capacity estimations based on HCM 2010 The field entry flows are found to be higher than that given by the HCM 2010 equation This is due to the lower critical gap acceptance behavior shown by the Indian drivers under mixed traffic compared to the homogenous traffic modeled in the HCM 2010 An adjustment factor, multiplicative to the entry flow estimation based on HCM 2010 equation, is proposed which can be used by field engineers directly This will be simpler than the approach based on critical gap computation, which is tedious and difficult

© 2015 The Authors Published by Elsevier B V

Selection and peer-review under responsibility of the Department of Civil Engineering, Indian Institute of Technology Bombay

Keywords: Roundabouts, entry capacity, critical gap, HCM 2010 ;

* Corresponding author Tel.: +91-13-3228-5447

E-mail address: rajatfce@iitr.ac.in

© 2016 The Authors Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license

( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).

Peer-review under responsibility of the Department of Civil Engineering, Indian Institute of Technology Bombay

1 Introduction

Roundabouts are used as intersection control measures for a number of traffic and site conditions as they do not require any active control in terms of the presence of a traffic police They are ideal at locations having more than four approach legs intersecting at acute angles and with sufficient space for the central island For moderate traffic, roundabouts increase the traffic handling capacity of an intersection and improve its performance by reducing delays and crashes Reduction in the number and severity of crashes is due to the decrease in the number of conflict points when an uncontrolled intersection is converted into a roundabout The traffic enters a roundabout after seeking a suitable gap in the circulating stream of vehicles thereby, the crossing conflicts which are the most severe are completely eliminated and converted to merging and diverging Quantitatively, the number of conflict point reduces from 32 in a Two-Way Stop Controlled (TWSC) intersection to 8 in the case of a roundabout Besides, during low flows, there is less likelihood of crashes due to over speeding vehicles as there are inherent geometric features in the approaches to a roundabout which discourage high vehicle speeds in approaches

The traffic handling ability of a roundabout largely depends on its geometry and to lesser extent on driver behavior The geometric elements include the diameter of the central island, width at entry, width at exit, width of the circulating roadway, weaving width, weaving length, etc The driver behavior affects the performance of a roundabout and it is taken into account by introducing the independent variables, namely critical gap and follow-up time The critical gap is defined as that gap in-between the circulating vehicles which would be considered appropriate by most of the drivers to enter into the circulating traffic It would depend upon the composition and volume of the entering traffic, as well as, the circulating flow The presence of pedestrians and cyclists on a roundabout leads to a decrease in its traffic handling capacity A provision of separate path for these road users would improve both the safety of these vehicles or users and traffic handling efficiency of the roundabout

2 Literature Review

Earlier studies on development of models for estimation of entry flow or approach capacity at a roundabout can

be broadly classified into two categories: one empirical models and other analytical models Empirical models like the Indian, U.K and Swiss methods are based on direct field data collected at the approaches to roundabouts, whereas, the analytical models like the U.S., German and Australian models are based on gap acceptance behavior

of the drivers The Indian formula (IRC-65 1976) for estimation of capacity of a rotary is based on Wardrop’s equation which is empirical in nature and takes into account the geometric elements like entry or exit width, length and width of weaving section, and the proportion of weaving traffic with respect to the total traffic in weaving section The entire roundabout is divided into separate weaving sections and the practical capacity of the roundabout

is synonymous with the weaving section having the least capacity The U.K method is based on the formula proposed by Transport and Road Research Laboratory (TRRL) It takes into account the geometric parameters like entry width, flare length, sharpness of the flare, entry bend radius, entry angle, inscribed circle diameter, etc (Kimber 1980) The Swiss method is similar to the U.K method but considers the effect of exiting traffic in the direction opposite to the entering traffic (Bovy et al 1991)

In contrast, the HCM (2010) proposes an analytical approach based on critical gap and follow-up time to determine the entry capacity of a roundabout The recommended values of critical gap and follow-up time are 4.1 – 4.6 s and 2.6 – 3.1 s respectively The general equation is modified for roundabouts with different combinations of entry lanes and circulating lanes It is also suggested to verify the critical gap and follow-up time at important locations in conditions different from those found in U.S.A The Australian formula given by Akcelik et al (1998) gives capacity lane by lane The entry lane having the largest entry flow is referred to as the dominant entry lane and the lane having the smallest entry flow as the subdominant entry lane Brilon et al (1997) proposed a formula which takes into account the circulating flow in front of the entry, number of circulating lanes, number of lanes in the subject entry, minimum headway between the circulating vehicles, critical gap and follow-up time The critical gap, follow-up time and the headway between the circulating vehicles are collectively referred to as the psycho-technical times and have been estimated as 4.12 s, 2.88 s and 2.1 s respectively, for German conditions

Al-Masaeid and Faddah (1997) developed an empirical model for estimating roundabout entry capacity for conditions in Jordon The research concluded that the entry width and the central island diameter have the greatest

effect and the circulating roadway width has the least effect on estimated entry capacity as compared to other geometric variables Polus and Shmueli (1997) studied six small to medium-sized roundabouts with single circulating lane in urban and suburban areas in Israel The developed model showed an exponential decrease in entry capacity with an increase in the circulating flow Polus et al (2003) studied the effect of waiting time of the approaching drivers on the critical gap acceptance behavior of the drivers and found that as the circulating flow changes, the critical gap also changes At high circulating flows, the effect of critical gap on capacity was found to

be more significant and at low circulating flows, the central island diameter was the factor which affected the entry capacity

The methods discussed in the preceding paragraphs vary in one dimension i.e complexity There are some methods which are not based on any theoretical foundation like the method in use in India for capacity estimation of rotaries Other methods considers large number of variables so as to incorporate influences of geometry, traffic flow and driver behavior This makes the estimation cumbersome HCM method is simpler as far as the number of variables is concerned But the estimation of these variables is tedious There are many methods to estimate critical gaps and the applicability of one out of all always remains questionable Moreover, implementing agencies may found it difficult to estimate critical gaps and follow-up-times at different locations and in different cities because these are traffic and location specific In such a condition a simpler approach is needed which is usable by people working in different walks of life This paper attempts to provide one such approach

3 Data Collection

Data collection was done in the city of Chandigarh, capital city of both, the states of Punjab and Haryana Most

of the intersections in the city are in the form of roundabouts having four approaches which are mutually perpendicular following the grid pattern Following criteria are considered for the selection of a roundabout:

x Four- approaches which are mutually perpendicular

x Uncontrolled traffic operation, i.e not having a traffic signal or police personal

x Flat longitudinal gradient on all of the approaches

x Negligible interference by pedestrians and cyclists

x Availability of a multi-storey building nearby for placing the camera

Two roundabouts were selected for the study purpose which fulfilled the above-mentioned criteria The traffic and operational conditions of the two roundabouts are shown in Figure 1 The locational details and inventory data

of the selected roundabouts are given in Table 1 The roundabouts are named as R25 and R37, where ‘R’ stands for

a roundabout and number (25 or 37) represents the diameter of the central island in meters

Figure 1 Traffic and operational condition of roundabouts

Table 1 Inventory data of selected roundabouts

The data collected can be broadly classified into two categories: inventory data and traffic volume data The inventory data includes the geometric details of the roundabout like central island diameter, entry width, approach width, weaving width, weaving length, etc The inventory data was collected using a tape or a measuring wheel Traffic volume data are taken by vehicle category both at the entry of an approach and on the circulating section, thus giving information regarding total traffic volume and its composition on the two sections This data were collected using a video camera which was installed at the top of a nearby building The data collection was done in the months of September and November 2013, which are considered to be the normal months as the traffic flow is least affected by environmental influences during this period The video was captured from 8 a.m to 12 a.m and 4 p.m to 7 p.m on a typical clear weekday

The PCU values for converting the heterogeneous traffic into a homogeneous one are taken from IRC 65: 1976 For conversion into pcu, two wheelers are 0.75 pcu, autos are 1.0 pcu and buses are assessed as 2.8 pcu The composition of entering traffic is shown in the form of a pie-chart in Figure 2 The traffic volume data from different approaches and in different directions (right, left or through) are given in Table 2

Figure 2 Composition of entering traffic from an approach Table 2 Traffic volume data at the selected roundabouts Name of

roundabout Direction

Entry volume (pcu/h) Total volume

(pcu/h)

Circulating volume (pcu/h)

R 25

R 37

36%

44%

16%

Car TW Auto Bus Others

Geometric element Name of the roundabout

R 25 (Sector 22-23-35-36) R 37 (35-36-42-43)

4 Analysis and Results

The traffic flow values are estimated in both, vehicles per hour and pcu/h These estimated values of traffic flow

at an entry from an approach and in circulating area in front of it are shown in Figure 3 and 4 for the two roundabouts respectively As mentioned before, the entry flows and circulating flows corresponds to the time period during which there is queue formation in the approach Queue formation represents the saturated condition of that approach The duration and composition of the queue is also recorded along with the corresponding circulating flow

Figure 3 Entry flow versus circulating flow for R 25 roundabout

It can be noted that, irrespective of the measurement form for flows, the entry flow reduces exponentially with an increase in the circulating flow The functional forms are found to be satisfactory or above with respect to R-square value of the estimated equations This is found similar to the one reported by Polus and Shmueli (1997) The relationship is supporting the normal belief that when the flow on circulating lanes is low, more number of vehicles can move in from an approach, but as vehicles add to the circulating flow lesser number of vehicles can move in Relative position of the plots in terms of vehicles per hour and pcu/h indicate towards the absence of big size vehicles in the flow

Figure 5 presents a comparison between the entry capacities (in vehicle per hour) of the two roundabouts The entry capacity of a larger central island diameter roundabout is found to be higher than that of a relatively smaller central island diameter roundabout The width of the entry approach and circulating section are more or less similar (can be defined as two lane system), and the traffic composition is also equivalent Still there is an increase in the entry capacity of the second roundabout This can only be attributed to the influence of increase in diameter of the central island, which causes an increase in the space within the weaving section, thus accommodating more traffic volume This is supported by the work of Al-Masaeid and Faddah (1997) done in Jordon

y = 2729e -2E-04x

R² = 0.7154

y = 2986.5e -3E-04x

R² = 0.7706

0 500 1000

1500

2000

2500

Circulating flow

Vehicles/Hour PCU's/Hour

Figure 4 Entry flow versus circulating flow for R 37 roundabout

Figure 5 Comparison between entry capacity and circulating flow

Next, the estimated values of entry flows with respect to the circulating flows for the two roundabouts are compared with the estimates obtained on using HCM 2010 equation

The HCM (2010) roundabout entry capacity model is expressed as given by equation (1)

c

B*V

e

Where,

f

3600

A =

t 0.5 * t

B =

3600



(3)

Vc = conflicting flow rate in pcu/h

y = 3487.3e -2E-04x

R² = 0.742

y = 3633.2e -3E-04x

R² = 0.8554

0 500

1000

1500

2000

2500

3000

Circulating flow

vehicles/Hour PCU's/Hour

0 500

1000

1500

2000

2500

3000

Circulating flow (veh/h)

D = 37.5 m

D = 25 m

tf = follow-up time (s)

tc = critical gap (s)

As traffic volume in HCM equation is considered in pcu/h, the traffic on the two roundabouts is re-estimated using the guidelines of IRC:65 as already mentioned The relationships and comparison are shown in Figure 6 It can

be noted that the proposed entry capacity of an approach based on HCM 2010 equation is quite low as compared to the Indian field conditions This can be attributed to two factors: one the traffic heterogeneity in Indian condition as compared to homogenous condition in the US, and the difference in driver behavior in two countries The mix of the traffic and the absence of large size vehicles in present condition allow sharing of road not on the basis of lane discipline but based on size of the vehicles The share of 44% of two-wheelers do not require a 3.5 m wide lane, rather two streams of two-wheelers can get accommodated in this much wide section of the road Therefore, the number of vehicles in the approaches and circulating area will be more than those when lane-based movement is followed Another reason is the difference in behavior of the Indian drivers as compared to their American counterparts in terms of gap acceptance Besides, the higher proportion of two wheelers in the Indian traffic, the drivers of different category of vehicles are observed accepting lower gap sizes as compared to those in the US This also led to an increase in the entry capacity

In order to understand the difference in the merging behavior of Indian drivers as compared to the US regarding traffic flows at roundabouts, the critical gap and follow-up times are computed at both the locations The critical gap and follow-up time are the independent variables on which the entry capacity is dependent The average value of critical gap and follow-up-time is taken as 4.5 s and 2.7 s (60% of critical gap) in the HCM 2010 The estimation of critical gap is done using Modified Raff’s method, which utilizes both the accepted and rejected gaps The follow-up-time is estimated from the video of the two sites The results are given in Table 3 It can be noted that for none of the vehicle types, the value of critical gap or follow-up-time are anywhere near to the values being adopted by HCM

2010 Even in the case of car, these are around 50 to 55% of those used by HCM In the case of two-wheelers, these are around 40% only These values are also different than those observed in Germany, another developed country with homogenous traffic (Brilon et al 1997) These clearly indicate that the drivers in Indian condition are relatively impatient in nature This may be the influence of more number of vehicles sharing the same road space and trying to move without stopping Another factor is the squeezing effect of small size vehicles in-between larger size vehicles and on lanes The ratio between follow-up time and critical gap (rt) is also computed for different category of vehicles on two roundabouts It is found to be less than 0.60, which is different than the ranges being reported in literature by different researchers (Brilon 1988; Hagring et al 2003; Tian et al 2000) They have reported this ratio

as 0.60 and above

Table 3 Critical gap and follow-up times for vehicles at the two roundabouts Roundabout Vehicle type Critical Gap (s) Follow-up time (s) r t

R 25

R 37

Once the values of critical gap and follow-up time are estimated for Indian traffic flow conditions, then these are used to find the traffic stream critical gap for the approach The stream critical gap and follow-up time are computed using weighted average approach The percent value of the composition of traffic is used as weight for the respective value of critical gaps and follow-up-times so as to arrive at the traffic stream value This gave a value of 2.2 s for critical gap and 1.2 s for follow-up time Using these values in the equation proposed by HCM 2010, the entry capacity was re-estimated with respect to the same values of circulating flows as used in previous analysis This variation between the two variables is then compared with the field data available for the two roundabouts These are also shown in Figure 6 It can now be noted that the difference between the field values under heterogeneous and

adjusted-homogenous traffic has reduced on account of use of real values But still the HCM 2010 equation is not able to replicate the traffic conditions existing under Indian conditions Therefore, there is a need to use a multiplicative adjustment factor which can raise the estimation using HCM 2010 equation to satisfy the Indian traffic condition

Figure 6 Comparison of field entry capacity with HCM 2010 and adjusted HCM 2010 for Indian Condition

The adjustment factor is proposed for the entry flow at different circulating flow values for both sizes of roundabouts as they represent different flow behaviours Looking at the cumbersome process of estimation of critical gaps and follow-up-times, two ranges of adjustment factors are suggested in this paper First set of adjustment factors are estimated with respect to the original HCM equation which considers critical gap as 4.5 s and follow-up-time as 2.7 s Second set of adjustment factors correspond to the adjusted HCM equation i.e one which considers actual values of critical gap (2.2 s) and follow-up-time (1.2 s) for traffic stream in India The adjustment factor is defined as the ratio between the field entry flow value and that given by HCM equation or adjusted HCM equation The adjustment factors are shown in Figure 7 and Figure 8, respectively

Figure 7 Adjustment factor with respect to HCM 2010

0 500

1000

1500

2000

2500

3000

Circulating flow (pcu/h)

D = 37.5 m

D = 25 m

Using computed tc and tf values HCM 2010

0

1

2

3

4

5

6

7

8

Circulating flow (pcu/h)

D = 37.5 m

D = 25 m

Central Island

Figure 8 Adjustment factor with respect to adjusted HCM 2010 equation

It is clear from the two figures that the variation in adjustment factor with an increase in circulating flow becomes quite large, from 2.0 to 5.5 for R25 roundabout and from 2.5 to 6.8 for R37 roundabout, when the original HCM equation for estimation of entry capacity is considered This is because of wide variation in the traffic flows in two countries As the flow conditions prevailing in India are embedded in the HCM equation, the variation in the adjustment factor reduces sharply, and varies from 1.45 to 1.75 for R25 roundabout and from 1.5 to 2.3 for R37 roundabout The exponential rise in the adjustment factor with the increase in circulating flow changes to flatter but curvilinear function form when the estimation shifts from original HCM equation to adjusted HCM equation Some factious values of two wheelers, cars, autos and buses has been taken to see the variations of entry capacity values with respect to different flow conditions and varying proportions as given in Table 4 The adjustment factors are extracted using figure 8 and multiply to the adjusted HCM 2010 equation to estimate the entry capacity The estimated entry capacity with respect to circulating flow is shown in figure 9

Table 4 Estimated entry capacity using adjustment factor Circulating Volume Adjustment Factor Estimated Entry Capacity (pcu/h)*

TW

(Veh/h)

Car (Veh/h)

Auto (Veh/h)

Bus (Veh/h)

Total (pcu/h) R 25 R 37 R 25 R 37

1000 800 280 60 1998 1.42 1.73 1747 2131

856 857 428 103 2215 1.47 1.79 1642 2003

1200 900 380 81 2407 1.51 1.84 1555 1897

1113 1142 428 77 2621 1.56 1.91 1463 1785

1280 1000 560 100 2800 1.61 1.96 1391 1696

1350 1125 430 155 3002 1.66 2.03 1313 1601

1512 1470 379 103 3271 1.73 2.12 1216 1483

* Adjusted HCM 2010 entry capacity

y = 1.25367e 0.00016x

R² = 0.99953

y = 1.02789e 0.00016x

R² = 0.99960

0 0.5 1 1.5 2 2.5

Circulating flow (pcu/h)

D = 37.5 m

D = 25 m

Central Island

Figure 9 Estimated entry capacity versus circulating flow

5 Conclusions

The estimation of entry capacity of any roundabout under conditions prevailing in developing countries is a tedious process because of heterogeneity in vehicle types having variation in their operational performance and the driver behavior, which is highly adaptable towards the prevailing traffic flow on the road rather than being influenced and governed by the geometrics and controls This paper tries to estimate the entry capacity of a roundabout based on the traffic flow conditions on a roundabout and drivers’ behavior depicted by the gaps being accepted or rejected while trying to enter the circulating flow It tries to come up with a simple approach which can

be easily implemented by the practicing engineers in field

Following points emerged from the analysis of the two roundabouts, one with diameter of central island as 25 m and other with 37.5 m The entry approach and circulating section are both classified as two-lane systems though there is some difference in the widths

1 The two roundabouts catered to light traffic as majority of the composition constituted cars, motorized two-wheelers and auto-rickshaws (motorized three-two-wheelers) This also got clear from the estimation of traffic in measurements units vehicle per hour and pcu per hour The trend of pcu/h traffic curve remained below the veh/h traffic curve The variation between the two increased with an increase in the circulating flow This probably indicated towards merging of small size vehicles more than cars or large size vehicles at higher traffic flows It further indicated that small size vehicles might be entering circulating flow by accepting smaller gaps which otherwise are rejected by larger size vehicles

2 The entry capacity of the roundabout with larger diameter central island is found to be more than that of roundabout with smaller diameter As other geometrics especially number of lanes at entry and in circulating section are found equivalent, the only reason looks to be the increase in spacing between entry/exit locations which can accommodate more number of vehicles

3 The relationship between entry capacity and circulating flow is found to be negative exponential i.e the entry capacity decreased exponentially with an increase in the circulating flow

4 The use of original equation as given in HCM 2010 for the estimation of entry capacity will give quite low values

in the traffic flow conditions prevailing in developing countries Two factors are identified behind this: one, traffic flow heterogeneity in developing countries as compared to the US and second, the driver behavior which

is governed by lane discipline in the US but is governed by the flow characteristics and opportunities arising for merging

5 The presence of about 40% wheelers in the traffic stream has led to higher value of entry flow as two-wheelers show higher aggressive or impatient behavior while entering the circulating roadway as compared to

y = 3083.7e -3E-04x

R² = 1

y = 3761e -3E-04x

R² = 1

0 500

1000

1500

2000

2500

3000

Circulating flow (pcu/h)

R25 R37