Impact of Inconsistent Behavior of Drivers on Estimation of Critical Gap at Multi-Lane Roundabouts

Abstract

Critical gap (CG) estimation, while taking into consideration inconsistent driver behavior resulting from heterogeneous traffic conditions, is a tedious task. Several methods dealing with CG estimation have been developed in the past but limited research has been done in this regard for developing countries and there is a lot of scope to explore this field considering varying traffic conditions on the roads. In this study, the maximum likelihood method (MLM), one of the most prominent methods of determining CG, has been compared with two other methods developed for traffic conditions prevailing in India. These methods use different techniques for calculating the CG, such as minimization of absolute differences of gaps given by Ahmad et al., and minimization of square root of standard deviation of actual gap value from the predicted CG as per the Indian Highway Capacity Manual (Indo-HCM). This paper discusses the estimation of CG for five different categories of vehicles using these methods to counter the heterogeneity of traffic. Data has been collected on two urban multi-lane roundabouts in India. SOLVER in MS Excel is used to optimize the functions defined in all three methods. The results reveal that the method suggested by Ahmad et al. gives the most consistent results which are close to actual value when driver behavior is inconsistent. The other two methods are also reasonably consistent, with the method given in Indo-HCM being slightly better than MLM. Further, two-way ANOVA was applied to check the consistency of results.

Keywords

critical gap roundabouts driver behaviour mixed traffic roundabout capacity

Roundabouts have served as a powerful infrastructural solution to many traffic problems arising when a particular type of intersection cannot be provided. These types of unsignalized intersections are beneficial as they are found to increase the connectivity, accessibility, and safety of all types of users. However, unlike signalized intersections, they do not provide any indication to the driver, and the responsibility of safely entering or leaving the intersection solely lies on the judgement of the driver. In such a scenario, drivers search for a safe opportunity or gap to access the intersection. This is technically termed as the gap acceptance behavior of drivers. The term “gap” signifies the time that elapses (in seconds) between the instance of the passing of the rear end of the leading vehicle and the front portion of the following vehicle through a common reference point. One of the most crucial traffic parameters used previously in the gap acceptance models is the “critical gap” (CG). It can be defined as the minimum possible gap that is accepted by the drivers in the traffic stream at a particular location. The design of any intersection is highly influenced by the value used for CG ( 1 ). Both the operational and safety perspectives need to be addressed when designing the intersection and, when the operational perspective is considered, the design capacity of the intersection should be such that it can accommodate the expected traffic while keeping traffic delays to a minimum value. Therefore, it is essential to estimate the capacity of the roundabout accurately. Whereas, when considering the safety perspective, the design should allow all the drivers to navigate the intersection safely ( 2 ).

CG is one of the criteria that is crucial for roundabout capacity estimation and, therefore, it is necessary to calculate the CG accurately. Even a minuscule deviation of CG value causes a notable difference in the capacity of the roundabout ( 3 ). This was confirmed by a study carried out by Vasconcelos et al. who reported that a capacity difference of up to 15% could be observed when the CG was changed by 0.5 s ( 4 ). However, CG cannot be estimated from direct measurements on the field and, therefore, determining the value of CG, especially for mixed traffic conditions that are generally encountered in advancing countries, has been a difficult task for the past few decades. This can be attributed to the poor lane changing behavior observed in such countries and limited priority being followed at roundabouts. This means that sometimes circulating traffic alters its headways, by slowing down, to permit vehicles at entry to proceed to the circulatory roadway ( 5 ). Estimation of CGs is very simple for homogenous traffic conditions as compared with heterogeneous conditions, as the various influencing parameters such as the size of the vehicle, its speed, and the following distances are kept at a constant value. On the contrary, in case of a heterogeneous mix, vehicles of varying types and sizes, with different operating characteristics and speeds, interact with each other on the road.

Additionally, as CG and follow-up times are highly influenced by the prevailing traffic conditions in a specific location, many implementing agencies generally face difficulties in estimation of these parameters at different locations and in different cities. Generally, vehicles are not supposed to overtake the leading vehicle while circulating at roundabouts. In the case of heterogeneous traffic conditions, as same road space is being shared by the variety of vehicles having different geometry and operational capability, sometimes aggressive drivers tend to overtake the leading vehicle even at roundabouts, thereby violating the concept of “following the leader.” Also, the priority rules are disobeyed very often. Better manoeuvrability and comparatively smaller size allow small-sized vehicles to use very small lags. There are many instances when no gaps are rejected under the conditions of free flow of traffic. These conditions necessitate accurate determination of CG to ensure safe design of roundabouts. Literature reports several methods that have been used for CG determination. However, these methods have been synthesized for developed countries where strict adherence to priority rules and homogenous traffic conditions are observed. The applicability of these methods on the traffic conditions dominating in still-advancing countries such as India cannot be ascertained.

This paper attempts to provide a detailed review of the various methods that have been used for estimation of CGs across varying traffic conditions all over the world. It also attempts to identify the CG estimation method that is best suited for developing countries experiencing mixed traffic conditions on their roads. The structure of the rest of the paper is that the next section provides a detailed review of the literature on gap estimation methods and their applicability across various conditions The section after that discusses the data collection and extraction methods to be used in the estimation of CGs. The penultimate section provides a detailed discussion of the analysis results for different methods along with their consistency check. The final section states the conclusions that have been drawn from this study concerning the suitability of CG estimation methods for traffic conditions prevailing in developing countries.

Literature Review

CG has been studied for a long time because it is a critical design parameter of road elements. The first step is developing an understanding about the concept of CG. Many researchers have studied CG in their research work and therefore given different definitions for the same. The first discussion on the theory of CG was carried out by Raff and Hart and they interpreted CG as “the size of gap for which the number of accepted gaps shorter than that value is equal to the number of rejected gaps that are longer than that value” ( 6 ). In the research that was carried out as an advancement of this work, Ashworth and Green became the first researchers to carry out gap measurements from the end of one transport unit to the front portion of the following transport unit ( 7 ). Adebisi came up with a new definition of gap in relation to major stream headway that is entirely usable by a vehicle that is waiting on a minor road ( 8 ). Gap has also been explained as the time period between two consecutive vehicles in the major road traffic ( 9 ). The Highway Capacity Manual (HCM) defined CG as “the minimum time interval in the circulating flow that allows intersection entry for one entry vehicle” ( 10 ). Another study by Polus et al. defines CG as a gap having an equal probability of being accepted or rejected ( 11 ). Thus, it can be inferred that many definitions for CG have been reported in the literature and have been used by researchers across the world in developing methods for the valuation of CG.

The last few decades have witnessed the synthesis of various methods for calculation of CGs for a particular type of vehicle across different parts of the world. These methods have been developed using traffic data for types of movement at two-way stop-controlled intersections and roundabouts. The most eminent methods as identified from the literature are Harder’s method, Ashworth’s method, Modified Raff’s method, maximum likelihood method (MLM), and Wu’s method ( 6 , 12 –15). The past decade has seen some advancement in the domain of CG estimation which used various techniques such as minimizing the sum of absolute differences of accepted gaps and root mean square (RMS) method ( 16 , 17 ). A detailed summary of the previously stated methods has been provided in Table 1.

Table 1.

Different Methods for the Estimation of Critical Gap (CG) ( 6 , 12 –18)

Method (Year)	Description	Mathematical visualization	Remarks
Harder’s method (1968)	• Based on probability of acceptance • The time scale is divided into constant duration intervals (Δt) having centre t_i • Observation of vehicle gaps provided by circulating vehicles to the vehicle entering the roundabout • These observations are used to calculate acceptance probability in a given interval and CG value	$P_{i} = \frac{a_{i}}{n_{i}}$ (2.1) $t_{c} = \sum_{i = 1}^{n} t_{i} * P_{i}$ (2.2)	n_i = quantum of gaps available for entering vehicle a_i = quantum of gaps accepted
Ashworth’s method (1970)	• Valuation of CG using the mean (μ_a) and standard deviation (σ_a)parameters of the gaps accepted by the drivers	$t_{c} = μ_{a} - p σ_{a}^{2}$ (2.3)	p = circulating traffic
Modified Raff method (1950)	• Based on graphical interpretation • CG is the indicated by the intersection of the graph for cumulative distribution function (CDF) of accepted gaps and reverse CDF of rejected gaps	The concept is shown in Figure 1	F_a(t) = CDF of accepted gaps F_r(t) = reverse CDF of rejected gaps CDF - Cumulative distribution function
Maximum likelihood method (MLM) (1992)	• Based on maximization of likelihood equation and consists of a series of steps • Identification of a set of maximum accepted and rejected gap for each driver (number of drivers = n) • Calculation of maximum likelihood for all drivers given by Equation 2.4 • Therefore, the logarithm of likelihood (L) is given by Equation 2.5 • Maximize Equation 2 corresponding to conditions in Equation 2.6 • Iterative solution of these equations gives values of μ and σ² • CG can be calculated using Equation 2.7	$Π_{i = 1}^{n} [F (y_{i}) - F (x_{i})]$ (2.4) $L = \sum_{i = 1}^{n} \ln [F (y_{i}) - F (x_{i})]$ (2.5) $\frac{\partial L}{\partial μ} = 0 and \frac{\partial L}{\partial σ^{2}} = 0$ (2.6) $t_{c} = e^{μ + 0.5 σ^{2}}$ (2.7)	y_i = ln (a_i); a_i = accepted gap for i^th vehicle entering the roundabout x _i = ln (r_i); r_i rejected gap for i^th vehicle entering the roundabout (0; in case of no rejection) σ² = variance of the logarithms of CGs as observed for individual drivers, I varies from 1 to n μ = mean of the logarithms of CGs as observed for individual drivers, i = 1 to n.
Wu’s method (2012)	• Based on probability equilibrium at a macroscopic level • Uses probability distribution functions (PDFs) of accepted gaps and rejected gaps • No assumption for a distribution type for CGs is required	$\begin{matrix} F_{tc} (t) = \frac{F_{a} (t)}{F_{a} (t) + {1 - F_{r} (t)}} \\ = 1 - \frac{{1 - F_{r} (t)}}{F_{a} (t) + {1 - F_{r} (t)}} \end{matrix}$ (2.8)	F_a(t) = PDF of the accepted gaps F_r(t) = PDF of the rejected gapsPDF - Probability distribution function
Bunker’s average central gap method (2014)	• The hypothesis used in this method is that the CG is the mid-point between the value of accepted and largest rejected gaps • It is calculated as the mean of all the largest rejected and accepted gaps	$\bar{t_{c}} = \frac{1}{2 n} \sum_{i = 1}^{n} (r_{i} + a_{i})$ (2.9)	r_i = largest rejected gaps by i^th entering vehicle (s) a _i = accepted gaps by the same vehicle (s)
Ahmad et al. ( 1 )	• Based on the assumption that the function (Fc(t)) of the CGs lies between the respective distribution functions (DFs) of rejected gaps (Fr(t)) and accepted gaps (Fa(t)) in a manner that the difference of these gaps takes a minimum value • The function for estimation of CG given by the authors is mentioned in the Equation 2.10 • This function was minimized and multiple iterations were done to estimate the CG (2.11)	f = {Abs (T_c−R_i) +Abs (A_i−T_c)} (2.10) $\min_{} [\sum_{i = 1}^{n} {A b s (T_{c} - R_{i}) + A b s (A_{i} - T_{c})}]$ (2.11)	A _i = gap accepted by the i^th entering vehicle (s) R _i = maximum gap rejected for the same vehicle (s) T_c = value of CG value (s)DFs - Distribution functions
Indian Highway Capacity Manual (Indo-HCM) ( 2 )	• Uses root mean square (RMS) method for estimation of CGs • RMS model uses information of accepted and rejected gaps for each driver • Average CG value is determined by minimizing the square root of mean squared deviation of rejected and accepted gap values from the expected value of CG • For mix traffic conditions, CG is calculated as given by equation	$\min_{} [\sum_{n = 1}^{n} \sqrt{\frac{{(A_{n} - T_{c})}^{2} + {(T_{c} - R_{n})}^{2}}{2}}]$ (2.12) $T_{c, mix} = \sum^{T_{c, j}} . P_{j}$ (2.13)	A _n = gap accepted by the n^th entering vehicle (s) R _n = maximum value of gap rejected by the n^th entering vehicle (s) T_c = CG value (s) T_c,j = CG for mode j P _j = proportion of mode j in the traffic stream

Figure 1.

Estimation of critical gap (CG) by Raff’s method ( 3 ).

Calculating CG purely based on inconsistent driver behavior is a difficult task ( 19 ). Developed countries have seen many studies based on the above discussed methods with the aim of examining their efficiency and estimation accuracy. One such study was carried out by Brilon et al., in which the authors carried out a comparison of Harder’s method, Ashworth’s method, and MLM in calculating the CG and concluded that the best and most reliable results were given by MLM ( 20 ). In a later study, Vasconcelos et al. inferred that Raff’s method, Wu’s method, and MLM are more reliable than other methods ( 21 ). In a comparison between Wu’s method and MLM, Troutbeck concluded that MLM had a slight edge over the former in relation to estimation accuracy ( 22 ).

The review of literature makes a clear indication that MLM has been suggested and adopted by researchers for CG estimation over the other methods because of its accuracy and reliability. However, in the condition where limited priority exists, adoption of this method also gives some unacceptable results. Some recent studies, such as those carried out by Ahmad et al. and as suggested in the Indian Highway Capacity Manual (Indo-HCM), claim to incorporate the limited priority condition in the valuation of CGs ( 16 , 17 ). However, the applicability of the above-discussed approaches under traffic conditions prevalent in developing nations such as India needs to be studied. Therefore, this paper provides a comparison of the three methods, that is, MLM, Ahmad et al., and Indo-HCM in the following sections and discusses the applicability of these methods on multi-lane roundabouts to identify the method that is most effective for the estimation of CGs ( 16 , 17 ). Table 2 shows the CG values proposed by various researchers at different locations.

Table 2.

Critical Gap (CG) Values as Reported in Literature ( 11 , 16 , 17 , 23 –28)

Researcher	Country	CG (s)
Troutbeck ( 23 )	Australia	1.4–4.9
Hagring et al. ( 24 )	Sweden	4.0–4.6
Polus et al. ( 11 )	Israel	4.0
Guo ( 25 )	China	2.65
Highway Capacity Manual 2010 ( 26 )	U.S.	4.11–5.19
Mensah et al. ( 27 )	U.S. (Maryland)	2.5–2.6
Romana ( 28 )	Poland	3.3–3.5
Ahmad et al. ( 16 )	India	1.50–2.55
Indian Highway Capacity Manual ( 17 )	India	1.61–2.01

Data Collection and Data Extraction

For this study, two four-legged multi-lane roundabouts were selected in the urban area of Panchkula city in North India. It was made sure that these sites were at least 500 m away from the adjacent intersections on both upstream and downstream sides. It was also ensured that the sites were clear from any bus stops, parking areas, or pedestrian interference. The inventory data, such as geometric features of roundabouts, were collected for both the sites by taking manual measurements as well as with the help of Google Earth software for greater precision, whereas traffic flow data was collected using a videographic technique by mounting a video camera on the roof of an adjoining building having a clear view of the roundabout. Data was obtained for a period of 6 hours including the peak periods for morning as well as evening. Indian roads witness several categories of vehicles traveling on them; therefore, to give a meaningful context to the analysis, vehicles having similar characteristics were put together in the same group. Therefore, this study has five categories of vehicles for which a total of 230 data sets were taken as shown in Table 3. The optimum number of data set recommended for estimation of CG for different categories of vehicles is 45 to 60, except for heavy vehicles (HVs) for which no such recommendation is made ( 16 ). Tables 4 and 5, respectively present the geometrical features of roundabouts and percentage composition of different vehicle types at both study locations.

Table 3.

Number of Data Sets for Each Vehicle Category

Vehicle category	Abbreviation	Number of data sets
Motorized two-wheeler	2W	50
Motorized three-wheeler	3W	50
Small cars	SC	50
Big cars/light commercial vehicles	BC/LCV	50
Heavy vehicles (bus/truck)	HV	30
Total		230

Table 4.

Geometric Features of Roundabouts

S. No.	Central island diameter (m)	Circulatory roadway width (m)	Entry width (m)	Exit width (m)	Weaving length (m)
RA₁	80	10.5	12	12	62.5
RA₂	51	10.5	10.5	10.5	46

Table 5.

Percentage Composition of Different Types of Vehicles

S. No.	Two-wheeler		Three-wheeler		Small car		Big car/light commercial vehicle		Heavy vehicle
S. No.	EF	CF	EF	CF	EF	CF	EF	CF	EF	CF
RA₁	46	43	11	12	24	25	16	17	3	3
RA₂	44	42	13	13	27	28	14	15	2	2

Note: CF = circulatory flow; EF = entry flow.

The extraction of desired information was done by playing video data on computer screen and thus the composition of traffic stream, and gaps accepted and rejected by a vehicle entering the roundabout were recorded. For extraction of accepted gap and rejected gap data, recorded videos were played at a speed of 25 frames per second. A sample set of rejected gap and accepted gap is shown frame by frame in Figures 2 and 3, respectively. Sample data for different vehicle types and the gaps accepted and rejected by them have been shown in Annexure: Table (i). The extracted data was then processed in MS Excel for further analysis.

Figure 2.

Entering vehicle (three-wheeler [3W]) rejected the gap between two-wheeler (2W) and 3W.Left = Frame 11992; Right = Frame 12022.

Figure 3.

Entering vehicle (three-wheeler [3W]) accepted the gap between 3W and two-wheeler (2W).Left = Frame 12046; Right = Frame 12099.

In Figure 2, gap between the two-wheeler (2W) at conflict line and the succeeding three-wheeler (3W) can be seen rejected by the entering 3W. In Figure 3, gap between the 3W at the conflict line and the succeeding 2W can be seen accepted by the entering 3W. The rejected gap will be calculated as the difference between the frames divided by the number of frames per second, that is, (12,022 – 11,992)/25 = 1.20 s. Similarly, the accepted gap in Figure 3 will be calculated as (12,099 – 12,046)/25 = 2.12 s.

Other driver behavior characteristics, such as entry speed and circulating speed at roundabouts, was checked for all five categories of vehicles. Speed data for both roundabouts was collected using a radar speed gun and are shown in Annexure: Table (vii). It can be observed that no significant difference was found between the speeds of different categories of vehicles at both the roundabouts. Therefore, because of small variation in speed of vehicles at both roundabouts, it was not suitable to consider speed as an influential parameter to estimate CG specifically at roundabouts.

Estimation of CG/Comparison of Methods

CG is calculated for the collected data for all five (namely, 2W, 3W, small car [SC], big car/light commercial vehicle [BC/LCV], and HV) categories of vehicles by the three above-mentioned methods, that is, MLM, Indo-HCM, and Ahmad et al. ( 16 ). It is observed that a similar value of CG for SC is estimated by MLM and Ahmad et al. All three methods estimated almost same value of CG for 3W, whereas different values of CGs are estimated for 2W, BC/LCV, and HV by all three methods. The estimated values are shown in Table 6 below.

Table 6.

Estimated Critical Gap Values (in seconds) for Different Categories of Vehicles

Method	Two-wheeler	Three-wheeler	Small car	Big car/light commercial vehicle	Heavy vehicle
Maximum likelihood method	1.62	1.98	2.06	2.21	2.61
Indian Highway Capacity Manual	1.58	1.97	2.01	2.18	2.58
Ahmad et al. ( 16 )	1.66	1.96	2.06	2.14	2.54

After estimating CG values for different vehicle types using all three methods, it was essential to determine the most efficient method for CG estimation. The acceptability of these methods to heterogeneous traffic conditions is judged by the method of percentage upsets. Upsets are defined as the values of accepted gaps and rejected gaps that fail to satisfy the criterion that all the rejected gaps should be less than the critical value and all the accepted gaps should be more than the critical value. To further understand the concept of upsets, let us take one example from the field data. Figure 4 shows the upsets for 2W, 8^th entry, in case of accepted gaps is 1.60 s. It is less than the CG value estimated by MLM and Ahmad et al. but more than the CG value estimated by the Indo-HCM method; thus, it is classified as upset by MLM and Ahmad et al., but not an upset by the Indo-HCM method ( 16 ). Similarly, upsets can be identified for other vehicle types, using Figures 5 to 8.

Figure 4.

Percentage upsets for two-wheelers (2W).

Figure 5.

Percentage upsets for three-wheelers (3W).

Figure 6.

Percentage upsets for small cars (SC).

Figure 7.

Percentage upsets for big cars/light commercial vehicles (BC/LCV).

Figure 8.

Percentage upsets for heavy vehicles (HV).

It has been observed that the method based on minimizing the sum of absolute differences given by Ahmad et al. ( 16 ) gives equal percentage of upsets in accepted gaps and rejected gaps data in three out of five categories (2W, BC/LCV and HV) of vehicles whereas the other two methods satisfy this criterion of equal percentage of upsets in accepted gaps and rejected gaps only in case of BC/LCV vehicle category (refer to Annexure: Tables ii to vi) Therefore, only Ahmad et al.’s method meets the expectations of the definition of CG that it has an equal probability of getting accepted or rejected ( 16 ). Apart from this, it also has the least number of percentage upsets in three out of five categories (3W, BC/LCV, and HV), whereas calculation based on the method provided in Indo-HCM, 2017, has the least number of percentage upsets only in the case of 2W, whereas in the case of SC, all three methods give an equal number of percentage upsets. As far as overall percentage of upsets are concerned (considering all categories of vehicles), the method based on minimizing the sum of absolute differences is still leading with least percentage of overall upsets at 22.17%, followed by Indo-HCM method and MLM with 23.04% and 25.65% overall upsets, respectively. Figures 4 to 8 shows the upsets for different categories of vehicles by the three methods.

Because of inconsistency in driving behavior, some drivers may not reject any gap available to them. It is evident in Figures 4 to 8 that this behavior is predominantly found in 2W because of their small size and better manoeuvrability; however, such a phenomenon is rare in the case of HV owing to their large size and limited manoeuvrability. In such situations, MLM can give some questionable results as logarithmic function of zero (no gap rejected) will become undefined. Therefore, the other two methods have slight edge over MLM as far as mixed traffic conditions prevail.

CG for the whole traffic stream can be calculated by adding the multiplication of each mode share with its estimated CG. The formula is written as:

T_{c} = \sum^{} t_{c, i} * p_{i}

where

T_c = CG for the whole traffic stream,

t_c,i = estimated CG for vehicle type i, and

p_i = proportion of vehicle type i in the traffic stream.

Table 7 shows the CG values estimated by different methods for the whole traffic stream.

Table 7.

Critical Gap (CG) for the Whole Traffic Stream

Method	CG for whole traffic stream (s)
Maximum likelihood method	1.86
Indian Highway Capacity Manual	1.83
Ahmad et al. ( 16 )	1.87

Two-Way ANOVA Analysis

The consistency in estimation of CGs using different methods, that is, MLM method, Indo-HCM method, Ahmad et al.’s method, has been checked by conducting two-way ANOVA analysis at 95% confidence level. The null hypothesis states that H_o: there is no significant difference between the values of CG obtained from the three methods. The results for this analysis have been shown in Table 8. It shows that the F value (1.53) for rows (different methods) is less than F-critical (4.45) and the P-value (0.27) is greater than 0.05. Therefore, based on this result, we fail to reject the null hypothesis at 95% confidence level.

Table 8.

Outcomes of Two-Way Analysis of Variance (ANOVA) Analysis

Summary	Count	Sum	Average	Variance
Maximum likelihood method	5	10.48	2.096	0.12963
Indian Highway Capacity Manual	5	10.32	2.064	0.13143
Ahmad et al.	5	10.36	2.072	0.10152
Two-wheeler	3	4.86	1.62	0.0016
Three-wheeler	3	5.91	1.97	0.0001
Small car	3	6.13	2.043333	0.000833
Big car/light commercial vehicle	3	6.53	2.176667	0.001233
Heavy vehicle	3	7.73	2.576667	0.001233
ANOVA
Source of variation	SS	df	MS	F	P-value	F crit
Rows	0.002773	2	0.001387	1.535055	0.272742	4.45897
Columns	1.443093	4	0.360773	399.3801	3.07E-09	3.837853
Error	0.007227	8	0.000903	na	na	na
Total	1.453093	14	na	na	na	na

Note: na = not applicable.

Conclusions

It can be concluded from the literature that one of the most crucial factors in estimating the capacity of roundabouts is the critical gap. A small error in the calculation of CG can lead to a significant error while estimating the capacity of a roundabout, especially in case of heterogeneous traffic flow conditions. The results reveal that the method of minimizing the sum of absolute values of differences given by Ahmad et al. is the most consistent and gives results similar to the real value when driver behavior is inconsistent. Even though this method may be considered as the most consistent, the other two methods are also reasonably consistent, with the method based on minimization of square root of the mean squared deviation of rejected gaps and accepted gaps as per Indo-HCM predicted value slightly better than MLM. Both these methods somewhat underestimated the CG values for 2W but overestimated the CG values, to some degree, in the case of BC/LCV and HV. MLM can give better results when there is consistency in the behavior of different drivers. These results have been confirmed by conducting two-way ANOVA analysis on the CG values obtained from the three methods. The study also shows the importance of calculation of CG for each mode separately under heterogeneous traffic flow conditions, as it can be observed that the CGs when valuated for whole traffic stream are almost similar regardless of the methodology used, which can be misleading.

The study not only predicted the best-suited approach for CG valuation under heterogeneous traffic conditions but also brings out the limitations that need to be curbed. It can be seen that even the most consistent method has a significant amount of percentage of upsets that cannot be ignored. Although the validity check indicates no statistically significant difference among the methods used, a small error in the calculation of CG can lead to a significant error while estimating the capacity of a roundabout, especially in case of heterogeneous traffic flow conditions. So, there is a need to develop a robust methodology for CG valuation taking care of the inconsistencies in driver behavior such that the percentage of upsets is minimized. Furthermore, because CGs are traffic and location specific, implementing agencies may find it challenging to forecast them at different sites and in different cities. Therefore, a comprehensive and simpler technique is required which can be used by traffic engineers and planners.

Supplemental Material

sj-docx-1-trr-10.1177_03611981231152467 – Supplemental material for Impact of Inconsistent Behavior of Drivers on Estimation of Critical Gap at Multi-Lane Roundabouts

Supplemental material, sj-docx-1-trr-10.1177_03611981231152467 for Impact of Inconsistent Behavior of Drivers on Estimation of Critical Gap at Multi-Lane Roundabouts by Chirag Bhasin and Pardeep Kumar in Transportation Research Record

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: C. Bhasin, P. Kumar; data collection: C. Bhasin; analysis and interpretation of results: C. Bhasin, P. Kumar; draft manuscript preparation: C. Bhasin, P. Kumar. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Supplemental Material

Supplemental material for this article is available online.

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