CAPACITY ANALYSIS ON MULTI-LANE ROUNDABOUTS: AN EVALUATION WITH HIGHWAY CAPACITY MANUAL 2010 CAPACITY MODEL ÇOKŞERİTLİ DÖNEL KAVŞAKLARDA KAPASİTE ANALİZİ: HIGHWAY CAPACITY MANUAL 2010 KAPASİTE MODELİYLE BİR DEĞERLENDİRME

Öz In this study, capacity estimations with the incorporation of Highway Capacity Manual (HCM) 2010 method are evaluated. Parameter based sensitivity analysis on calculations with the new HCM formula and a comparative evaluation of the new methodology with two most common capacity analysis methods, i.e., the method of critical gap acceptance and the method of regression analysis, are performed. Maximum and minimum headway intervals of follow up time and critical gap parameters are alternated within the sensitivity analysis. The Transport Research Laboratory formula for regression and Australian formula for gap acceptance method are considered in comparison. Relative comparisons of predictions on capacity by HCM2010 method, regression analysis and gap acceptance method are presented considering field data obtained by observations at two roundabouts in Izmir, Turkey. The results of the study show that the HCM2010 formula led to lower capacity estimates than regression analysis and higher estimates than the gap acceptance method. Regarding the real capacity observations under high circulating flowrates the HCM2010 method yielded to more appropriate results than the regression method. In addition to comparisons, studies on the sensitivity analysis show that entry capacity estimates possess sharper changes as smaller follow up headways are accepted. Bu çalışmada, genel kabul görmüş çok şeritli dönel kavşak kapasite hesap yöntemlerinin uygulanabilirliği, yeni Highway Capacity Manual (HCM) 2010 yöntemiyle karşılaştırılmıştır. Yöntemlerden elde edilen sonuçlar, yerel çalışmalardan toplanan verilerin ışığında değerlendirilmiştir. Karşılaştırma için regresyon analiz yöntemini temsilen Transportation Research Laboratory (TRL) formülasyonu, Kritik aralık kabulü yöntemini temsilen Avusturya Hesap Yöntemi seçilmiştir. Bunlara ek olarak, sınırlı öncelik ve ters öncelik koşullarının göz önünde bulundurulduğu kalibre edilmiş kritik aralık yöntemi ve HCM 2010 da yerel uygulamalar için öngörülen kalibre edilmiş formüller ile hesaplamalar yapılmış ve HCM 2010’un olağan değerleriyle karşılaştırılmıştır. Çalışmanın sonucunda elde edilenler, kritik aralık kabul yöntemi ve regresyon yönteminin HCM 2010 olağan değerlerine kıyasla genellikle daha yüksek sonuçlar verdiğini göstermiştir. Yöntemler arasında yapılan regresyon analizleri sonucu, özellikle yüksek dönen akımlar altında kritik aralık kabul yönteminin HCM 2010 yönteminden daha uygun sonuçlar verdiği görülmüştür. Ancak HCM 2010’da yerel uygulamalar için kalibrasyon yapılmasını sağlayan formülasyon sonucunda elde edilenler, olağan formülasyonun verdiği düşük kapasite tahminlerini daha uygun değerlere yükseltmiştir.


Introduction
A modern roundabout is a type of intersection design that controls and diverts traffic flow around a central island.Roundabouts are differentiated from other traffic circles in traffic control, pedestrian access, parking and direction of circulation features.Efficient use of capacity on roundabout design brings higher functional performance.Roundabouts are preferred as a part of the transportation system for preventing lock-up under high traffic volumes and improving safety performance.Various studies investigating the safety performance are made in Europe and United states.Federal Highway Administration (FHWA)'s guide gathered together the mean reduction of crashes after building roundabout [1].This paper discusses the parameter sensitivity of new Highway Capacity Manual (HCM) 2010 formula and comparison of new methodology with critical gap acceptance and regression models considering field observations.Australian model summarized in [2] is used for gap acceptance formula.United Kingdom model also known as Transportation Research Laboratory (TRL) method is used for regression analysis.Obtained results are compared with in site data collected from two roundabouts in [3].
In the first part, fundamentals of design and traffic flows at roundabouts are stated.Secondly, capacity analysis used in comparison, HCM 2010 [4], gap acceptance and regression methods are introduced.In the following section HCM 2010 is compared with both methods and observed data.In the last part of the study sensitivity analysis of HCM 2010 on parameters follow-up time, Tf, and critical gap, Tc, are investigated.
Considering the validity of applied methods it is useful to mention the design differences between investigated sites in Turkey and typical sites used to develop compared models in the US, Australia and UK.The findings represent application of those models to Turkish data only for the studied roundabouts and are not generalized for different sites.

Fundamentals of Design and Traffic Flows at Roundabouts
A well designed roundabout ensures safety for all types of vehicles those defined in user category.Layout of the Three fundamental elements must be determined in the preliminary design stage; the optimal roundabout size, position, alignment and arrangement of approach leg [1].

Roundabout Design
Geometric design elements have significant importance on operational performance and safety objectives of a roundabout.In addition to individual importance of each element, the interaction between each component should be studied for a well-designed layout.Geometric design elements detailed in the following topics are; Inscribed circle diameter, entry width, circulatory roadway, central island, entry curves, exit curves, splitter island and stopping sight distance.Table 1 presents the geometric parameters and their symbols commonly used in regression models.Figure 1 depicts a roundabout geometry with elements used in TRL formulae.Geometric elements showed in the table above are also showed in Figure 1 those taken from the original work of Kimber ([5]).
Figure 1: Geometric elements used in the TRL formula.

Traffic Flows at Roundabouts
For a given volume of circulating vehicles, capacity is defined as the maximum number of vehicles that can reasonably enter the roundabout within 1 hour.The entry/circulating (Qe/Qc) flow ratio is also useful to express the entry capacity relation of the roundabout with circulation flow.Basic parameters defined inside circulating stream are explained in the following sections.

Basic Definitions
The interval between successive vehicles in a traffic lane as they pass a point on the highway in terms of time is named 'headway'.It is measured in seconds, from front bumper to front bumper of vehicles.
Gap is the headway between two consecutive vehicles passing the same reference point in the circulating stream.If an entering vehicle on the approaching leg arrives at the yield bar after the gap has already started, the remainder of the gap is called lag.
The minimum gap in terms of time that is acceptable to the entering stream driver to enter the roundabout, is called critical headway (or critical gap), Tc.The traditional gap acceptance method assumes that the drivers of the approach lane accept any gap greater or equal to the critical gap and reject any gap smaller than the critical gap [6].Follow-up time, Tf, is the additional time required after the critical gap for following vehicles to enter the roundabout.Every driver can accept different gaps.It is possible to encounter such circumstances that a critical gap much longer than accepted by a driver could be rejected by another one [7].

Merging Conditions
Hangring defines gap forcing as a situation that vehicles entering the circulating flow use so small gaps that vehicles in the circulating flow are forced to give way and have to decelerate or completely stop [8].In addition to gap forcing it is also possible to define limited priority and reverse priority as merging systems those can occur under over saturated conditions.At high levels of both entering and conflicting flow HCM 2010 defines limited priority as a condition which circulating traffic adjusts its headways to allow entering vehicles to enter and reverse priority as a condition which entering traffic forces circulating traffic to yield [4].

Capacity Analysis of Roundabouts
Most of the European countries and US formed their own capacity formulas according to their needs and highway standards.The consideration parameter in each formula changes with different methodologies.Two main methodologies, regression analysis and gap acceptance theory are accepted.In Germany and Switzerland Brilon and Bovy formulations consider the number of circle lanes and leg lanes.
In UK detailed roundabout geometry is taken into account.In addition to these geometric aspects, the users' behaviors, psycho-technical times, Tc, critical gap, and follow-up time, Tf, are also used by France, Germany and US in improved capacity formulations.
Specifically, a series of works have been being conducted considering traffic circles in Turkey including ultimate capacity determination for single-lane roundabouts [9], [10], comparative evaluation of a series of capacity [3], [11] and delay measure [12] estimation methods, and impact of traffic composition on roundabout and merging flow capacity [13], [14].

Capacity Analysis: A Case Study
The case study in this paper presents a brief comparison of HCM 2010 formulation with regression and gap acceptance theories.Methodologies are discussed considering field data.

Methods Used
The HCM 2010 [4], the linear Transport and Road Research Laboratory (TRRL) capacity formula [5] and the gap acceptance model [2] are used in comparative evaluations.

Highway Capacity Manual 2010 Model
HCM 2010, the fifth edition, developed new methodologies for evaluating roundabout performance.In difference to HCM 2000 edition, multilane roundabouts with up to two entry lanes and one bypass lane per approach were considered in capacity estimates.New method of HCM 2010 presents a lane based capacity model with combination of a simple lane based regression and gap acceptance models for both single and double lane roundabouts [4].Akçelik describes new capacity model as a nonlinear empirical (regression) model with a theoretical basis in gap acceptance that covers both regression and gap acceptance theory as expressed in the Eq. ( 1) [15]; Where; fHVe is heavy vehicle factor for entry lane capacity, fp is pedestrian factor for the effect of pedestrians crossing in front of entry lanes.fA and fB are adjustment factors for parameter A and B respectively where, fA=fB means Tc/Tf is kept unchanged.Qc' is circulating flow rate in front of the entry (adjusted for heavy vehicles) in pcu/h.fHVe can be calculated by Eq. ( 2);   Where ET is the passenger car equivalent of a heavy vehicle for gap acceptance theory in pcu/veh and PT is the proportion of heavy vehicles in the entry lane.Adjusted Qc' can be determined by Eq. (3); Where Qc' is the adjusted circulating flow rate in pcu/h, Qc is the circulating flow rate in veh/h and fHVc is heavy vehicle factor.It is possible to calculate fHVc with Eq. ( 3) by adjusting PT to circulating lane ratios.HCM defines default values shown in the Table 2 and Table 3 for capacity models according to observations made at US roundabouts in 2003 [4].
Where To is the parameter that relates critical gap and follow up time parameters in s unit, Tf is follow-up headway and Tc is critical gap headway.

Regression Model
The relationship defining the "Linear Capacity formula" by means of capacity and entry flow is proposed in [5].TRRL expresses the capacity of a roundabout as a function of the leg and geometric features of the circulating flow in the circle, Qc, in front of the entry.The relevant entry capacity formula is shown in the following Eq.( 6) in a linear form. Where:   (12) In this formula roundabout geometric elements are used as input and the disturbing flow, Qd, is directly expressed by circulating flow, Qc.

Gap Acceptance Model
The guide by Austroads [16] is the basic design guide for roundabouts.Australian model is summarized on the basis of gap acceptance methodology in [2].Australian studies examined multilane roundabouts capacity for each entry lane those could differ in capacity.The lane with the higher capacity named dominant stream and other lanes called subdominant stream.General capacity formula of gap acceptance method is shown by Eq. (13).
Where qe is the entry capacity in veh/s, qc is the circulating stream volume in veh/s, f(t) is the density function for the distribution of gaps in the circulating stream and g(t) is the number of entering stream vehicles those can enter into the circulating stream in the time gap sized "t" [17].Australian entry capacity formula built in [18] is given by Eq. ( 14).

 
Where; Pamukkale Univ Muh Bilim Derg, 20 (6), [225][226][227][228][229][230][231]2014 Pamukkale Univ J Eng Sci, 20 (6) Qe is the capacity of the entry lane in veh/h, Qg is minimum capacity estimate using the gap acceptance method in veh/h, Qm is minimum capacity in veh/h, qc is total circulating flow rate flow in pcu/h, nm is minimum number of vehicles can enter the circulating stream under heavy flow conditions in veh/min, fod is origin destination adjustment factor, fqc is calibration parameter, pcd and pqd are proportion of the total roundabout circulating flow that originated from the dominant lane and proportion of queued vehicles on the dominant approaching lane respectively, nc is number of circulating flow lanes, c is minimum intra-bunch headway in circulating stream which is 2.0 s for nc=1 and 1.2s for nc=2 and λ is arrival headway distribution factor.Various definitions exist for .In [19] defined  is defined as decay constant as given by Eq. ( 18).

 
Different equations exist to define the proportion of free vehicles  .Eq. ( 19) in [20] is used to determine  value.
Where kd is traffic delay/bunching parameter.The value suggested for kd is 2.2 for roundabouts.fod equations according to circulating lane number are given in the Table 4. Table 4: fod relations according to circulating lane number.

Multi-lane Circulating Flow
In Case 0.04+0.00015qc0.04+0.00015qcqc <600 0.0007qc-0.29600 qc1200 0.00035qc-0.08 600 qc1800 55 qc>1200 55 qc>1800 Tf and Tc are follow-up headway and critical gap.Follow-up headways are calculated for dominant and subdominant lane with following Eq.( 21) and Eq. ( 22) in [21] respectively.Where, Di is inscribed circle diameter in m, ne is the number of entry lanes and rds is ratio of dominant to subdominant qd/qs flow rate.The critical gap is calculated for dominant and subdominant lane with following Eq.(22).
Where wL is the average entry lane width in meters.

Field Data
The data for the evaluation of HCM 2010 capacity model is obtained from Tanyel's [3] studies on Montro and Lozan roundabouts.Both intersections are located in Central İzmir.Geometric features of the Lozan and Montro roundabouts are given in Table 5.The schematic presentation of Lozan and Montro Roundabouts are given in the Figure 2a and 2b respectively.On Lozan Roundabout, Alsancak approach shown in Figure 2 with number 3, is observed.There are two entering and two exiting lanes on Alsancak approach split with a 7.00 m refuge and approach lane widths are 3.00 m.
On Montro Roundabout, Cumhuriyet approach shown in Figure 2b with number 5, is observed.There are two entering lanes on Cumhuriyet approach with 3.00 m width.Test data used in the evaluations are maintained from observations made by Tanyel [3].According to [22], the best way to determine the capacity of a roundabout is the direct measurement of the maximum incoming vehicle number from approaching lanes with observations.In order to obtain such kind of data there should be a constant queue of vehicles waiting on the approaching leg for 30 minutes long.Under these circumstances, data of 1 min and 5 min periods are adequate for capacity estimates [22].
Data collected from the observations of Lozan and Montro consist of 1 min periods those are 46 min and 45 min groups respectively.According to recordings made at mornings and evenings peak hours; circulatory flow rate in veh/h and veh/min, number of entering vehicles in veh/h and veh/min, circulatory roadway headways in sec, follow-up times in sec and critical gap headways in sec data are obtained.

Numerical Analysis
As previously mentioned, TRL method is the representative capacity analysis method for regression models, therefore it is chosen for comparison of HCM 2010 with a regression model.TRL entry capacity formula, Eq. ( 6) is used for Lozan and Montro Roundabouts.
Regression formula calculated according to geometric characteristics of each roundabout.Figure 3 and Figure 4 show observed field data with Qe, the results of regression analysis with Qecal and predicted results of HCM 2010 with QeHCM for Lozan and Montro roundabouts respectively.
A linear regression is done between Qe observed values and estimated values of regression analysis and HCM 2010 values.
The linear relationship and the coefficient of determination, 'r2' for the regression and the HCM methods are respectively given by equations 24 and 25.   6. Troutbeck's formula in Eq. ( 15) is used in this study for evaluating dominant and subdominant lane capacities and Eq. ( 19) for proportion of free vehicles for each data group.Predicted capacity values were determined by summation of dominant and subdominant lane capacities.Decay constants were calculated with Eq. ( 18) defined for roundabouts in Turkey in [19].
Gap acceptance method and HCM 2010 results for Lozan and Montro roundabouts are shown in the Figure 5 and Figure 6 respectively.
A linear regression is done between observed values and estimated values of gap acceptance analysis and HCM 2010.
The linear relationship and the coefficient of determination, 'r 2 ' for the gap acceptance and the HCM methods are respectively given by equations 26 and 27.As can be seen from the figures, HCM 2010 generally gives lower capacity estimates than gap acceptance analysis.In low circulating flow HCM 2010 gave more accurate results in comparison with gap acceptance.Under higher circulating flow conditions HCM 2010 model derived slightly under the observed conditions.
Besides HCM 2010 default values seem to give lower capacity estimates than gap acceptance and regression methods, it should not be forgotten that it is also possible to calibrate HCM formulation with Eq. ( 4) and Eq.(3).The potential impact of Tc and Tf in capacity estimate is examined by varying the two main parameters between minimum and maximum limits under different circulating flows (Qc).Circulating flow values are fictitious those range such 1 veh/h, 100 veh/h, 200 veh/h to 1600 veh/h with 100 veh/h intervals.Change of capacity estimates with parameters Tf and Tc are shown in the Figure 7a and Figure 7b respectively.
As can be seen from above figures, HCM 2010 calibrated formulation estimates higher capacity for entry if smaller critical gap and follow up values are accepted by drivers.

Conclusions
In this paper, data obtained from one approaching leg of two roundabouts in Izmir are studied in order to make comparison between HCM 2010 default values, regression model an gap acceptance model.
Gap acceptance and regression models generally resulted in higher values than HCM2010 default value formulation.Especially for high circulating volumes gap acceptance methodology is found to be more accurate than HCM2010 default value estimations and regression analysis.Lower capacity estimate of HCM2010 under high traffic volumes could be regenerated by using calibrated formulations.Results obtained are valid for sample roundabouts because of site specific characteristics.
HCM 2010 default value formulations are found to be more appropriate for lower circulating volumes.However UK model might be more applicable in relation to the range of geometric conditions those could be adjusted for studied roundabouts.Within the calibrated model of HCM 2010 it is possible to obtain specialized results for different site conditions using Tc and Tf values.
In order to obtain better correlation coefficients for studied models, reversal priority and gap forcing conditions should be considered during the evaluations.In this study the obtained data groups are limited.To achieve better results the number of examples should be increased and a detailed research should be done on the effect of driver behaviors for capacity estimation.

Table 3 :
A and B values for Multi-lane circulating stream[4

Figure 3 :
Figure 3: Comparison of capacity models for Lozan roundabout.

Figure 4 :
Figure 4: Comparison of capacity models for Montro roundabout.As can be seen from the figures, HCM 2010 generally gives lower capacity estimates than regression analysis.Especially in low circulating flow, in Lozan, HCM 2010 gave more accurate results in comparison with linear regression.Under higher circulating flow conditions, in Montro, HCM 2010 model derived slightly under the observed conditions where the scatter of the TRL model estimates define more appropriate Qe values.For the evaluation of capacity according to gap acceptance method, Troutbeck's Tc and Tf formulations for dominant and sub dominant lanes are used.Exiting flow effect on the capacity is neglected.Mean values of evaluated critical

Figure 5 :
Figure 5: Comparison of capacity models for Lozan Roundabout.

Figure 6 :
Figure 6: Comparison of capacity models for Montro Roundabout.

Figure 7 :
Figure 7: Change of capacity estimates with parameter a) Tf, b) Tc.

Table 1 :
Geometric parameters used by the regression models.

Table 6 :
Mean Tc and Tf values.