Evaluation of the Intersection Sight Distance at Stop-Controlled Intersections in a Mixed Vehicle Environment

Abstract

The introduction of autonomous vehicles (AVs) on roadways will result in a mixed vehicle environment consisting of these vehicles and manual vehicles (MVs). This vehicular environment will impact intersection sight distances (ISDs) due to differences in the driving behaviors of AVs and MVs. Currently, ISD design values for stop-controlled intersections are based on AASHTO’s guidelines, which account only for human driver behaviors. However, with AVs in the traffic stream, it is important to assess whether the existing MV-based ISDs are compliant when an AV is present at an intersecting roadway. Hence, this study utilizes the Monte Carlo Simulation method to compute the PNC of various object locations on the major and minor roadways for possible vehicle interaction types in a mixed vehicle environment at a stop-controlled intersection. Scenarios generated considered these variables and the major roadway speed limits and sight distance triangles (SDTs). ISD non-compliance was determined by examining the PNC metric, which occurred when the demand exceeded the supply. The results indicated that when AV–MV interaction was present at the intersection, the MV-based ISD design was non-compliant. However, it is possible to correct this non-compliance issue by reducing the AV speed limit.

1. Introduction

As autonomous vehicles (AVs) are gradually deployed on roadways, it is expected that these vehicle types will share the roadway with the conventional driver-operated manual vehicles (MVs). As they share the roadway, these vehicle types will interact with each other while performing basic driving tasks, such as lane-changing, car-following, crossing, merging, and turning at intersections. Currently, intersections are the most critical locations due to the complex nature of the movement of vehicles and their interaction with the different roadway users [1]. Intersections are formed where a major and minor roadway joins or crosses, and they do not usually have more than four legs. At-grade intersections are considered the most complicated element of the highway system, requiring various design criteria and control strategies to ensure safe and efficient vehicle movement. These control strategies include all-way stop control, signal control, yield control, and two-way stop control on the minor roadway [2]. Intersections with stop control on the minor roadway are called “stop-controlled intersections”. At these facilities, drivers along the major road have priority for movement over those on the minor road. Several geometric design considerations are required for this type of intersection. One critical design consideration is intersection sight distance (ISD). ISD is essential for all roadway users on intersection approaches so that they have enough distance and time to react appropriately when executing vehicular movements (crossing and turning) to ensure safety. The most widely used guideline on ISD criteria for stop-controlled intersections in North America is “A Policy on Geometric Design of Highways and Streets by the American Association of Highway and State Transportation Officials (AASHTO)” [3]. In this book, ISD should be considered in situations where a minor road vehicle is departing an intersection from a stopped position. ISD lengths and other distances form an area known as the sight distance triangle (SDT). SDTs are essential to ensure drivers have an unobstructed view of the major roadway when crossing or turning from a stopped position on a minor roadway. The concept behind SDT is to ensure that the triangular area formed by the vehicle stopped at the intersection and sight distance points along the major roadway must be clear to allow the driver on the minor road to see potential conflicting vehicles before departing from a stopped position [3].

Currently, the ISD guidelines in the American Association of Highway and Transportation Officials (AASHTO) Greenbook [3] are designed to accommodate MVs only. The models developed for ISDs are based only on human-driven vehicles. However, the introduction of AVs into the vehicular fleet may affect these models due to their technological capabilities and the vehicle-to-vehicle interactions between these types of vehicles and MVs. Also, this guideline recommends deterministic ISD models, which are based on driving behaviors and the speed of vehicles. Hence, the true nature of these parameters where variations exist is not represented. Several studies have explored variations in driver behavior and road and vehicle characteristics using probabilistic analysis [4,5,6,7,8].

Previous studies utilized reliability analysis techniques to evaluate sight distances at signalized and unsignalized intersections. Easa [6] utilized the first-order-second-moment (FOSM) method of reliability analysis to evaluate AASHTO’s deterministic design of unsignalized intersections. This study assumed that the function of several variables is normally distributed. The results of the sensitivity analysis conducted on the design variables indicated that vehicle speed, coefficient of friction, and maximum speed in a selected gear are highly sensitive compared to perception-reaction time and vehicle length. A range of design values and associated reliability levels were presented to provide designers with flexibility when making decisions. This reliability method was also used by Hussain and Easa [7] and Easa et al. [8] to evaluate ISD designs for left-turning vehicles at signalized intersections and roundabouts, respectively. Similarly, the study by Hussain and Easa [7] presented reliability levels for current deterministic AASHTO’s ISD design values for left-turning vehicles at signalized intersections. The probability of non-compliance (PNC) was based on the offset value between the medians of left-turn and opposing left-turn vehicles at 90° signalized intersections where left-turning movement is permitted. The major roadway was a four-lane roadway intersecting with a four-lane or two-lane minor roadway. Easa et al. [8] assessed the required ISD for the entry vehicle on the left and the vehicle on the circulatory roadway on a roundabout using reliability analysis. The probability distributions of several random variables were assumed to be normally distributed. The FOSM method of reliability analysis was also used by Easa and Hussain [5] to assess the ISD for stop-controlled intersections. The developed model could be applied to any number of lanes on the minor and major roadways with or without a median. The results indicated that the AASHTO’s method provides a high level of reliability when the PNC is less than 1%. Also, the study indicated that the obstruction clearance is sensitive to vehicle speed, the distance between the driver’s eye and the vehicle front, and gap time. Osama et al. [4] used the First-Order Reliability Method (FORM) to compute the PNC of sight distance provided for permitted left-turn movements when an opposing left-turn vehicle is present at an intersection. The FOSM method of reliability was not utilized due to several shortcomings, such as the assumption of normal distribution of the input ISD design parameters. In FORM, variables are presented using their original distributions, and each design input parameter can be examined using sensitivity analysis. The results indicated that the PNC was more sensitive to the time gap compared to the vehicle speed. Sarran and Hassan [9] evaluated ISD design values for a mixed-traffic environment containing MVs and AVs at uncontrolled intersections. In this study, Monte Carlo Simulation (MCS) was used to estimate the PNC for various vehicle interaction types in a mixed-traffic environment. The vehicle interaction types were defined based on the type of vehicle (AV or MV) on the minor and major roadways. In these studies, it is evident that reliability analysis can be used to assess ISDs for signalized and un-signalized intersections. The reliability models developed were mostly based on MVs, except for the study by Sarran and Hassan [9], which considered a mixed-traffic environment containing AVs. However, this study only investigated uncontrolled intersections. Therefore, ISD needs to be controlled for stop-controlled intersections in a mixed-traffic environment.

This study attempts to fill the research gap by using the MCS method of reliability analysis to evaluate the ISD at stop-controlled intersections. According to AASHTO, a four-legged design is the most common intersection configuration. Additionally, it was stated that roadways at a stop-controlled intersection should cross at −90°. Hence, a four-legged, right-angled intersection is considered. The intersecting roadways (major and minor) are designed to be two-laned, undivided, zero-graded, and median-free since this is the most prevalent design due to moderate traffic conditions in urban or suburban areas. The lane width and position of the stop bar on the minor roadway are fixed values and are assumed based on the literature. The vehicle types considered are AV and MV passenger cars. According to Sarran and Hassan [9], Connected Autonomous Vehicles (CAVs) were not studied since these vehicles do not require ISD analysis due to their ability to detect each other by communicating with one another. However, should a CAV interact with a vehicle without connectivity (AVs), both vehicles require a clear line of sight for detection at an intersection.

In the near future, it is expected that AVs will be added to the existing vehicular fleet on roadways. Considering the possibility of a mixed-traffic environment, this research will offer many benefits to practitioners. This study offers guidance to practitioners on whether existing ISDs conform to a mixed vehicle environment containing AVs and MVs. Currently, AASHTO guidelines are used to design ISD for stop-controlled intersections. All of these designs are based on MV-only driving behaviors. However, with AVs being gradually introduced into the traffic stream, it is expected that the interaction at these intersections will involve AVs and MVs. Hence, providing a method of assessing whether existing MV ISDs are compliant when AVs are present on an intersecting roadway is important since these vehicles will have different driving behaviors due to their robotic nature. This research will provide practitioners with the ability to determine if an existing intersection is compliant with the sight distance requirement for AVs, should an AV be present on an approach intersecting leg. This research also provides recommendations for adjustments in the AV driving behavior or the posted speed limit if the ISD is found to be non-compliant. This study can also be used by researchers as a base case study when evaluating ISDs for other vehicle types (busses, etc.) or road users and different intersection characteristics (number of lanes, etc.).

2. Methods

This study examined the impact a mixed vehicular environment consisting of MVs and AVs would have on ISD at stop-controlled intersections. AASHTO’s [3] SDT models were used to evaluate sight distances at this type of intersection. This model required data on the characteristics of the intersection and vehicle interaction types based on the vehicular fleet. The models associated with SDT leg lengths were defined, and their input parameters and probability distributions were gathered. MCS was then used to provide a surrogate measure of safety for the intersection at various AV traffic shares. The following subsections provide a detailed description of each stage of the method used to determine the compliance of existing ISD in a mixed vehicle environment.

2.1. Vehicle Interactions

Sarran and Hassan [9] identified the interactions emanating from a mixed traffic environment comprising MVs and AVs at intersections. These interactions accounted for both vehicle types on the two intersecting roadways (i.e., major and minor) of an intersection. The major roadway gives priority to the traffic traveling along it, while the minor roadway controls the traffic by a stop sign, effectively requiring vehicles to stop completely before entering the major roadway. The interactions include the following:

• MV (major road)–MV (minor road) [MV–MV].
• MV (major road)–AV (minor road) [MV–AV].
• AV (major road)–MV (minor road) [AV–MV].
• AV (major road)–AV (minor road) [AV–AV].

2.2. Sight Distance

The sight distance at stop-controlled intersections requires analyzing a pair of approach sight triangles for left-turning and crossing maneuvers since vehicles can approach the intersection from the left or right along the major roadway. For right-turning movements, only one SDT is considered. Figure 1, Figure 2, Figure 3, Figure 4 and Figure 5 illustrate the sight triangles applicable to a stop-controlled intersection. An object representing potential sight obstruction is located at distances $m$ and $n$ from the near edges of the major and minor roads, respectively. Based on the geometry in Figure 1, Figure 2, Figure 3, Figure 4 and Figure 5, and assuming both roads have the same lane width, the distances $a$ and $b$ from the sight obstruction to the centerlines of the major and minor are defined. Length $B$ represents the edge of the sight triangle on the minor road, and length $A$ denotes the edge on the major road. ISD at a stop-controlled intersection is affiliated with length $A$, where the demand and supply ISDs are referred to as $A_D$ and $A_S$, respectively. Lengths $A_D$, $B$, $a$ and $b$ are defined for the various vehicle interaction types at a stop-controlled intersection; see Equations (1)–(32) in Table 1. Length $A_S$ is defined in Section 2.2.2.

Table 1. ISD Equations for stop-controlled intersections.

Interaction Type	LHS Sight Triangle	Equation	RHS Sight Triangle	Equation
MV–MV	$$a=m+l_w+x+y$$ (1)		$$a=m+l_w-x-y$$ (2)
	$$b=n+l_w-x-w_d$$ (3)		$$b=n+l_w+x$$ (4)
	$$B=z+s+l_w-x-w_d$$ (5)		$$B=z+s+l_w+x$$ (6)
	$$A_D=S_m+l_w+x+y$$ (7)		$$A_D=S_m+l_w-x-y$$ (8)
MV–AV	$$a=m+{1.5l}_w$$ (9)		$$a=m+{0.5l}_w$$ (10)
	$$b=n+l_w-x-w_d$$ (11)		$$b=n+l_w+x$$ (12)
	$$B=r+s+l_w-x-w_d$$ (13)		$$B=r+s+l_w+x$$ (14)
	$$A_D=S_m+{1.5l}_w$$ (15)		$$A_D=S_m+{0.5l}_w$$ (16)
AV–MV	$$a=m+l_w+x+y$$ (17)		$$a=m+l_w-x-y$$ (18)
	$$b=n+{0.5l}_w-0.5w_a$$ (19)		$$b=n+{1.5l}_w-0.5w_a$$ (20)
	$$B=z+{0.5l}_w-0.5w_a$$ (21)		$$B=z+s+1.5l_w-0.5w_a$$ (22)
	$$A_D=S_m+l_w+x+y$$ (23)		$$A_D=S_m+l_w-x-y$$ (24)
AV–AV	$$a=m+{1.5l}_w$$ (25)		$$a=m+{0.5l}_w$$ (26)
	$$b=n+{0.5l}_w-0.5w_a$$ (27)		$$b=n+{1.5l}_w-0.5w_a$$ (28)
	$$B=r+s+{0.5l}_w-0.5w_a$$ (29)		$$B=r+s+{1.5l}_w-0.5w_a$$ (30)
	$$A_D=S_m+{1.5l}_w$$ (31)		$$A_D=S_m+{0.5l}_w$$ (32)

$A_D$ = demand length of SDT leg along a major road; $B$ = length of SDT leg along a minor road; $a$ = distance from the object to SDT leg along the minor road; $b$ = distance from the object to SDT leg along the major road; $S_m$ = required ISD for the vehicle; $m$ = distance from the object to the outer edge of the minor road; $n$ = distance from the object to the outer edge of the major road; $z$ = distance from vehicle’s front bumper to driver’s eye; $r$ = distance from the vehicle’s front bumper to the vehicle’s detection device; $s$ = distance from stop bar to edge of major road; $l_w$ = lane width; $x$ = lateral distance from the left edge of the lane to the left side of the vehicle; $y$ = lateral distance from the left side of the vehicle to the driver’s eye; $w_d$ = MV width; and $w_a$ = AV width. All lengths are meters (m).

Table 1. ISD Equations for stop-controlled intersections.

Interaction Type	LHS Sight Triangle	Equation	RHS Sight Triangle	Equation
MV–MV	$$a=m+l_w+x+y$$ (1)		$$a=m+l_w-x-y$$ (2)
	$$b=n+l_w-x-w_d$$ (3)		$$b=n+l_w+x$$ (4)
	$$B=z+s+l_w-x-w_d$$ (5)		$$B=z+s+l_w+x$$ (6)
	$$A_D=S_m+l_w+x+y$$ (7)		$$A_D=S_m+l_w-x-y$$ (8)
MV–AV	$$a=m+{1.5l}_w$$ (9)		$$a=m+{0.5l}_w$$ (10)
	$$b=n+l_w-x-w_d$$ (11)		$$b=n+l_w+x$$ (12)
	$$B=r+s+l_w-x-w_d$$ (13)		$$B=r+s+l_w+x$$ (14)
	$$A_D=S_m+{1.5l}_w$$ (15)		$$A_D=S_m+{0.5l}_w$$ (16)
AV–MV	$$a=m+l_w+x+y$$ (17)		$$a=m+l_w-x-y$$ (18)
	$$b=n+{0.5l}_w-0.5w_a$$ (19)		$$b=n+{1.5l}_w-0.5w_a$$ (20)
	$$B=z+{0.5l}_w-0.5w_a$$ (21)		$$B=z+s+1.5l_w-0.5w_a$$ (22)
	$$A_D=S_m+l_w+x+y$$ (23)		$$A_D=S_m+l_w-x-y$$ (24)
AV–AV	$$a=m+{1.5l}_w$$ (25)		$$a=m+{0.5l}_w$$ (26)
	$$b=n+{0.5l}_w-0.5w_a$$ (27)		$$b=n+{1.5l}_w-0.5w_a$$ (28)
	$$B=r+s+{0.5l}_w-0.5w_a$$ (29)		$$B=r+s+{1.5l}_w-0.5w_a$$ (30)
	$$A_D=S_m+{1.5l}_w$$ (31)		$$A_D=S_m+{0.5l}_w$$ (32)

$A_D$ = demand length of SDT leg along a major road; $B$ = length of SDT leg along a minor road; $a$ = distance from the object to SDT leg along the minor road; $b$ = distance from the object to SDT leg along the major road; $S_m$ = required ISD for the vehicle; $m$ = distance from the object to the outer edge of the minor road; $n$ = distance from the object to the outer edge of the major road; $z$ = distance from vehicle’s front bumper to driver’s eye; $r$ = distance from the vehicle’s front bumper to the vehicle’s detection device; $s$ = distance from stop bar to edge of major road; $l_w$ = lane width; $x$ = lateral distance from the left edge of the lane to the left side of the vehicle; $y$ = lateral distance from the left side of the vehicle to the driver’s eye; $w_d$ = MV width; and $w_a$ = AV width. All lengths are meters (m).

2.2.1. Demand Models

As stated previously, the ISD at a stop-controlled intersection is based on the length of the SDT along the major road, $A$. The demand for ISD, $A_D$, defers depending on the maneuver type, crossing or turning, and the SDT, right-hand side (RHS), and left-hand side (LHS). Differences are in the parameter values considered for each maneuver and associated SDT. Equations (7), (15), (23), (31), (8), (16), (24) and (32) show the various demand models for LHS and RHS SDTs associated with different vehicle interaction types.

According to AASHTO [3], vehicles on the major road of a stop-controlled intersection have priority for traffic movement. Therefore, no stopping action is required. Sight distance along this major roadway depends on the speed of the traveling vehicle and a critical time gap associated with the stopped vehicle on the minor road. A time gap is the time accepted by a driver or vehicle on the minor road of an intersection to cross safely or turn into a traffic stream on the major roadway. Considering a mixed traffic environment or MVs and AVs, the formula for ISD varies according to the interaction type, see Equations (33)–(36).

$$\mathrm{MV}–\mathrm{MV}: S_m=v_{md}{t}_{gd}$$

(33)

$$\mathrm{MV}–\mathrm{AV}: S_m=v_{md}{t}_{ga}$$

(34)

$$\mathrm{AV}–\mathrm{M}: S_m=v_{ma}{t}_{gd}$$

(35)

$$\mathrm{AV}–\mathrm{AV}: S_m=v_{ma}{t}_{ga}$$

(36)

where $S_m$ = sight distance along major roadway (m), $v_{md}$ = MV speed on major roadway (m/s), $v_{ma}$ = AV speed on major roadway (m/s), $t_{gd}$ = time gap associated with the minor road MV (s) and $t_{ga}$ = time gap associated with the minor road AV (s).

• Crossing Manoeuvre

According to Harwood et al. [10], the time gaps for crossing vehicles on the minor roadway of a stop-controlled intersection are computed as the total time required by the vehicle to travel from the start of the perception (detection) and reaction process to the point at which it completely crosses the major roadway. The time gap to completely cross the major road from the stopped position for both MVs and AVs, $t_{g,DV}$ and $t_{g,AV}$, are shown in Equations (37) and (38), respectively. These equations assume that human drivers and AVs linearly accelerate when moving from the stopped position is initiated.

$$t_{gd}=t_{pr}+{\left[{\displaystyle \frac{2\left(s+q{l}_w+l_{vd}\right)}{a_d}}\right]}^{{\displaystyle \frac{1}{2}}}$$

(37)

where $t_{gd}$ = time gap associated with the minor road MV (s), $t_{pr}$ = perception–reaction time for the minor road AV to initiate a maneuver (s), $s$ = distance from the stop bar to the edge of a major road (m), $q$ = quantity of lanes to cross, $l_w$ = lane width (m), $l_{vd}$ = length of minor road MV vehicle (m), and $a_d$ = MV acceleration from standstill (m/s²).

$$t_{ga}=t_{dr}+{\left[{\displaystyle \frac{2\left(s+q{l}_w+l_{va}\right)}{a_a}}\right]}^{{\displaystyle \frac{1}{2}}}$$

(38)

where $t_{ga}$ = time gap associated with the minor road AV (s), $t_{dr}$ = detection–reaction time for the minor road AV to initiate a maneuver (s), $s$ = distance from the stop bar to the edge of a major road (m), $q$ = quantity of lanes crossed, $l_w$ = lane width (m), $l_{va}$ = length of minor road AV vehicle (m), and $a_a$ = passenger comfortable acceleration rate (m/s²).

• Left-turning and Right-turning Manoeuvres

In this study, differences exist in the models used to represent left-turning and right-turning vehicles at stop-controlled intersections. The accepted time gap for MVs, $t_{gd}$, turning left at a stop-controlled intersection from a minor roadway was assumed to adopt the value presented in the study by Li et al. [11]. For AVs, the study by Sarran and Hassan [9] was used to determine the input parameter values for the time gap, $t_{ga}$, model, which was developed in this study, see Equation (40).

For Equations (39) and (40), the time gap is the summation of the perception (or detection) reaction time and the travel time taken from the stop bar on the minor roadway to the point at which the vehicle safely completes the turning maneuver, fully positioning itself on the major roadway. Equation (40) assumes that the AV will travel a path of a circular arc that is a product of a turning radius, $R$.

$$t_{gd}=t_{pr}+{\left({\displaystyle \frac{\pi R}{a_d}}\right)}^{{\displaystyle \frac{1}{2}}}$$

(39)

where $t_{gd}$ = time gap associated with the minor road MV (s), $t_{pr}$ = perception–reaction time for the minor road AV to initiate a maneuver (s), and $a_d$ = MV acceleration from a standstill (m/s²).

$$t_{ga}=t_{dr}+{\left({\displaystyle \frac{\pi R}{a_a}}\right)}^{{\displaystyle \frac{1}{2}}}$$

(40)

where $t_{ga}$ = time gap associated with the minor road AV (s), $t_{dr}$ = detection–reaction time for the minor road AV to initiate a maneuver (s), and $a_a$ = passenger comfortable acceleration rate (m/s²).

Models applicable to RHS and LHS SDTs of left-turning maneuvers and right-turning maneuvers, respectively, were developed to determine the time gap associated with AVs when turning from the minor road. These models were based on a time gap related to an AV accelerating from the stopped position on the minor road and reaching its travel speed on the major road while maintaining a safe following distance from a lagging major road vehicle [12]. These models are shown in Equations (41)–(48).

$$t_{g,AV}=t_{dr}+\left({\displaystyle \frac{E+F-R-G}{v_m}}\right)$$

(41)

where $t_{g_{AV}}$ = time gap for stopped AV on non-priority road to completely cross the intersection (s), $t_{dr}$ = reaction time (s), $E$ = distance traveled by the vehicle on the major road during the time it takes for the minor road vehicle to reach its desired speed (m), $F$ = safe distance headway between major and minor road vehicles (m), $R$ = projected horizontal distance of minor road vehicle turning distance (m), $G$ = the distance along the major road required for the turned vehicle to reach its desired speed (m), and $v_m$ = speed of vehicle on the major road (km/h).

Equation (41) parameters $E$, $F$, $R,$ and $G$ relate to various components of the traffic environment at stop-controlled intersections, such as acceleration and headway distance between following vehicles. The projected horizontal distance of minor road AV turning distance, $R$, is calculated using Equation (42). This equation is based on the AV completing the turning movement and positioning itself in the center of a major roadway lane. This parameter is the radius of the turning movement, which is assumed to follow a circular path. The radius of the turning movement differs for the RHS and LHS SDTs due to the number of traveled lanes involved in the turning maneuver. For instance, only the immediate travel lane is considered when a vehicle is turning right from the minor roadway to the major roadway. However, a vehicle will need to consider additional lanes when turning left.

$$R=s+c{l}_w-0.5l_w$$

(42)

where $R$ = projected horizontal distance of minor road vehicle turning distance or turning radius (m), $s$ = distance from stop bar to edge of major road (m), $c$ = number of lanes involved in turning movement, and $l_w$ = lane width (m).

Previous studies have indicated that human drivers at intersections do not constantly accelerate their vehicles. Rather, the acceleration follows a pattern of linear decrease. However, given the robotic nature of AVs, the acceleration behavior of these vehicles is assumed to have very little variability compared to human-driven vehicles [9]. Parameter $E$ in Equation (41) varied depending on the interaction types involving an AV on the minor roadway. This consideration resulted in two models, Equations (43) and (44). The time parameter ($t_{m,AV}$) in these equations were found using Equation (45).

$$\mathrm{MV}–\mathrm{AV}: E={\displaystyle \frac{\left(v_{md}^2-v_{ma}^2\right)t_{ma}}{2\left(v_{md}-v_{ma}\right)}}$$

(43)

$$\mathrm{AV}–\mathrm{AV}: E=v_{ma}{t}_{ma}$$

(44)

$$t_{ma}={\left({\displaystyle \frac{\pi R}{a_a}}\right)}^{{\displaystyle \frac{1}{2}}}+{\displaystyle \frac{{v_{ma}-\left(\pi a_{a}R\right)}^{\frac{1}{2}}}{a_a}}$$

(45)

where $E$ = distance traveled by the vehicle on the major road during the time it takes for the minor road vehicle to reach its desired speed (m), $v_{md}$ = MV speed on the major road (m/s), $v_{ma}$ = AV speed on the major road (m/s), $t_{ma}$ = time taken for minor road AV to travel from a stopped position to the speed of the major road (s), $R$ = projected horizontal distance of minor road vehicle turning distance or turning radius (m), and $a_a$ = passenger comfortable acceleration rate (m/s²).

Time headways for following MVs and AVs may differ due to the differences in driving behavior. Hence, Equations (46) and (47) were formulated to represent the behaviors of a following AV and MV.

$$Following MV: F=v_{md}{t}_{hd}$$

(46)

$$Following AV: F=v_{ma}{t}_{ha}$$

(47)

where $F$ = safe distance headway between major and minor road vehicles (m), $v_{md}$ = MV speed on the major road (m/s), $v_{ma}$ = MV speed on the major road (m/s), $t_{hd}$ = time headway between following MV and leading AV (s), and $t_{ha}$ = time headway between following AV and leading MV (s).

The distance along the major roadway required for the turned vehicle to reach its desired speed, $G$, is calculated using Equation (48).

$$G=\left({\displaystyle \frac{v_{ma}^2-\left(\pi a_{a}R\right)}{{2a}_a}}\right)$$

(48)

where $G$ = the distance along the major road required for the turned vehicle to reach its desired speed (m), $v_{ma}$ = AV speed on the major road (km/h), $R$ = projected horizontal distance of minor road vehicle turning distance or turning radius (m), and $a_a$ = passenger comfortable acceleration rate (m/s²).

2.2.2. Supply Sight Distance Models

The supply sight distance is the available distance for completing a right turn, a left turn, or a crossing maneuver [5]. Based on the length of the SDT along the major roadway, $A$, as shown in Figure 1, Figure 2, Figure 3, Figure 4 and Figure 5, previously referred to as $A_S$ (supply ISD), is geometrically derived from the principle of similar triangles utilizing the lengths $B$, $a$ and $b$. In similar triangles, the ratios of corresponding sides are proportional to each other, and the corresponding angles are equal. Equation (49) shows the geometric relationship of the mentioned parameters.

$$A_S={\displaystyle \frac{B\times a}{b}}$$

(49)

where $A_S$ = supply length of SDT leg along major road (m), $B$ = length of SDT leg along minor road (m), $a$ = distance from the object to SDT leg along minor road, and $b$ = distance from the object to SDT leg along major road.

2.3. Probabilistic Assessment

In transportation engineering, the probability of non-compliance (PNC) is used as a measure of the system demand exceeding the system supply [13]. This measure is obtained through a probabilistic evaluation of the system. In this study, demand and supply models were used to define a safety margin ($D$). Followed by defining the distribution of parameters of the safety margin and the other statistical parameters. The PNC for interactions relative to object locations was determined for each interaction type using the MCS technique. The PNC for the AV-related interactions was then examined against the PNC of the MV–MV interaction based on AASHTO [3] design values.

2.3.1. Safety Margin

As previously stated, the demand and supply functions define Safety Margins. According to Singh et al. [14], the safety margin is the difference between the two functions. A system failure occurs when there is a negative value for the safety margin, i.e., the system supply is less than the system demand. Since $A_D$ and $A_S$ represent the demand and supply of the intersection, the safety margin, $D$, was defined accordingly, see Equation (50).

$$D=A_S-A_D$$

(50)

where $D$ = safety margin, $A_S$ = supply length of SDT leg along major road (m), and $A_D$ = demand length of SDT leg along major road (m).

2.3.2. Driver and Vehicle Statistical Parameters

This study considered several MV, AV, and roadway-related parameters. Each parameter considered was defined by its associated distribution. Each distribution has statistical elements such as the mean, standard deviation, minimum and maximum values, shape parameter, scale parameter, and location parameter. Most of the MV parameter values were obtained from the existing literature sources [9,11,15,16]. Speed data for MV parameters were obtained from the City of Ottawa in Canada and contained values of mean and standard deviation for posted speed limits. AV statistical parameter values were sourced from the literature [9,17,18,19,20]. However, there was a lack of distribution information for the speed and time headway variables. To account for this shortcoming, it was assumed that the distribution of the AV parameters follows a normal distribution with the means ($\mu$) being equal to the sourced values. Also, it was assumed that the variation around the mean, represented by a coefficient of CV of 2%, is small owing to the vehicles’ computerized operations [9,17]. The standard deviation values of the associated variables were calculated using the statistical relationship shown in Equation (51). The input parameters for AVs and MVs are characterized in

Table 2. AV parameters.

Design Parameter	Symbol	Distribution	Statistical Parameters/Value	Source
posted speed 20 km/h	$v_{ma}$	Normal	$\mu$$=20 \mathrm{km}/\mathrm{h}, \sigma$ = 0.39 km/h	Equation (51)
posted speed 30 km/h	$v_{ma}$	Normal	$\mu$$=30 \mathrm{km}/\mathrm{h}, \sigma$ = 0.59 km/h	Equation (51)
posted speed 40 km/h	$v_{ma}$	Normal	$\mu$$=40 \mathrm{km}/\mathrm{h}, \sigma$ = 0.78 km/h	Equation (51)
posted speed 50 km/h	$v_{ma}$	Normal	$\mu$$=50 \mathrm{km}/\mathrm{h}, \sigma$ = 0.98 km/h	Equation (51)
posted speed 60 km/h	$v_{ma}$	Normal	$\mu$$=60 \mathrm{km}/\mathrm{h}, \sigma$ = 1.18 km/h	Equation (51)
posted speed 70 km/h	$v_{ma}$	Normal	$\mu$$=70 \mathrm{km}/\mathrm{h}, \sigma$ = 1.37 km/h	Equation (51)
posted speed 80 km/h	$v_{ma}$	Normal	$\mu$$=80 \mathrm{km}/\mathrm{h}, \sigma$ = 1.57 km/h	Equation (51)
posted speed 90 km/h	$v_{ma}$	Normal	$\mu$$=90 \mathrm{km}/\mathrm{h}, \sigma$ = 1.76 km/h	Equation (51)
posted speed 100 km/h	$v_{ma}$	Normal	$\mu$$=100 \mathrm{km}/\mathrm{h}, \sigma$ = 1.96 km/h	Equation (51)
posted speed 110 km/h	$v_{ma}$	Normal	$\mu$$=110 \mathrm{km}/\mathrm{h}, \sigma$ = 2.16 km/h	Equation (51)
posted speed 120 km/h	$v_{ma}$	Normal	$\mu$$=120 \mathrm{km}/\mathrm{h}, \sigma$ = 2.35 km/h	Equation (51)
posted speed 130 km/h	$v_{ma}$	Normal	$\mu$$=130 \mathrm{km}/\mathrm{h}, \sigma$ = 2.55 km/h	Equation (51)
time headway	$t_{ha}$	Normal	$\mu$$=0.90 \mathrm{s}, \sigma$ = 0.018 s	[17]
acceleration from standstill	$a_a$	Normal	$\mu$$=2.10 \mathrm{m}/{\mathrm{s}}^2, \sigma$ = 0.04 m/s2	[20]
detection–reaction time	$t_{dr}$	Normal	$\mu$$=0.53 \mathrm{s}, \sigma$ = 0.01 s	[18]
vehicle length	$l_{va}$	Uniform	minimum = 3.969 m, maximum = 5.057 m	[19]
vehicle width	$w_a$	Uniform	minimum = 1.978 m, maximum = 2.271 m	[19]
distance from detection device to front of vehicle	$r$	Uniform	minimum = 1.66 m, maximum = 2.64 m	[9]

$\mu$ = mean, $\sigma$ = standard deviation.

and

Table 3. MV parameters.

Design Parameter	Symbol	Distribution	Statistical Parameters/Value	Source
posted speed 20 km/h	$v_{md}$	Normal	$\mu$$=17.08 \mathrm{km}/\mathrm{h}, \sigma$ = 3.56 km/h	Data
posted speed 30 km/h	$v_{md}$	Normal	$\mu$$=23.53 \mathrm{km}/\mathrm{h}, \sigma$ = 5.29 km/h	Data
posted speed 40 km/h	$v_{md}$	Normal	$\mu$$=46.20 \mathrm{km}/\mathrm{h}, \sigma$ = 7.03 km/h	Data
posted speed 50 km/h	$v_{md}$	Normal	$\mu$$=46.97 \mathrm{km}/\mathrm{h}, \sigma$ = 8.66 km/h	Data
posted speed 60 km/h	$v_{md}$	Normal	$\mu$$=56.48 \mathrm{km}/\mathrm{h}, \sigma$ = 7.34 km/h	Data
posted speed 70 km/h	$v_{md}$	Normal	$\mu$$=65.48 \mathrm{km}/\mathrm{h}, \sigma$ = 8.56 km/h	Data
posted speed 80 km/h	$v_{md}$	Normal	$\mu$$=75.60 \mathrm{km}/\mathrm{h}, \sigma$ = 9.92 km/h	Data
posted speed 90 km/h	$v_{md}$	Normal	$\mu$$=89.87 \mathrm{km}/\mathrm{h}, \sigma$ = 10.07 km/h	Data
posted speed 100 km/h	$v_{md}$	Normal	$\mu$$=95.80 \mathrm{km}/\mathrm{h}, \sigma$ = 13.70 km/h	[21]
posted speed 110 km/h	$v_{md}$	Normal	$\mu$$=103.53 \mathrm{km}/\mathrm{h}, \sigma$ = 15.89 km/h	[21]
posted speed 120 km/h	$v_{md}$	Normal	$\mu$$=110.81 \mathrm{km}/\mathrm{h}, \sigma$ = 18.52 km/h	[21]
posted speed 130 km/h	$v_{md}$	Normal	$\mu$$=117.6 \mathrm{km}/\mathrm{h}, \sigma$ = 21.61 km/h	[21]
acceleration from standstill	$a_d$	Generalized Extreme Value	$k$$=0.1426 \mathrm{m}/{\mathrm{s}}^2, \theta$$=0.1930 \mathrm{m}/{\mathrm{s}}^2,$ l = 1.0457 m/s2	[15]
perception-reaction time	$t_{pr}$	Lognormal	$\mu$$=1.5 \mathrm{s}, \sigma$ = 0.4 s	[16]
time headway	$t_{hd}$	Lognormal	$\mu$$=1.156 \mathrm{s}, \sigma$ = 0.756 s	[9]
distance from left side of vehicle to lane edge	$x$	Gamma	$k$$=6.54 \mathrm{m}, \theta$ = 0.10	[9]
distance from driver eye to left side of vehicle	$y$	Normal	$\mu$$=0.45 \mathrm{m}, \sigma$ = 0.04 m	[9]
distance from driver eye to front of vehicle	$z$	Normal	$\mu$$=2.45 \mathrm{m}, \sigma$ = 0.17 m	[9]
vehicle length	$l_{vd}$	Lognormal	$\mu$$=4.813 \mathrm{m}, \sigma$ = 0.45 m	[9]
vehicle width	$w_d$	Logistic	$\mu$$=1.891 \mathrm{m}, \sigma$ = 0.061 m	[9]
accepted time gap of driver—right turn	$t_{gd}$	Lognormal	$\mu$$=4.877 \mathrm{m}, \sigma$ = 1.096 m	[11]
accepted time gap of driver—left turn	$t_{gd}$	Lognormal	$\mu$$=6.583 \mathrm{m}, \sigma$ = 1.253 m	[11]

$\mu$ = mean, $\sigma$ = standard deviation, k = shape parameter, $\theta$ = scale parameter, $l$ = location parameter.

, respectively.

$$\sigma ={\displaystyle \frac{X\times CV}{\left(1+CV\right)}}$$

(51)

where $\mu$ = mean of the random variable; $X$ = value of the random variable associated with a certain percentile; $Z$ = standardized score; $CV$= coefficient of variation of the random variable; $\sigma$ = standard deviation of the random variable.

2.4. Correlation of Parameters

Correlation among driving behaviors of AV is not expected since these vehicles follow a programmed logic. Therefore, only potential correlations among driving behavior-based variables for MVs were considered. The examined parameters included traveling speeds, reaction times, acceleration, vehicle position within the lane, and time headway. However, the study by Sarran and Hassan [9] stated little or no correlation among the former three variables. Also, for an intersection, the lane width is fixed, and the distance of the stop bar to the intersection is almost constant. Therefore, the correlation regarding these variables is not relevant. Also, several studies have suggested that the time headway variable is constant over various speeds [22,23]. According to AASHTO [3], the accepted time gaps increase with the number of lanes, roadway grades, or vehicle types. However, these parameters do not change for specific intersections. Additionally, no relationship between driver behavior and vehicle-related distance variables was considered since the latter was based on the design of the vehicle. As a result, correlations were not considered in this study.

2.5. Interaction-Based PNC

MCS was the technique selected to compute the PNC of object locations for a vehicle interaction type. MCS is a repeated [21] random sampling reliability approach that has been widely adopted for reliability studies [21,24]. According to Huang et al. [24], MCS can be applied with accuracy to many cases requiring probabilistic analysis. MCS was performed using a MATLAB 2024 software script. However, the accuracy of this method hinges on the number of simulations performed [14]. The study by Andrade-Catano et al. [21] considered 150,000 to be a large enough number of simulation runs when computing PNC using MCS. However, the study by Sarran and Hassan [9] used 200,000 simulation runs. According to Andrade-Catano et al. [21], and Abdelnaby and Hassan [13], using these large numbers of simulation runs results in low MCS standard error or PNC coefficient of variation values. Hence, considering the literature, in this study, the value used by Sarran and Hassan [9] was adopted as the number of simulation runs, $N$. Each simulation run computed the difference between $A_s$ and $A_d$ for randomly selected parameter values. Non-compliance ($F$) was defined as a negative result of a simulation run. The distribution of a function of numerous random variables, such as the safety margin in this study, $D$, tends to be normal even if it contains non-normal variables [5,7]. Therefore, the proposed probabilistic approach was used to test the results of the safety margin to ensure it follows a normal distribution. Upon validating the model, Equation (52) was used to obtain the PNC.

$${\mathrm{P}\mathrm{N}\mathrm{C}}_i={\displaystyle \frac{F_r}{N_r}}$$

(52)

where ${\mathrm{P}\mathrm{N}\mathrm{C}}_i$ = interaction-based PNC of scenario; $F_r$ = number of failure runs; $N_r$ = number of simulation runs.

PNC was obtained for MV-only and AV-related interactions at specific object locations on major roads of different speeds. Three cases of a fixed object distance along the minor road, $n$, were examined for changing object distance along the major road, $m$. These n case distances were 1 m, 2 m, and 3 m. Also, twelve major road speeds and five SDTs were considered. With four possible vehicle interactions, as mentioned in Section 2.1, a total of 720 scenarios (3 $\times$ 5 $\times$ 12 $\times$ 4) were investigated in this study.

2.6. Comparison of PNC Values for MV-Only and AV-Related Interactions

As stated previously, ISD designs are based on MV models that describe their operations [3]. These designs provide deterministic values for the distance of sides of SDTs. In deterministic studies, variables are represented without accounting for their uncertainty or variation. However, the results emanating from a probabilistic analysis better represent a system whose variables randomly fluctuate. In this paper, the previous sections explained the probabilistic approach of using the PNC to determine the reliability of the four-vehicle interactions at a stop-controlled intersection in a mixed-traffic environment. From this outcome, the PNC values associated with the MV–MV interaction were selected as the reference interaction, and a comparison was made to the PNC of the AV-related interactions. At any one specific object, the MV–MV interaction PNC value indicated the maximum allowed PNC value. Therefore, any exceeding AV-related PNC value would suggest that the intersection is not suitable for that interaction type. In such cases, corrective actions were examined. These actions included adjusting certain vehicle parameters, such as the vehicle speed, to reduce the PNC values.

3. Results and Discussion

This section presents and discusses the results of the PNC of various vehicle interaction types at a stop-controlled intersection. As mentioned previously, a total of 720 scenarios were examined. These scenarios consisted of AV and MV vehicle interaction types, SDTs, object distances, and roadway speeds. The interaction types studied are MV–MV, MV–AV, AV–MV, and AV–AV. The PNC values were computed by using the difference between the supply and demand sight distance functions. PNC was calculated for several object locations defined by combinations of distances along the major (m) and minor (n) roadways. The object distance along the minor road, $n$, were examined for changing object distances along the major road, $m$. The distance along the minor roadway was fixed and assumed to be 1 m, 2 m, and 3 m. The speed limit on the major roadway ranged from 20 to 130 km/h in 10 km/h increments. A check was performed using MCS to validate that the safety margin for each vehicle interaction type was normally distributed. A comparison was performed by analyzing the PNC values of MV–MV interactions to the AV-based vehicle interactions (MV–AV, AV–MV, and AV–AV).

3.1. Validation of Results

Considering the large number of scenarios (i.e., 720) generated for this study, a particular case of a 60 km/h major road speed and $n$ distance of 1 m was selected for testing the distribution of the output safety margin values for the four interaction types and five SDTs. The outcome of this process is demonstrated in Figure 6, which shows a plot of the frequency against the results of the safety margin. Figure 6 confirms the assumption of normality of the safety margin for all interaction types. Similar results exist for the other scenarios in this paper. Hence, the assumption of normality of the safety margin is reasonable in this study.

3.2. PNC of Interactions

For the four interaction types, graphs related to object distances (fixed $n$ distance and changing $m$ distances) versus the PNC for a specific major speed were constructed for each SDT. Figure 7, Figure 8 and Figure 9 illustrate the MCS results of the five SDTs for all four interaction types. For example, a case where the major road speed is 60 km/h and several object locations involving fixed n distances of 1 m, 2 m, and 3 m, and variable m distances. The results show that PNC approaches full compliance, i.e., PNC = 0, for any fixed distance of n as the $m$ distance increases for all interaction cases. This finding is intuitive since the sightline between vehicles along the major and minor roadways is less likely to be obstructed the further away an object is from the intersection. For increasing values of $n$, full compliance is achieved at shorter $m$ distances. This result has a similar principle to the previous finding in that sightlines are less likely to be unobstructed the further the object is from the intersection. For a specific SDT, the mentioned pattern of results regarding $m$ and $n$ values remained the same for all scenarios. However, the actual PNC values increased with higher major roadway speeds. This increase is because PNC depends on the deemed sight distance, which becomes greater as the speed of the major roadway increases. The results regarding the other scenarios considered in this study were similar to those of the case displayed. These results can be found in Figures S1–S33 in the Supplementary Materials section.

3.3. PNC Comparison Between MV-Only and Each AV-Related Interaction

The PNC value differed for each interaction type when examining the 720 scenarios at specific object locations. For these locations, the PNC value associated with MV–MV interaction was selected as the benchmark for comparison to the other interaction types. The MV–MV interaction was selected as the base case since current ISD designs are based on the MV models. For all these cases, the major road speed, changing $m$ distances for fixed $n$ distances, and SDTs were evaluated. The graphical plots generated show that the PNC values associated with MV–AV and AV–AV in a majority of cases were significantly lower than reference MV–MV PNC values. In this case, AVs were on the minor roadway. Compared to MVs, AVs have a shorter time gap owing to their higher acceleration values from a standstill position and a shorter detection reaction time. These characteristics resulted in shorter demand sight distances compared to cases where MVs were on the minor roadway. Generally, mixed results were obtained when comparing the size of the AV–MV PNC to that of the MV–MV values. For particular scenarios, the latter PNC values were smaller for some values of $m$ and larger in the other instances, increasing $m$ values. Figure 7a shows an example of this case where the MV–MV and AV–MV lines cross each other. In this example, the results for the PNC related to the object location $m$ = 75 and $n$ = 1 m show that PNC values of 29.04% and 35.19% were obtained for the MV–MV and AV–MV interaction types, respectively. A second instance, $m$ = 85 m and $n$ = 1 m, sees PNC values of 9.69% and 5.62% for the MV–MV and AV–MV. In other scenarios, the PNC for the MV–MV interaction type was completely higher, as seen in Figure 7e.

3.4. Corrective Actions

Corrective action is warranted if an AV-related PNC value is comparatively higher than that of a PNC value associated with the MV–MV interaction. Corrective actions may include adjusting certain parameter(s) to give the desired outputs. AV parameters such as speed, acceleration from a standstill, and detection–reaction times were examined to see if adjustments can be made to lower the output demand ISD and, by extension, the PNC. Changing the latter two values would affect the time gap values for vehicles on the minor road. However, the results showed that AVs’ time gaps were shorter than that of MVs without any adjustment. This finding meant that interactions affiliated with an AV on the minor road are likely to result in PNC values that are less than that of the reference MV–MV interaction. Therefore, intervention, as it relates to adjusting AV parameters such as acceleration or detection–reaction times to lower gap time, may not be necessary. Conversely, the speed of an AV on a major road has implications for the demand of ISD and, by extension, the PNC. Hence, a practical corrective action may be to adjust (decrease) the AV speed on the major roadway. This strategy was applied to all scenarios that had instances of exceeded MV–MV PNC values.

An example of the application of this action is demonstrated using the example case detailed in Section 3.1. It was seen that the reduction of the major road speed for AVs from 60 to 50 km/h was sufficient to ensure all AV-related interaction PNC values remained lower than that of the MV–MV interaction. The results associated with this corrective action are shown in Figure 10, Figure 11 and Figure 12. The application of a speed reduction to all other scenarios yielded similar results; see Figures S34–S66 of the Supplementary Materials section. However, similar speed reductions are only applicable to scenarios with major road speeds from 20 to 80 km/h. For speeds beyond this range, a 20 km/h speed reduction was required to obtain the desired results. However, the strategy is only effective for road speeds up to 110 km/h. Further reductions in the AV speeds did not alter the outcome for the 120 and 130 km/h major road speeds. Therefore, major road speeds should be kept to a maximum speed of 110 km/h in a mixed vehicle environment.

4. Conclusions

As AVs are gradually adopted, there will be a mixed traffic environment. Hence, the vehicle interactions at intersections will involve DVs and AVs. Currently, ISDs are based on human-driver vehicles. Hence, it is expected that with a vehicular fleet of AVs, the sight distance characteristics at intersections may be an issue due to the different driving behaviors of the various vehicles. This study evaluates the sight distance characteristics of various vehicle interaction types and roadway speeds for a four-legged, right-angled, two-lane stop-controlled intersection with no median. MCS was used to estimate the PNC of four vehicle interaction types (DV–DV, DV–AV, AV–DV, AV–AV), five SDTs, roadway speeds ranging from 20 km/h to 130 km/h in 10 km/h increments, and three object distance location along the minor roadway associated with varying distances along the major roadway. Hence, a total of 720 scenarios were examined. Using the PNC metric, ISD was determined to be non-compliant when demand exceeded supply. A comparative analysis was performed using the PNC value for DV-only interaction and AV-related interactions since existing designs are based on DV-only interactions.

The results obtained in this study showed that the PNC for the DV-only traffic was surpassed by the AV–DV and AV–AV. This result was consistent for all major road speeds and the five SDTs. This finding means that current stop-controlled intersections with obstructions at certain locations may require treatment to reduce the associated PNC value. A potential strategy that can be adopted may be to reduce the posted speed on the major roadway. Investigation into this strategy yielded a reduction in the PNC value obtained for the AV-related interaction when compared to the DV-only interaction. Hence, the AV speed reduction corrective strategy can be applied in the event of non-compliant PNC values. Reduced road speeds can be set for AVs through a speed assistance system, which allows them to determine their road speed from a database of map-based speed limits [25]. Alternatively, speed reduction can be achieved by installing designated vehicle-to-infrastructure (V2I) speed limit signs specifically for AVs on roadways [9]. If speed adjustment is deemed impractical, alternative strategies, such as redesigning the intersection, changing the intersection type to one that is signal-controlled, or implementing adaptive traffic control systems, may be explored.

This study contributes to the existing literature and can assist practitioners with identifying the possibility of safety issues at stop-controlled intersections. The results of this study discuss the likelihood of an intersection experiencing safety issues if the vehicular traffic at an intersection contains AVs. It provides a baseline understanding of how the introduction of AVs into the traffic network would affect the associated ISD. More especially, it shows the PNC value for all interaction types and their conformance with existing MV-only intersection designs. Hence, practitioners are able to obtain a general understanding of the impact of the introduction of AVs on ISD at stop-controlled intersections. However, it is important to note that the assumptions made in this study can be improved once a mixed-traffic environment is prevalent. Data can be collected on varying acceleration and deceleration rates, and profiles can be formulated for AVs. Also, AVs equipped with accurate sensor capabilities may reduce time gaps, potentially enabling more efficient coordination at intersections.

Although this study investigated serval scenarios, additional research can be conducted to provide a more detailed understanding of ISD in a mixed-traffic environment. The impact of ISD on other intersection types, configurations, and designs, such as skewed intersections, can be investigated. Changes in the comfortable deceleration and acceleration rate due to environmental conditions such as rain or snow can also be investigated to assess the impact they may have on these results. Also, intersection safety, specifically ISD, for other motorized and non-motorized vehicles besides the passenger car, such as trucks, cyclists, pedestrians, etc., could be examined. Future research can also evaluate the actual distribution patterns of AV parameters used in the MCS method at the time when AVs are present in the vehicular fleet on roadways. Evaluating these distribution patterns would provide a more realistic assessment of ISD at stop-controlled intersections in a mixed-traffic environment.