Time–Space Analysis of Transport Infrastructures: A Pilot Study of Shibuya-Type Crossings for Signalized Intersections in Developing Cities

Abstract

Cities are growing larger, and congestion is becoming a major issue. Walking is increasingly becoming an important mode of transport in developing cities. One of the reasons for the high death toll is the lack of pedestrian facilities at transport infrastructures such as signalized intersections, where a conflict arises between vehicles turning right and pedestrians crossing at different speeds. This conflict, known as the vehicle–pedestrian conflict (in right-driving jurisdictions), occurs when the green light for vehicles is shared with the green pedestrian light. Additionally, if the intersection is congested due to high pedestrian flow, vehicles will turn right only during the yellow light, trying to find a gap in the pedestrian flow. As a result, delays increase for both pedestrians and vehicles, reducing the intersection’s capacity. To reduce the vehicle–pedestrian conflict, various pedestrian facilities can be implemented, such as Shibuya-type crossings, which include an exclusive pedestrian phase and diagonal crossing. When applying this type of solution, vehicle delays are reduced up to 81% on average, increasing the efficiency and safety of the space used at the intersection. However, pedestrian delays might increase up to 5 times, due to the need to wait for the third exclusive phase for them to cross the intersection in all directions. The method is applied in a case of study in Valparaiso, Chile, and therefore can be expanded in further research to other developing cities in Chile and specifically Latin America.

1. Introduction

Cities are becoming larger, and congestion is becoming the main problem. People often think that this problem focuses solely on car congestion; however, in developing cities such as Valparaíso, Chile [1], 33% of daily trips are made by car, while 27% are made on foot, and the remainder is primarily by public transportation (39%). Similarly, in developed cities like London [2], over 60% of daily trips are made using sustainable, efficient, and active modes such as public transport, walking, and cycling, with the remainder primarily using private vehicles.

Within sustainable, efficient, and active modes, walking is becoming an important mode of transportation within the city. But are cities prepared for this? Considering the high number of trips made by car, the biggest challenge in cities is to reduce traffic and improve safety conditions at pedestrian crossings. However, since 1990, the number of deaths caused by traffic accidents in Chile has ranged between 1400 and 2000 per year, reaching the highest value in the last 10 years in 2022 with 1745 fatalities, many of them pedestrians [3]. Similarly, in developed countries like the United Kingdom, the number of fatalities increased in 2017 compared to 2016, with 1793 people killed, 26% of whom were pedestrians [4].

One of the causes of the high fatality rate is related to the lack of pedestrian facilities at transport infrastructures such as signalized intersections, as there is a conflict between vehicles turning right (in right-driving jurisdictions) and pedestrians who wish to cross at different speeds. This conflict can be referred to as the vehicle–pedestrian conflict, where the green light for vehicles is shared with the pedestrian green light to cross (see Figure 1a). Furthermore, if the intersection is congested due to high pedestrian flow, vehicles will only turn right during the yellow light, as they need to find a gap in the space between pedestrians crossing the street. As a result, delays for both pedestrians and vehicles increase, reducing the capacity and the space used at the intersection [5].

To reduce the vehicle–pedestrian conflict, different pedestrian facilities can be implemented, such as Shibuya-style crossings, which include an exclusive pedestrian phase and a diagonal crossing [6]. This type of solution considers an exclusive green phase in all directions, allowing pedestrians to cross in all directions, while all vehicle movements are stopped with a red light at the signalized intersection. This solution also includes pavement markings and other accessibility facilities (see Figure 1b).

Although these facilities have also been implemented at some intersections in Chile, there is still a lack of methods to determine the effect on the efficiency and safety in order to reduce delays for both pedestrians and vehicles, which is the main goal of this research. The specific objectives of this study are (a) to identify the variables that reduce the vehicle–pedestrian conflict; (b) to develop a method to implement a Shibuya-style crossing; (c) to apply this method to an existing signalized intersection; and (d) to develop a model that allows a free-to-use graphical interface to simulate a Shibuya-style crossing.

This paper is composed of six sections. In Section 2, the literature review is described, followed by the method developed in this study. In Section 4, the results analyzed. In Section 5, the discussion is addressed, followed by the conclusions in Section 6.

2. Literature Review

Special attention has been given to studying intersections and their effects on efficiency and safety in recent decades. If the intersection is not well designed, pedestrians will wait too long for the green light and, as a result, may cross during the red light or in the middle of the street, creating an unsafe situation [7]. Other authors [8,9] argue that it is more effective to focus on reducing waiting times and improving the design of pedestrian spaces at intersections. Shortening pedestrian wait times reduces the temptation to cross at unsafe moments, decreasing risky behavior. Additionally, better-designed spaces like wider sidewalks, visible crossings, and marked pedestrian zones improve safety and accessibility. These improvements allow for more efficient crossings and enhance visibility, helping both pedestrians and drivers make quicker, safer decisions. Together, these measures reduce pedestrian–vehicle conflicts and improve overall traffic safety.

According to [10], older individuals are at a higher risk of being involved in traffic accidents due to various factors associated with aging, such as physical, cognitive, and perceptual declines. Studies have shown that, in general, older people are less likely to engage in risky behaviors such as crossing during a red light or rushing across the street. Their increased awareness of the risks associated with traffic may make them more inclined to wait for the proper signal before crossing, which can ultimately reduce their chances of being involved in an accident. For example, ref. [11] found that older pedestrians often require additional time to cross intersections due to their slower walking speeds. This can create challenges in completing crossings within the allotted signal time, especially in busy or high-traffic areas.

Other authors, such as [12], have conducted studies on pedestrian speed and step length when implementing Shibuya-type crossings, analyzing the differences in behavior based on factors such as gender and age. These studies are important because they shed light on how various demographic groups navigate intersections differently and how these differences impact the effectiveness and safety of pedestrian facilities. However, research specifically focused on children’s behavior at crossings is limited. Lupton et al. [13] identified that young children’s cognitive abilities are not fully developed, which affects their decision-making capabilities at intersections. These cognitive limitations mean that children are at a higher risk of making poor judgments when navigating traffic, increasing their chances of accidents. Since children typically do not have the ability to assess risks and make safe crossing decisions as adults do, they are more vulnerable in traffic environments. More recent studies, such as those conducted by [14], have found that parents perceive the speed of vehicles as a significant barrier to their children’s safety at intersections. Most parents considered intersections to be particularly dangerous for children or teenagers traveling to school, noting that high vehicle speeds and the lack of adequate safety measures increased the likelihood of accidents. Addressing these concerns is essential to reducing the risk that children face while navigating intersections, ultimately making the transportation system safer for all age groups.

Culture and gender are also related to efficiency and safety at transport infrastructures such as intersections. Reed and Sen [15] found that African Americans and Chinese individuals were more aware of pedestrian safety and laws than their Caucasian counterparts. Additionally, ref. [16] discovered that Arabic- and Chinese-speaking parents considered the street environment less dangerous for their children (ages 4 to 12) compared to Vietnamese- and English-speaking parents. Steenbekkers et al. [17] found that men and women differ in their body dimensions and the force they exert at intersections. However, they did not find differences in sensory and cognitive characteristics. Furthermore, for [17], women perceive more risk when crossing the street than men.

To create safer crossings, some authors [18,19,20,21,22] have taken a more specific approach to understanding pedestrian interactions and attitudes, analyzing the relationship between safety conditions and pedestrian facilities. By looking at these elements, researchers can identify key areas for improvement, such as how to better design intersections or implement new technologies to reduce accidents and delays. These insights are particularly valuable in addressing the needs of vulnerable pedestrians, such as the elderly or children, who may face greater risks at intersections. Additionally, some authors [23,24,25,26,27,28] have studied the use of Shibuya-type crossings, which are designed to allow pedestrians to cross in multiple directions, including diagonally, and simultaneously with vehicle traffic coming to a stop. These crossings, named after the famous Shibuya Crossing in Tokyo, Japan, have been shown to improve pedestrian flow and reduce conflicts between pedestrians and vehicles. However, despite their success in certain locations, there is still a lack of clear guidelines on when and how to implement these types of crossings in different urban contexts. Research indicates that Shibuya-type crossings can have significant benefits in terms of reducing delays, especially in high-traffic areas where pedestrian flow is high and vehicle movements need to be carefully coordinated. However, the effect of these crossings on the overall transport infrastructure is not fully understood. The implementation of diagonal crossing phases can impact traffic flow and cause delays for vehicles, especially during peak times.

From a modeling approach, ref. [29] reported that the effectiveness of the diagonal crossing depends on the flow of vehicles and pedestrians crossing the intersection, achieving a capacity increase of 36%. However, if pedestrian flow exceeds 4800 pedestrians per hour, delay savings are obtained regardless of vehicle flow. Additionally, ref. [30] reported that an exclusive pedestrian phase can reduce delays for both vehicles and pedestrians at the intersection, especially when traffic is high. Even more recent studies highlight the importance of evaluating the effectiveness of exclusive pedestrian phases without the need for diagonal crossings, reducing the number of accidents and conflicts at signalized intersections [31]. For [32], the benefits of reduced delays when using exclusive pedestrian phases and diagonal crossings also apply to smaller intersections, such as those with two lanes per direction, for flows greater than 1600 vehicles per hour and 900 pedestrians per hour. Benefits are also observed with up to a 31% reduction in delays, indicating an optimization of the intersection [33].

Despite the significant research conducted, methods tailored to the local realities of congested cities are still lacking to identify the effect of a Shibuya-type crossing on efficiency and safety to reduce pedestrian and vehicle delays at signalized intersections, which is the purpose of this study.

3. Method

The method of Webster and Cobbe [34], Akçelik [35], and MTT [36] was used as the basis for traffic signal programming at a Shibuya-style crossing. The following outlines each step of the method used.

3.1. Input Variables

This method considers intersections with 4 branches and bidirectional vehicular flow, with one main street and one secondary street, each having one lane per direction (see Figure 2). The conflict area is defined as the zone where vehicles make right turns and pedestrians cross. In Illustration 2, four vehicle movements can be identified, where movement 1 is identical to movement 3, while movement 2 is equal to movement 4. Regarding pedestrian movements, four movements can be identified, P1, P2, P3, and P4. In phase 1, the movements 2, 4, P1, and P3 are in green light, while the other movements are in red light. The opposite is presented in phase 2. The vehicle–pedestrian conflict is presented, for example between movements 2 and P1 (when vehicles are turning right).

To carry out the traffic signal programming, firstly it is necessary to define the variables that will serve as inputs in the method (see Table 1). The braking rate (f) is considered equal to 3 m/s², assuming an intersection where the streets have no slope. The pedestrian speed (vp) is assumed to be 1.1 m/s, under the assumption that adults and young people are crossing the intersection. In cases where elderly people, children, or individuals with reduced mobility are crossing, the pedestrian speed should be considered as 0.9 m/s. The constant k = 0 in Akçelik’s method is used to minimize delays, as this is the primary objective of the study. The rest of the variables can be adjusted if necessary to fit the specific conditions of a given intersection.

3.2. Cycle Time

As a second step in the method, the cycle time is calculated. To this end, the red-red time or RR (in seconds) must be calculated according to Equation (1). Similarly, the yellow time or AA (in seconds) is obtained according to Equation (2). For safety reasons, the minimum and maximum values of AA were considered to be 3 s and 6 s, respectively. Regarding RR, a value greater than 3 s could confuse vehicles into using it as part of the AA phase, causing them to start moving before the vehicle green light.

(1)$RR={\displaystyle \frac{(n·W)+L_a}{v}}$

(2)$AA=t_r+{\displaystyle \frac{v}{2·f}}$

The losses (L) are obtained from the sum of RR and AA. Since the initial loss (ƛ1) and final gain (ƛ2) vary between 2 and 2.5 s, they are considered equal (and thus cancel each other out).

Additionally, the minimum pedestrian green time (G_min) is calculated using Equation (3), where D represents the maximum walking distance for pedestrians to cross. In the case without a Shibuya-type crossing, D is obtained by multiplying the number of lanes (n) by the lane width (W) for each branch of the intersection. However, in the case with a Shibuya-type crossing, D is calculated using the expression in Equation (4), where n₁ and n₂ refer to the number of lanes per branch of the intersection.

(3)$G_{min}=max\{8 ; 5+{\displaystyle \frac{D}{v_p}}\}$

(4)$D_{diag}=\sqrt{{(n_1·W)}^2+{(n_2·W)}^2}$

The load factors (y_i) for each branch of the intersection are obtained using the expression in Equation (5), where q_i represents the vehicular flow and S_i is the saturation flow for each movement i. The vehicular flow refers to the total flow per movement on each branch of the intersection, and S is the sum of the saturation flows for each lane. Then, Y will be the sum of the y_i values, considering only the critical movements i (those with the highest required green time).

In the case of two branches in the intersection with bidirectional flow, the critical movement will be the right-turn movement for each branch.

(5)$y_i={\displaystyle \frac{q_i}{S_i}}$

To obtain the cycle time (c), the minimum cycle time (C_min), optimal cycle time (C_o), and practical cycle time (C_p) must be calculated. The minimum value between C_min, C_o, and C_p is then chosen. The maximum value for the cycle time (C) is defined as 120 s, while the minimum value for C is set to 40 s. However, in the case of Shibuya-type crossing, a cycle time C′ is considered as the sum between C and G_min, considering D_diag.

(6)$C_{min}={\displaystyle \frac{L}{1-Y}}$

(7)$C_{o\_webster}={\displaystyle \frac{1.5·L+5}{1-Y}}$

(8)$C_{o\_akcelik}={\displaystyle \frac{\left(1.4+k\right)·L+6}{1-Y}}$

(9)$C_p={\displaystyle \frac{L}{1-1.1·Y}}$

In Equation (8), k is Akçelik’s constant, which can be assigned a value based on its objective function. If k = 0, then the delays are minimized.

To calculate the effective green time distribution (v_ei) for each vehicular movement i, the expression in Equation (10) is used, where v_ei must be greater than or equal to G_min. In the case where v_ei < G_min, it must be established that v_ei is equal to G_min.

(10)$v_{ei}=(C-L)·{\displaystyle \frac{y_i}{Y}}$

When there is a vehicle–pedestrian conflict, vehicles can only make the turn during the yellow phase, so v_ei = AA. On the other hand, for a Shibuya-style crossing, the exclusive pedestrian phase (phase 3) allows vehicles to make the turn using the entire effective green time from the previous phases (phase 1 and phase 2) (see Figure 3).

3.3. Delays

The third step of the method is the calculation of the vehicles and pedestrian delays. The average uniform delay per vehicle (du) is calculated in seconds per vehicle (s/veh) using Equation (11), where u is the effective green ratio and Q is the capacity.

This equation helps estimate the delay experienced by each vehicle at an intersection based on the effective green time (u) and the intersection’s capacity (Q).

(11)$du={\displaystyle \frac{C·{(1-u)}^2}{2(1-y_i)}}$

(12)$u={\displaystyle \frac{v_{ei}}{C}}$

(13)$Q=u·S$

In the case of pedestrian delay (dp), it is calculated in seconds per pedestrian (s/peat) using adapted equations from [37]. This adapted equation considers various factors, such as pedestrian flow, the time required for pedestrians to cross, and the interaction between vehicle and pedestrian movements, to estimate the average delay experienced by pedestrians at an intersection. The aim is to accurately model the time pedestrians spend waiting to cross the street, as well as the time spent crossing, depending on factors such as traffic conditions and pedestrian traffic volume. It is assumed that pedestrians arrive at the intersection using a uniform distribution; the cycle time C is fixed and the green time for pedestrians (G) is calculated as an isolated signalized intersection.

(14)$dp=\left({\displaystyle \frac{({C-G)}^2}{2·C}}\right)$

4. Results

4.1. Modeled Scenarios

The method was applied to 15 hypothetical scenarios, with an intersection of two lanes in each direction, bidirectional. The study area was considered in the vehicle–pedestrian conflict zone. The vehicular flow on the main road started at 500 vehicles per hour (veh/h) and increased by 100 veh/h until it reached 1900 veh/h, which was very close to the saturation flow. The vehicular flow on the secondary road was considered to be half of the vehicular flow on the main road. The input values for the method are those used as an example in Table 1 (Section 3.1).

Table 2 shows the flow and saturation grade for vehicles. As explained earlier, the vehicular flow on the main road started at 500 vehicles per hour (veh/h) and increased by 100 veh/h increments until it reached 1900 veh/h. The flow on the secondary road was half of the flow on the main road. The saturation grade was low for flows less than 900 veh/h; however, for flows above 900 veh/h, the saturation grade approached a value of 1. The saturation grade is an important metric that represents the degree of congestion at an intersection or road. A saturation grade of 1 means that the intersection is operating at its full capacity, where the demand for space and time exceeds the available capacity, leading to congestion and delays. As the vehicular flow increases, especially beyond 900 veh/h, the saturation grade rises, indicating that the road and intersection are nearing their maximum capacity, which can lead to significant delays and inefficiencies if not managed properly. Understanding this behavior is crucial for optimizing traffic signal timings and managing the balance between traffic flow and pedestrian safety, especially during peak hours when congestion is at its highest.

The cycle time of the signalized intersection was obtained for each modeled scenario using the method described in Section 3. The difference between the cases with and without the Shibuya-type crossing is presented in Table 3. In the case of the Shibuya-type crossing, a 3-phase signal crossing is presented (see Figure 3 in Section 3), while the opposite is presented with a 2-phase signal crossing.

The green time is obtained using the proposed method for each modeled scenario (see Table 4). In the case of the 2-phase signal crossing, the green time is equal to the yellow time (defined as AA in Table 1, see Section 3). In addition, it is important to note that in the case of a Shibuya-type crossing, the green time must account for the diagonal distance of the crossing.

The delays are presented in the following tables (see Table 5 and Table 6), providing a comparative analysis of different scenarios at the signalized intersection. In the case of a Shibuya-type crossing, the results indicate that vehicles experience time savings up to 81%, as shown by the negative values in the delay data for vehicle movements. This reduction in delay for vehicles is due to the fact that, during the exclusive pedestrian phase, vehicles are not required to yield to pedestrians, allowing for uninterrupted flow in all directions.

However, this improvement in vehicle efficiency comes at a cost to pedestrians. As pedestrians are granted an exclusive green phase to cross in all directions, including diagonally, they must wait for an additional phase, which increases their overall delay compared to traditional crossings up to five times. This added waiting time results from the need to coordinate all pedestrian movements, including diagonal crossings, within the third phase of the signal cycle. As a consequence, while vehicles benefit from improved flow and reduced waiting times, pedestrians experience a higher total delay due to the longer wait times required for crossing in multiple directions.

In summary, while a Shibuya-type crossing offers significant benefits for vehicle flow, it presents trade-offs in terms of pedestrian delay, highlighting the balance between optimizing vehicle efficiency and maintaining pedestrian safety and convenience.

As a result of the modeling scenarios, a simulation interface was proposed to facilitate the graphical representation and visualization of results (see Appendix A). For this purpose, the AnyLogic 2023 [38] software was used, which is a traffic simulation tool that allows the movement of vehicles and pedestrians to be represented at a signalized intersection. This software is similar to other simulation tools such as Vissim [39,40].

4.2. Case of Study

To validate the scenarios with the method, a case study was considered. To this end, the study area corresponds to the intersection of Avenida Francia with Avenida Errazuriz, located just steps from the Francia Station of the Valparaíso metro-train (see Figure 4). This area is popularly known as the “University District” because it is home to several higher education institutions. Due to its proximity to these schools, the aforementioned intersection is one of the main access routes to the University District, as it is located near Francia Station and a bus stop serving both urban and interurban routes, facilitating student access to their respective schools. As a consequence, during peak hours, the intersection experiences a large flow of pedestrians, most of whom are students. These pedestrians often cross the street diagonally, disregarding the designated crossing markings, which can lead to potential accidents with vehicles. For this reason, it is necessary to examine the possibility of adjusting the traffic signal timings at the intersection to prevent such accidents. Additionally, the study explores the presence of pedestrians with reduced mobility such as wheelchair users, cane users, and trolley users to ensure that the intersection is accessible and safe for all users.

Avenida Francia runs in a north–south and south–north direction, and it is classified as a collector road. On the other hand, Avenida Errazuriz runs in an east–west and west–east direction and is considered a main thoroughfare. The intersection of these two avenues is the study area, where Avenida Errazuriz experiences a higher volume of vehicular traffic. This difference in traffic flow between the two avenues is an important factor to consider when analyzing the overall dynamics of the intersection, particularly in terms of vehicle and pedestrian interactions (see Figure 5).

Avenida Errazuriz, when moving from west to east, has three lanes, each 3 m wide. In the opposite direction (east to west), it consists of two lanes, each 3.5 m wide, and features a median that is 3.4 m wide. The south sidewalk of Avenida Errazuriz is 3 m wide. On the other hand, Avenida Francia, running from south to north, has two lanes, each 3 m wide, and includes a 2 m wide parking lane. In the opposite direction (north to south), Avenida Francia also has two lanes, each 3 m wide, and a 2 m wide parking lane. The sidewalk on the west side of Avenida Francia is 4.8 m wide, while the sidewalk on the east side is 3 m wide. These dimensions are crucial for understanding pedestrian movement and vehicular traffic flow at the intersection, as they influence the capacity, safety, and the potential need for adjustments in signal timing to optimize traffic and pedestrian crossings (see Figure 6).

Table 7 and Table 8 shows the flow measured at the intersection in the case study. During the morning peak hour (MPH, from 8:00 to 9:00 a.m.), a large number of private vehicles can be observed, with similar quantities traveling in both directions on Avenida Errazuriz. At the afternoon peak hour (APH, from 5:00 to 6:00 p.m.), a significant difference in the number of cars traveling eastward on Avenida Errazuriz can be observed, with a difference of 1268 private vehicles compared to those traveling westward.

As observed in Table 9, during the morning peak hours there is a noticeable pattern where pedestrians frequently cross the intersection diagonally. This behavior is driven by the perception of safety among pedestrians, as many others are seen doing the same. The social influence of seeing others cross in this manner encourages more pedestrians to follow suit, creating a self-reinforcing cycle. This happens consistently during every weekday, particularly in the busy morning hours when the flow of pedestrians is highest. However, this form of crossing, although seemingly harmless to pedestrians, poses significant risks. It disrupts the normal traffic flow and creates a conflict between pedestrians and vehicles, especially in intersections with heavy traffic. Drivers, who are not expecting pedestrians to cross diagonally, may not have enough time to react when a pedestrian suddenly appears in their path. This behavior increases the likelihood of accidents, as vehicles and pedestrians are competing for the same space at the same time, without a clear understanding of each other’s movements. The risk is particularly heightened in areas where traffic lights and pedestrian signals are not synchronized to account for such crossing behavior. Pedestrians may end up in the middle of the intersection when vehicles have the green light, resulting in dangerous situations. Moreover, as this behavior is habitual and widespread, it might not only be limited to a few individuals but could become a norm, further exacerbating the potential for accidents. Therefore, addressing this issue is critical for improving pedestrian and driver safety, and more effective intersection management, including adjusting signal timings and pedestrian infrastructure, may be necessary to prevent future incidents.

The vehicle–pedestrian conflict occurs between the pedestrian movements 1P-2P or 2P-1P and the vehicular flow 2-1, because vehicles wishing to turn right at the intersection can only do so during the yellow light or must wait to find a safe gap between pedestrians to make the turn. This type of conflict is particularly dangerous at intersections with a high volume of pedestrians, where diagonal crossings or unconventional pedestrian movements hinder visibility and the drivers’ ability to find a suitable gap to turn without risking pedestrian safety. During the yellow light, vehicles may be attempting to complete their turn before the traffic light changes to red. However, if pedestrians are crossing, drivers may feel pressured to turn quickly, increasing the risk of accidents. Moreover, if vehicles cannot find an adequate gap to turn safely, they may be forced to stop in the intersection, leading to congestion and, in turn, increasing the risk of conflicts with pedestrians crossing at the same time. These situations highlight the importance of proper traffic light synchronization and the design of crossings that prioritize both pedestrian safety and the smooth flow of vehicle traffic, minimizing dangerous interactions between both user groups. Implementing exclusive pedestrian phases or improving crossing signage could reduce these conflicts and enhance safety at intersections.

In this signalized intersection, the cycle time of the traffic light is 115 s, which is determined from field observations. The main road (Avenida Errazuriz) has a vehicular green light of 80 s, while the secondary road (Avenida Francia) has a vehicular green light of 30 s. If a Shibuya-type crossing were to be proposed, a third phase would need to be created, which includes green time for pedestrians to cross diagonally. This green time is calculated using Equations (3) and (4) outlined in Section 3, yielding a value of 16 s. Therefore, the total cycle time of 115 s would need to be adjusted to include the 16 s for the Shibuya-type crossing, bringing the total cycle time to 131 s (see Table 10).

As shown in Table 11, the implementation of a Shibuya-type crossing and the resulting adjustments to the traffic signal cycle significantly reduce the average delays for vehicles making a right turn (movement 2-1) by an impressive 77%. This reduction leads to improved overall traffic flow and greater efficiency, as vehicles are able to complete their maneuvers more quickly and with fewer interruptions. Moreover, by minimizing delays for turning vehicles, the intersection becomes safer, as drivers are less likely to experience confusion or frustration from extended wait times, which could otherwise lead to risky behavior or accidents. However, the introduction of a third phase dedicated exclusively to pedestrian crossings comes with a trade-off. For pedestrians, the benefits of a third phase—designed to ensure that they can cross in all directions, including diagonally—result in longer waiting times. Pedestrians are now required to wait for the exclusive pedestrian phase, during which they must remain on the curb until the signal changes. As a result, pedestrian delays nearly double compared to the previous scenario, when they might have crossed during the earlier phases.

5. Discussion

The implementation of a Shibuya-type crossing enhances both efficiency and safety at the signalized intersection by reducing delays for vehicles in the vehicle–pedestrian conflict. This improvement occurs because vehicles making right turns can now move more freely without the need to wait for gaps in pedestrian traffic, leading to smoother and faster flow. The reduction in vehicle delays directly contributes to better overall intersection performance, minimizing the risk of congestion and potential accidents.

However, while the Shibuya-type crossing brings notable benefits for vehicles, it also results in increased delays for pedestrians. To accommodate pedestrians crossing in all directions, including diagonally, a third exclusive pedestrian phase is introduced. This third phase requires pedestrians to wait for the signal to change before they can cross, which means that their overall waiting time increases compared to a traditional signal cycle.

This trade-off between vehicle efficiency and pedestrian delay highlights a key consideration in intersection design. While vehicles benefit from reduced delays and enhanced safety, the added pedestrian phase can lead to frustration for pedestrians who must wait longer to cross. Consequently, careful planning and adjustments are necessary to strike a balance that ensures both vehicular and pedestrian needs are met efficiently, without compromising safety or convenience for either group.

This change underscores a significant trade-off between improving vehicle flow and minimizing pedestrian delays. While the third pedestrian phase undoubtedly enhances safety by allowing pedestrians to cross without interference from vehicles, it also introduces a notable inconvenience for pedestrians, particularly during peak traffic hours. Increased waiting times could lead to frustration among pedestrians and potentially reduce the overall convenience of the intersection, especially for those who are in a hurry or need to cross quickly, such as students or workers. Moreover, the increase in pedestrian delays may have indirect consequences on pedestrian behavior. As waiting times increase, some pedestrians may be more likely to take risks, such as crossing during red lights or when the pedestrian phase is not active, which could compromise their safety. This situation highlights the complexity of intersection design, where the need to balance the safety and convenience of both vehicle and pedestrian users must be carefully considered. Therefore, any solution should prioritize not only the reduction in vehicle delays but also ensure that pedestrians are not unduly inconvenienced or placed at greater risk. In light of this, further refinements or adjustments to the signal timing might be needed to achieve a more balanced outcome.

The main point is that implementing a Shibuya-style crossing can enhance the functionality of a typical intersection, particularly one that experiences a high volume of right-turning traffic and pedestrian crossings. In many intersections, the challenge arises when vehicles turning right have to share the space with pedestrians crossing the street, leading to conflicts and delays. This often results in a situation where traffic cannot flow smoothly, and vehicles are unable to clear the first lane effectively.

By adopting a Shibuya-style crossing, where pedestrian phases are completely separated from vehicle turning phases, this issue can be mitigated. Pedestrians are allowed to cross the intersection during dedicated phases, without interference from vehicles making turns. This approach eliminates the bottleneck that occurs when vehicles are waiting for pedestrians to clear the crosswalk, allowing vehicles to turn without obstruction.

As a result, traffic flow is improved, and vehicles can move through the intersection more efficiently. Moreover, pedestrian safety is enhanced because they are not forced to navigate through turning vehicles. This separation of phases—vehicle turning and pedestrian crossing—creates a more organized and predictable traffic environment, helping both vehicles and pedestrians coexist more harmoniously, reducing congestion and improving overall traffic management at busy intersections.

When applied to a simulation, the methodology allows for the analysis of mobility-related costs, with results indicating that the system begins to be overwhelmed when there are 1,600 pedestrians per side of the crossing. Therefore, for this specific intersection, it is recommended to use this system up to that level of increased pedestrian traffic. Moreover, while the Shibuya crossing increases pedestrian delays, it also reduces vehicle congestion, making it a favorable option in terms of traffic flow management.

This study paves the way for future research, both in symmetric crossings and in further exploration of the methodology’s application to other asymmetric intersections. It also suggests modifying the crossing area itself (such as through widening) and studying its impact. Additionally, the feasibility of implementing a Shibuya-style crossing could be explored. A Shibuya crossing would create a dedicated pedestrian phase, where no vehicle movements occur, allowing pedestrians to cross in all directions. However, implementing such a crossing would require studying the time needed for individuals with reduced mobility to cross diagonally (since the crossing distance would increase), and analyzing the impact of this additional time on the overall crossing operation. Further research would be needed to assess the feasibility and implications of such a system.

In addition, this study can be expanded to other intersections by taking into account local realities, such as the distribution of vehicular and pedestrian flow arriving at the intersection. Local variations, including traffic patterns, peak hours, and the specific characteristics of the area, should be considered in order to accurately simulate and predict traffic behavior.

Incorporating adjustments for delays is crucial, as vehicles and pedestrians may exhibit risky behaviors that could affect safety and efficiency. For example, pedestrians may cross the intersection while the signal is red, leading to potential conflicts with vehicles. Similarly, vehicles may attempt to make turns or change lanes under less than optimal conditions, causing congestion or unsafe situations. These factors can significantly influence the flow and safety of the intersection, making it important to account for such behaviors when modeling the intersection’s performance.

Additionally, various scenarios, such as different weather conditions, changes in pedestrian volume, or even special events that might increase pedestrian or vehicle traffic, should be simulated to test the intersection’s adaptability. Implementing real-time data, such as the use of sensors or smart traffic signals, could further improve the accuracy of the simulations, allowing for dynamic adjustments based on actual traffic conditions.

By expanding the study to incorporate these local conditions and behaviors, more comprehensive and effective traffic management strategies can be developed. This approach would not only improve the efficiency of intersections but also enhance the safety of both pedestrians and vehicles, reducing the likelihood of accidents and improving the overall transportation experience.

6. Conclusions

This study makes a comparison between a Shibuya-type crossing (with a third exclusive pedestrian phase) and the typical situation of a two-phase signalized intersection, where the vehicle green phase is shared with the pedestrian green phase. To achieve this, a method is developed that includes the modeling of hypothetical scenarios and a graphical interface to simulate the movement of vehicles and pedestrians at the signalized intersection. To validate the method, it is applied to a case study in Valparaiso, Chile.

In the case of the Shibuya-type crossing, the introduction of a third exclusive pedestrian phase allows pedestrians to cross in any direction, including diagonally, without interfering with vehicular traffic. This phase improves pedestrian safety by reducing the potential for conflicts with turning vehicles. However, it also introduces longer pedestrian delays, as pedestrians must wait for the dedicated pedestrian phase to cross.

In contrast, the two-phase signalized intersection commonly found in many cities, including the studied intersection in Valparaiso, requires pedestrians to cross during the same green phase as vehicles, leading to potential conflicts and increased risk for pedestrians. While this system is generally more efficient for vehicles, it poses challenges for pedestrian safety, particularly when pedestrian volume is high.

The method developed in this study allows for the simulation of both scenarios, providing insights into the trade-offs between vehicle flow and pedestrian safety. By applying the method to the specific case study in Valparaiso, the study offers valuable data on the effectiveness of different intersection configurations in terms of both traffic efficiency and pedestrian safety.

This comparison highlights the importance of considering pedestrian needs in the design of signalized intersections, particularly in areas with high foot traffic, such as near universities or transportation hubs. The findings from this study can help inform traffic management strategies that balance the needs of both pedestrians and vehicles, improving overall intersection safety and efficiency.

The impact of a Shibuya-style crossing will ultimately depend on whether the combined waiting times for both vehicles and pedestrians, along with the crossing times, do not exceed the total time required by the previous signal setup. One key feature of a Shibuya-style crossing is the introduction of a dedicated pedestrian phase, which allows pedestrians to cross in all directions without interference from turning vehicles. While this is a clear advantage in terms of pedestrian safety and ease of movement, it can also result in longer signal cycles since vehicles must wait for the entire pedestrian phase to finish before they can move.

If the cycle length becomes too long to accommodate the pedestrian phase, it can create new challenges. For pedestrians, the longer waiting time for the pedestrian signal could outweigh the benefits of uninterrupted crossing, especially if the total wait time increases significantly compared to the previous setup. In such a scenario, pedestrians may find themselves waiting longer to cross, which could potentially negate the improvements in safety and convenience provided by the Shibuya-style crossing.

Moreover, while a Shibuya crossing offers significant advantages in intersections with heavy right-turning traffic, where vehicle and pedestrian movements often conflict, its benefits are not necessarily uniform across all user groups. For vehicles, the separation of pedestrian and turning phases allows for smoother traffic flow, especially in busy areas where right-turning vehicles previously had to wait for pedestrians to cross. However, if the signal cycle becomes too long, traffic flow could also suffer, leading to congestion and delays that were not present in the original system.

Ultimately, the success of a Shibuya-style crossing in improving the intersection depends on careful balancing. The pedestrian phase needs to be timed properly to avoid excessive wait times, while still ensuring that the turning vehicles are able to move efficiently. In practice, while this style of crossing can enhance pedestrian safety and traffic flow in certain conditions, if not carefully optimized, it could inadvertently lead to longer waits for pedestrians and potentially more congestion for both pedestrians and vehicles.

Author Contributions

Conceptualization, S.S., A.L., V.A. and T.F.; Methodology, S.S., A.L., V.A., A.P. and T.F.; Software, N.O. and G.D.; Validation, B.A.; Formal analysis, S.S., A.L., N.O. and G.D.; Investigation, S.S. and A.L.; Resources, A.P.; Data curation, B.A. and A.L.; Writing—original draft, S.S.; Writing—review & editing, V.A., A.P. and T.F.; Visualization, B.A. and A.L.; Supervision, S.S.; Project administration, S.S.; Funding acquisition, A.P. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Transport infrastructure: (a) vehicle–pedestrian conflict when sharing the green light at signalized intersections in Chile; (b) exclusive phase with diagonal crossing in the UK.

Figure 2. Movements at the 2-phase signalized intersection: (a) phase 1; (b) phase 2.

Figure 3. Movements at the 3-phase signalized intersection: (a) phase 1; (b) phase 2; (c) phase 3.

Figure 4. Location of the case study in Valparaiso, Chile.

Figure 5. Pedestrians at the case study in Valparaiso, Chile.

Figure 6. Movements at the intersection in the case study in Valparaiso, Chile.

Table 1

Input variables used in the method.

Variable	Unit	Example to be Used	Acronym
Number of branches at the intersection	Quantity	4	Nr
Number of street lanes at the intersection	Quantity	1	n
Traffic direction	unid. o bidir.	bidir.	St
Vehicle flow per movement in each branch at the intersection	veh/h	800	qv
Percentage of vehicles turning right at the intersection	%	30	Pv
Street lane width	cant.	3.5	W
Turning radius	m	5	r
Vehicle speed	km/h	50	v
Vehicle length	m	5	La
Break rate	m/s2	3	f
Driver reaction time	s	1	tr
Akcelik constant (0 if delays are minimized)	Without units	0	k
Vehicle saturation practical grade (design)	Without units	0.9	Xp
Vehicle saturation flow (central lane)	veh/h	2141	Sc
Vehicle saturation flow (turning right lane)	veh/h	1933	Sd
Vehicle saturation flow (turning left lane)	veh/h	1922	Si
Pedestrian flow per movement in each Branch at the intersection	veh/h	2000	qp
Walking speed	m/s	0.9	Vp
Pedestrian density (design)	peat/m2	1	d
Width of the pedestrian pathway	m	2	Wp
Pedestrian saturation practical grade (design)		0.9	Xpe
Pedestrian saturation flow (Xpeat = 3600 × Wp × vp × d)	peat/h	7920	Sp

Table 2

Vehicle flow at each scenario modeled using the method.

Scenario	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Flow main road (veh/h)	500	600	700	800	900	1000	1100	1200	1300	1400	1500	1600	1700	1800	1900
Vehicle saturation grade (main road)	0.260	0.312	0.364	0.416	0.468	0.520	0.572	0.624	0.676	0.728	0.780	0.832	0.884	0.937	0.989
Flow secondary road (veh/h)	250	300	350	400	450	500	550	600	650	700	750	800	850	900	950
Vehicle saturation grade (secondary road)	0.130	0.156	0.182	0.208	0.234	0.260	0.286	0.312	0.338	0.364	0.390	0.416	0.442	0.468	0.494

Table 3

Cycle time at each scenario modeled using the method.

Scenario	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
2-phase signal crossing	40.00	40.00	40.00	40.00	40.00	40.00	40.00	40.00	40.00	41.70	51.33	66.74	120.00	120.00	120.00
3-phase signal crossing (Shibuya-type crossing)	50.00	50.00	50.00	50.00	50.00	50.00	50.00	50.00	50.00	51.70	61.33	76.74	130.00	130.00	130.00

Table 4

Green time at each scenario modeled using the method.

Scenario		1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
2-phase signal crossing	Main road	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31
	Secondary road	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31	3.31
3-phase signal crossing (Shibuya-type crossing)	Main road	24.05	24.05	24.05	24.05	24.05	24.05	24.05	24.05	24.05	25.18	31.60	41.88	77.38	77.38	77.38
	Secondary road	12.02	12.02	12.02	12.02	12.02	12.02	12.02	12.02	12.02	12.59	15.80	20.94	38.69	38.69	38.69
	Diagonal crossing	10	10	10	10	10	10	10	10	10	10	10	10	10	10	10

Table 5

Average vehicle uniform delay at each modeled scenario.

Scenario		1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
2-phase signal crossing	Main road (1)	22.69	24.39	26.37	28.70	31.48	34.85	39.04	44.36	51.37	64.07	100.25	174.95	470.65	824.52	3323.06
	Secondary road (2)	19.32	19.91	20.54	21.21	21.93	22.69	23.51	24.39	25.35	27.69	36.69	51.42	101.26	106.16	111.56
3-phase signal crossing (Shibuya-type crossing)	Main road (3)	9.08	9.77	10.56	11.49	12.60	13.95	15.63	17.76	20.57	24.66	32.16	45.97	88.34	154.77	623.75
	Secondary road (4)	16.56	17.07	17.61	18.18	18.80	19.45	20.16	20.91	21.73	23.19	27.61	34.61	57.23	60.00	63.06
Difference	(1)-(3)	−60%	−60%	−60%	−60%	−60%	−60%	−60%	−60%	−60%	−62%	−68%	−74%	−81%	−81%	−81%
	(2)-(4)	−14%	−14%	−14%	−14%	−14%	−14%	−14%	−14%	−14%	−16%	−25%	−33%	−43%	−43%	−43%

Table 6

Average pedestrian delay at each modeled scenario.

Scenario		1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
2-phase signal crossing	Main road (1)	9.78	9.78	9.78	9.78	9.78	9.78	9.78	9.78	9.78	10.16	12.30	15.72	27.55	27.55	27.55
	Secondary road (2)	6.73	6.73	6.73	6.73	6.73	6.73	6.73	6.73	6.73	6.80	7.20	7.92	10.65	10.65	10.65
3-phase signal crossing (Shibuya-type crossing)	Main road (3)	16.00	16.00	16.00	16.00	16.00	16.00	16.00	16.00	16.00	16.82	21.48	29.02	55.38	55.38	55.38
	Secondary road (4)	16.00	16.00	16.00	16.00	16.00	16.00	16.00	16.00	16.00	16.82	21.48	29.02	55.38	55.38	55.38
Difference	(1)-(3)	64%	64%	64%	64%	64%	64%	64%	64%	64%	66%	75%	85%	101%	101%	101%
	(2)-(4)	138%	138%	138%	138%	138%	138%	138%	138%	138%	147%	198%	266%	420%	420%	420%

Table 7

Vehicle flow measured during the MPH at the intersection in the case study in Valparaiso, Chile.

Type of Vehicle per Movement	2-3	2-1	3-2	3-1	1-3
Car	65	17	109	1058	1103
Buses	0	0	0	130	133
Truck	12	7	4	35	27
Taxi	1	1	2	65	51
Motorcycle	5	1	1	23	16
Bicycle	0	0	0	7	5

Table 8

Vehicle flow measured during the APH at the intersection in the case study in Valparaiso, Chile.

Type of Vehicle per Movement	2-3	2-1	3-2	3-1	1-3
Car	149	55	80	1970	702
Buses	1	0	0	121	103
Truck	4	1	4	30	21
Taxi	8	3	2	53	52
Motorcycle	5	3	4	71	28
Bicycle	1	1	0	20	8

Table 9

Pedestrian flow measured during the MPH and APH at the intersection in the case study in Valparaiso, Chile.

	Total Pedestrians		Total Pedestrians with Reduced Mobility (Wheelchair Users, Cane Users, and Trolley Users)
Movement	MPH	APH	MPH	APH
Movement 1P–2P	903	294	12	22
Movement 2P–1P	135	606	16	17
Movement 3P–2P	73	338	4	6
Movement 2P–3P	833	168	8	7
Movement 1P–3P	867	0	6	0

Table 10

Green time at the signalized intersection in the case study.

	Phase 1	Phase 2	Phase 3	Cycle Time (s)
Green time (s) with 2-phase signalized intersection	80	30	-	115
Green time (s) with 3-phase signalized intersection	80	30	16	131

Table 11

Delays for vehicles turning right and pedestrians crossing at the signalized intersection in the case study.

Average Delays per Vehicle and Pedestrian	Average Delays 2-Phase Signalized Intersection	Average Delays 3-Phase Signalized Intersection	Difference (%)
Turning right vehicles (s/veh)	55.52	12.75	−77%
Pedestrians crossing (s/ped)	26.49	50.47	91%

Appendix A

The software provides a dynamic environment for simulating traffic flow, helping to analyze and optimize traffic signal timing, pedestrian movement, and vehicle flow under various conditions. The interface designed in this case aims to display key performance indicators such as vehicle delays, pedestrian waiting times, and overall traffic efficiency, enabling users to observe the effects of different strategies and adjustments in real time. This simulation approach will allow for a more effective analysis of potential solutions to reduce conflicts between vehicles and pedestrians, improving safety and minimizing delays. By visualizing the flow of both vehicles and pedestrians, the simulation helps to identify bottlenecks and optimize signal phases, particularly in complex scenarios such as Shibuya-type crossings or intersections with high pedestrian traffic.

Figure A1. Simulation of the signalized intersection using AnyLogic software: (a) 2-phase (without Shibuya-type crossing); (b) 3-phase (with Shibuya-type crossing) [38].

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