Evaluation of Selected Factors Affecting the Speed of Drivers at Signal-Controlled Intersections in Poland

Abstract

In traffic engineering, vehicle speed is a critical determinant of both the risk and severity of road crashes, a fact that holds particularly important for signalized intersections. Accurately selecting vehicle speeds is crucial not only for minimizing accident risks but also for ensuring the proper calculation of intergreen times, which directly influences the efficiency and safety of traffic flow. Traditionally, the design of signal programs relies on fixed speed parameters, such as the posted speed limit or the operational speed, typically represented by the 85th percentile speed from speed distribution data. Furthermore, many design guidelines allow for the selection of these critical speed values based on the designer’s own experience. However, such practices may lead to discrepancies in intergreen time calculations, potentially compromising safety and efficiency at intersections. Our research underscores the substantial variability in the speeds of passenger vehicles traveling intersections under free-flow conditions. This study encompassed numerous intersections with the highest number of accidents, using unmanned aerial vehicles to conduct surveys in three Polish cities: Toruń, Bydgoszcz, and Warsaw. The captured video footage of vehicle movements at predetermined measurement sections was analyzed to find appropriate speeds for various travel maneuvers through these sections, encompassing straight-through, left-turn, and right-turn relations. Our analysis focused on how specific infrastructure-related factors influence driver behavior. The following were evaluated: intersection type, traffic organization, approach lane width, number of lanes, longitudinal road gradient, trams or pedestrian or bicycle crossing presence, and even roadside obstacles such as buildings, barriers or trees, and others. The results reveal that these factors significantly affect drivers’ speed choices, particularly in turning maneuvers. Furthermore, it was observed that the average speeds chosen by drivers at signalized intersections did not reach the permissible speed limit of 50 km/h as established in typical Polish urban areas. A key outcome of our analysis is the recommendation for a more precise speed model that contributes to the design of signal programs, enhancing road safety, and aligning with sustainable transport development policies. Based on our statistical analyses, we propose adopting a more sophisticated model to determine actual vehicle speeds more accurately. It was proved that, using the developed model, the results of calculating the intergreen times are statistically significantly higher. This recommendation is particularly pertinent to the design of signal programs. Furthermore, by improving speed accuracy values in intergreen calculation models with a clear impact on increasing road safety, we anticipate reductions in operational costs for the transportation system, which will contribute to both economic and environmental goals.

1. Introduction

Managing vehicle speed at signalized intersections involves many challenges arising from technological, behavioral, and infrastructural factors. Data on driver behavior while passing through intersections are of paramount importance from the perspectives of both traffic efficiency and safety.

Factors influencing vehicle speed primarily include: weather conditions (including visibility and road slipperiness), time of day (including traffic level-of-service on the road network), visibility conditions (i.e., the presence of obstacles in the vicinity of the intersection that hinder the visibility, legibility, and comprehensibility of traffic organization or other road infrastructure users), and human psychomotor factors (e.g., risk tolerance, familiarity with the intersection, level of distraction or attention during driving, current stress levels due to the day’s events, or the presence of traffic violation recording systems). Vehicle speed is also affected by the design of the signal timing plan, especially the duration of green signals and even the use of other informational devices, such as countdown timers.

The multitude of these factors makes predicting driver behavior in the main conflict areas of signalized intersections difficult. This is particularly important in the design of signal timing programs, where the calculation of intergreen periods is a key parameter affecting traffic safety. In many countries, speed selection is determined solely by arbitrarily set speed limits, whether design or operational speeds, regardless of the trajectory of the conflicting stream, such as in Poland [1], Germany [2], Sweden [3], the Netherlands [4], or the United States [5]. The research presented in this article aims to model the actual speed of vehicles at intersections, considering basic geometric characteristics to account for observed differences in driver behavior in the field. This study focuses exclusively on servicing passenger cars during periods of stable traffic flow under uncongested conditions. This assumption is due to the significant share of passenger cars in urban traffic during peak periods.

2. Literature Review

Many research studies focus on the analysis of external factors influencing the choice of travel speed through intersections. For example, in [6], vehicle speeds were examined for right-turning vehicles at channelized intersections under free-flow conditions. It was found that a linear relationship exists between speed values and the turning radius or the length of the curvilinear section, with the model fitting well to empirical data. This confirms earlier observations from [7]. A less precise model fit was obtained for speed values compared to the available sight distance. Different results regarding driver behavior before making a turn at the considered intersections were presented in [8]. It was found that drivers behave more cautiously when following a preceding vehicle and begin braking significantly earlier than in the case of free-flow conditions. Other research results from [9] suggest that lane traffic density has the greatest influence on the degree of concentration during a right turn and related behaviors.

Studies [10,11] highlight the increased risk for traffic after a signalized intersection when there is insufficient sight distance for left turns, which leads to riskier behaviors, such as leaving the intersection at higher speeds and with shorter gaps between vehicles in the conflict zone. Additionally, [10] demonstrated a correlation between more frequent red-light running for dedicated left-turn lanes and less stable travel trajectories (greater variance in the driving path). In contrast, [12] proved that the longest waiting times for green signal and short green signal periods pose the greatest risk for red-light running.

Speed studies under free-flow conditions have been assessed as riskier due to increased dispersion of gaps between vehicles and higher speeds [13]. This study analyzed driver behaviors using a driving simulator. Regarding safety, the authors of [14] indicated that lane width, intersection density, and traffic volume correlate with a higher frequency of accidents. Besides these factors, greater speed dispersion among vehicles also influences accident risk. Similar conclusions were drawn in [15], highlighting the conflict between safety strategies and traffic efficiency. Another study analyzed behaviors when passing through signalized versus non-signalized intersections [16] and demonstrated that human behavior differs significantly depending on the presence or absence of traffic signals.

Studies of vehicle speeds when entering on a green signal from a stopped queue showed over a 50% decrease in speed when the traffic stream includes a diverse vehicle mix. It was also demonstrated that vehicles moving straight have higher speeds than turning vehicles [17]. Another study indicates that drivers exhibit different behavior patterns depending on their type of multi-track vehicle (light or heavy), even during the approach to the intersection [18]. The results from [19] confirm that motorcyclists also behave differently than car drivers, with an average speed of approximately 3 km/h higher and an operational speed of about 5 km/h greater for motorcycles compared to cars. The likelihood of exceeding the speed limit for this group of users is over three times higher than for drivers of multi-track vehicles.

An important factor affecting vehicle speeds at signalized intersections is the ‘dilemma zone’, where drivers decide whether to stop or proceed during the yellow signal phase [20,21,22,23]. Understanding driver behavior in this zone is crucial for accurately modeling speeds for intergreen time calculations. These studies also show that drivers most often increase speed at the initial onset of the yellow or red signal in under-saturated traffic conditions. A study [24] verified the additional impact of time pressure during simulations of the “dilemma zone.” It was found that this pressure negatively affects drivers, causing them to increase speed and take more risks. Conversely, [25] determined that external factors influencing speed choice are primarily traffic volume, type of signal, vehicle type, and driver gender. Notably, peak hours had almost six times more impact on the risk of exceeding the speed limit. This phenomenon was further commented on in an earlier study focusing on driver age and vehicle type [26]. This study found, for example, that vehicle type does not correlate with different behavior patterns during the onset of the yellow signal, but there is a correlation with vehicle age (the newer the vehicle, the more likely drivers are to enter the intersection during this critical period).

Additionally, devices like signal countdown timers influence these behaviors by providing drivers with information about the remaining time before signal changes [27]. These factors directly impact the determination of appropriate intergreen times to enhance intersection safety. Analyses from this study show that using these devices at signalized intersections significantly increases vehicle speeds. On the other hand, driver behavior while waiting for a green signal was characterized in [28]. It was found that, in the initial period after stopping, over 70% of drivers start using their cell phones, which may cause greater distraction when the green signal begins. The findings of [29] showed that the vast majority of drivers do not comply with the rules regarding mandatory stops before a signalized intersection and permitted right turns. This phenomenon was also confirmed in Poland [30]. Moreover, a study [31] also confirmed improper behaviors of drivers during U-turns, noting that it is a common occurrence in Poland. However, this behavior was found not to lead to a statistically significant increase in accidents.

Different conclusions emerge from studies on improving autonomous transportation (e.g., [32,33,34]). There are also known research results which predict vehicle speeds approaching signalized intersections to optimize traffic signal programs (controlling green signal lengths) [35]. There are also studies where vehicle speed data are continuously processed to optimize traffic signal programs [36]. Simulation results from this study shows that using these data improve traffic efficiency, especially with longer signal cycles.

The review of the state of knowledge shows that many research studies are devoted to vehicle speed through signalized intersections. The main conclusions for further work from the literature review are:

• there is an increased risk of severe accidents at signalized intersections during off-peak periods due to the dispersion of vehicle columns passing through the signalized intersection, while most driver behavior studies were conducted via simulation;
• drivers in dispersed (free-flow) traffic conditions are less likely to follow speed limits, particularly when they are in the so-called dilemma zone (after the onset of the yellow signal);
• the impact of the intersection travel relationship on speed value was shown to depend significantly on the horizontal curve radius.

Hence, it was decided to conduct our research on the impact of intersection-selected geometry factors on empirical speed choice by drivers in free-flow conditions. It is hypothesized that it is possible to more reliably select speed values, e.g., for calculating intergreen times. This should contribute to improving traffic safety during critical phase transitions at signalized intersections, particularly during off-peak periods.

Attention is drawn to the fact that the primary task of a traffic signal program designer is to adhere to road safety principles. The designer creates an intergreen time matrix based on which signals are determined during phase transitions, separating mutually conflicting traffic streams to prevent simultaneous green signals. Numerous articles have already pointed out that the speed parameter used in this calculation procedure for a specific signalized intersection should not be directly dependent on the allowable speed, as driver behaviors are significantly more complex and vary greatly compared to average behaviors [37,38,39]. The authors thus highlight that the intergreen time matrix in phase-based and group-based control will have paramount importance for traffic safety at signalized intersections. Which is why selecting the correct values is crucial.

Despite the fact that, in the analyzed methods in various countries [1,2,3,4,5], the selection of the permissible speed value (i.e., applicable at the intersection approach) is indicated when calculating intergreen times, certain recommendations should also be emphasized. In Germany, Sweden, and the Netherlands, the designer can consider the traffic characteristics at the given approach based on their own experience [2,3,4]. In the United States, the designer should also be guided by the 85th percentile value from the speed distribution on a given road section [5]. These are examples where, in practice, when designing traffic signals, the designer should have knowledge of the actual behaviors of drivers at signalized intersections. In Poland [1], there are currently no such requirements.

Given the identified need for more reliable speed models that account for infrastructure features and actual driver behavior, we hypothesize that:

• A comprehensive model incorporating multiple road infrastructure variables can accurately predict vehicle speeds at signalized intersections.
• Utilizing this model for calculating intergreen times will yield results that significantly differ from current methods used in Poland, potentially enhancing intersection safety.

It is expected that the models will not be highly accurate due to discrepancies in driver behaviors under free-flow conditions. It is suggested that the actual speed values selected, based on the developed dependencies in the traffic signal design procedure, may contribute to increased safety for all users of signalized intersections.

These studies will allow for determining the actual behaviors of drivers during critical traffic control moments, directly affecting safety. It is hypothesized that arbitrarily selecting the allowable speed for intergreen time calculations is inappropriate. The selection of this parameter should consider the more complex specifics of regulated traffic using traffic signals, particularly the speeds of evacuating vehicles on different trajectories.

3. Materials and Methods

The study of vehicle driver behavior was conducted using drones recording video footage over intersections in three cities in Poland: Toruń, Bydgoszcz, and Warsaw. This method enabled the collection of video material capturing natural, unaltered transport behaviors of intersection users (the subjects were not informed about the traffic measurements). In each of these cities, vehicle speeds at signalized intersections were analyzed and classified by the general type of intersection. Three main types of intersections were distinguished according to the methodology used in Poland [40] (Figure 1):

• Simple (I-1): defined as intersections of roads with an accessible surface where collision traffic streams intersect, without traffic channelization elements (with the possible exception of pavement guiding lines).
• Channelized (I-2): at least one of the intersecting roads has a dividing lane, and the main collision plane may or may not have channelization with curbed islands or marked exclusion zones.
• Rotary (I-3): a channelized intersection where the collision area has a central island around which left-turning traffic moves and the road around the island can also serve as a vehicle accumulation area.

All geometric data for the studied intersections and traffic organization were provided by the relevant road management units (including geodetic and digital numerical maps). For data on turning radii, the radius value of the inner radius of the traffic corridor of left or right turning movement was selected. In cases where there were no horizontal markings, the data of left turn movements’ radii were determined arbitrarily as the most probable edge of those traffic corridors.

Vehicle speeds were determined using a proprietary video application [41]. The raw footage from the unmanned aerial vehicle (recordings of 1080 p resolution captured at a 25-fps sample rate) was played back by a specially trained individual who recorded sectional speed measurements. This measurement was conducted solely for passenger cars in undisrupted traffic (only accepted at least 3 s apart from the preceding vehicle while passing through the measurement base). The 3-s headway value was arbitrarily established to eliminate potential interactions between vehicles during the service period under saturated traffic conditions. According to [42], as the duration of the green signal increases and more vehicles are serviced during the saturation period, the standard deviation of headways around the average value increases. This indicates greater variability in driver behavior, justifying the need for a larger time gap to ensure free-flow conditions.

The measurement section as the observation base consisted of the section from the pedestrian crossing at the intersection entrance to the section from the pedestrian crossing at its exit for a specific relation. Speed measurement registration was based on noting the time a specific vehicle passed through the measurement base. The segment length was determined using a digital map of the given intersection along the lane axis. Figure 2 shows the data reading process for a selected intersection in Warsaw. The segment length was determined with an accuracy of 0.1 m, and the travel time with an accuracy of 0.1 s.

The video analyses were conducted by specialists equipped with special software (ver. 1.0.5) allowing real-time retrieval of data in slow-motion (0.5× normal speed). The data were logged in a spreadsheet, giving the captured frame number for each observed vehicle. Knowing the length of travel through the test section, it was possible to calculate the space mean speed to a 1 km/h level of accuracy. All the test sections were located in the main area of signalized intersections having ±3% longitudinal gradients. Steeper intersections were excluded. The average sectional speed error for the entire test range was assumed based on the law of error propagation. The error in the measurement of a car’s time through the measurement base was arbitrarily assumed to be ±0.1 s (i.e., the accepted reaction time of the person analyzing the measurement from the video footage). On this basis, a root mean squared estimation error (RMSE) of ±1.28 km/h was calculated for all tested areas. The authors acknowledge that the semi-automated research method is not as precise as a fully automated method, as shown in [43].

Further data analysis required data loading and organization. The work was carried out using R language (ver. 4.4.1) [44] with the packages of stringi (ver. 1.8.4) [45] and tidyverse (ver. 2.0.0) [46]. A data table was created holding one observation per row, along with the lane and vehicle relation characteristics. For each intersection, lane, turning radius, and movement relation, the lower and upper quartiles were calculated. For each lane, turning radius, and relation, measurements exceeding the range (Q1-1,5·IQR; Q3 + 1,5·IQR) were considered outliers and discarded. The data were then divided into two groups:

• turning relations (left-turn, right-turn, and U-turn);
• straight-through relations.

Separate analysis procedures were adopted for each group. Intersection, lane number, and relation grouped the data. The distribution of measurement data was checked for normality using the Pearson χ² test, with a significance level of 0.05. In most cases, the data conformed to a normal distribution; however, some measurements did not show such conformity. The results of this analysis are presented in

Table 1. The results of the test for fit of the speed measurement results with the normal distribution for the straight-through and turning relations.

City	Straight-Through Relations		Turning Relations
	FALSE	TRUE	FALSE	TRUE
Bydgoszcz	5	1	4	15
Toruń	5	1	3	16
Warsaw	20	95	8	54

. A greater proportion of results conforming to a normal distribution was observed for turning relations compared to straight-through relations. Due to the presence of non-normally distributed results, further analysis used non-parametric methods. The Kruskal–Wallis test was used for comparing two groups, and the Dunn test was used for comparisons among multiple groups. Because of the nonlinear nature of the influence, continuous variables such as lane width, entry width, and longitudinal slope were converted to categorical variables defined by intervals.

For the straight-through relations, the following factors were hypothesized to influence the speed of intersection passage: intersection type (f_it), signal type (f_st), presence of traffic channelization (f_ch), lane width (f_lw), number of lanes (f_nl), cross-section of the approach road (f_csa), approach width (f_aw), longitudinal slope (f_ls), presence of a pedestrian crossing at the entry (f_pc-en), presence of a pedestrian crossing at the exit (f_pc-ex), presence of a bicycle crossing at the entry (f_bc-en), presence of a bicycle crossing at the exit (f_bc-ex), presence of a tram crossing (f_tc), presence of a buildings at the approach road edge (f_b), presence of other obstacles at the approach road edge such as road barriers, fences, trees, etc. (f_oo), and priority regulation (traffic organization signs) at the approach (f_ks).

Regarding the entry marking f_ks, five categories were distinguished based on the signs set up according to the Vienna Convention [47]—marked with sign:

• B-1 “yield”—subordinated approach;
• B-1 and sign D-3—approach to an intersection with widened entries and exits with a central island and circular traffic;
• B-2 “stop”—subordinated approach, compulsory stop before entering the intersection if the traffic signals is not functioning;
• B-3—approach with priority and the main road goes straight;
• B-3 and H-8—approach with priority, but the main road changes direction at the intersection.

For the straight-through, left-, and right-turning relations, a regression model was developed to show the influence of individual variables on the travel speed, in addition to verifying the impact of individual features. The model is a linear regression defined by Equation (1). For categorical variables, the number of variables equals the number of levels of the feature. For the reference value, the coefficient for the variable is 0.

$$v={\beta }_0+\sum _{i=1}^n{\beta }_i{x}_i+{\epsilon }_i$$

(1)

where: v—vehicle speed for all relations, β₀—intercept, x_i—a variable describing a given feature (0 or 1 if a categorical variable), β_i—coefficient for a variable describing a given feature (0 for reference value), and ε_i—model residual value.

For turning relations, an additional factor influencing speed was considered: the turning radius of the vehicle’s trajectory. The study found that, due to model fitting and the nature of the phenomenon studied, the best model includes a logarithmic relationship between speed increase and radius increase. For turning relations, the relation in which vehicles move was also considered, distinguishing left-turn, right-turn, and U-turn relations. The model is a linear regression defined by Equation (2).

$$v_t={\beta }_0+{\beta }_i·\log \left(\rho \right)+\sum _{i=1}^n{\beta }_i{x}_i+{\epsilon }_i$$

(2)

where: v_t—vehicle speed for the turning relations, ρ—radius of the horizontal curve (path of motion), log—natural logarithm, and other variables as mentioned previously.

In further analysis, the significance of individual model coefficients was examined, their confidence intervals were determined, and characteristics describing model quality (R², AIC) were calculated. In the next step, models were evaluated, and linearly dependent variables were eliminated or combined. The variance inflation factor (VIF) was used as a tool to assess variables, describing collinearity in multiple regression models. Subsequently, for the developed model for turning relations, the 0.15 and 0.85 quantiles of prediction estimates were calculated. Simplified regression models for the 0.15 and 0.85 quantiles were then developed, considering only the turning radius.

4. Results

Descriptive statistics of the study results are presented in

Table 2. Descriptive statistics of the study results.

Variables	Bydgoszcz, N = 3452 1	Toruń, N = 3522 1	Warsaw, N = 5779 1
Speed [km/h]	29, [27], /10/, (20; 39)	28, [27], /9/, (19; 37)	43, [43], /14/, (28; 57)
Relation type
straight-through	1269, 37%	1174, 33%	5180, 90%
left-turn	934, 27%	1175, 33%	147, 2.5%
right-turn	1249, 36%	1173, 33%	450, 7.8%
U-turn	0, 0%	0, 0%	2, <0.1%
Intersection type
simple (I-1)	1002, 29%	816, 23%	900, 16%
channelized (I-2)	1053, 31%	1400, 40%	4879, 84%
rotary (I-3)	1397, 40%	1306, 37%	0, 0%
Signal type
direction-only	1167, 34%	1639, 47%	32, 0.6%
general	2285, 66%	1883, 53%	5747, 99%
Radius of the horizontal curve	18, [16], /5/, (12; 25)	25, [25], /12/, (12; 36)	17, [14], /9/, (11; 26)
Lane width [m]
2.75	0, 0%	0, 0%	14, 0.2%
3.00	1580, 46%	1409, 40%	4616, 80%
3.25	233, 6.7%	0, 0%	108, 1.9%
3.30	0, 0%	0, 0%	206, 3.6%
3.50	1639, 47%	2113, 60%	322, 5.6%
3.75	0, 0%	0, 0%	469, 8.1%
4.00	0, 0%	0, 0%	26, 0.4%
5.25	0, 0%	0, 0%	18, 0.3%
Channelized type
none	3452, 100%	3047, 87%	5644, 98%
horizontal marking (traffic closed area)	0, 0%	0, 0%	37, 0.6%
island with curb	0, 0%	475, 13%	98, 1.7%
Number of lanes
2	716, 21%	944, 27%	1031, 18%
3	985, 29%	1397, 40%	3670, 64%
4	1526, 44%	1181, 34%	925, 16%
5	225, 6.5%	0, 0%	153, 2.6%
Cross-section entry type (number of roadways / number of lanes)
(1/2)	1002, 29%	816, 23%	799, 14%
(1/4)	0, 0%	0, 0%	195, 3.4%
(2/2)	2450, 71%	2706, 77%	1126, 19%
(2/3)	0, 0%	0, 0%	3659, 63%
Approach width [m]	11.03, [13.00], /3.23/, (6.00; 14.00)	10.25, [10.00], /2.80/, (6.00; 13.50)	10.02, [9.00], /1.64/, (9.00; 12.00)
Longitudinal slope at approach [%]	0.05, [0.40], /0.89/, (−1.00; 0.60)	0.29, [0.50], /1.19/, (−1.00; 1.40)	−0.20, [−0.20], /0.89/, (−0.80; 0.50)
Trams crossing presence
no	2409, 70%	2694, 76%	4245, 73%
yes	1043, 30%	828, 24%	1534, 27%
Building presence
no	2979, 86%	2934, 83%	4795, 83%
yes	473, 14%	588, 17%	984, 17%
Other obstacles presence
no	2763, 80%	2468, 70%	4320, 75%
yes	689, 20%	1054, 30%	1459, 25%
Traffic organization signs at approach
B-1	716, 21%	934, 27%	1388, 24%
B-1/D-3	1397, 40%	475, 13%	0, 0%
B-2	0, 0%	120, 3.4%	0, 0%
B-3	1339, 39%	1532, 43%	4391, 76%
B-3/H-8	0, 0%	461, 13%	0, 0%
Pedestrian crossing presence
none	0, 0%	239, 6.8%	0, 0%
both	3452, 100%	2926, 83%	4804, 83%
approach only	0, 0%	238, 6.8%	513, 8.9%
exit only	0, 0%	119, 3.4%	462, 8.0%
Bicycle crossing presence
none	1002, 29%	710, 20%	3565, 62%
both	2450, 71%	2110, 60%	871, 15%
approach only	0, 0%	471, 13%	708, 12%
exit only	0, 0%	231, 6.6%	635, 11%

¹ Mean, [Median], /SD/, (15%; 85%); n, %.

. The study covered all traffic movements at the intersections, although the sample size for U-turn movements was small (one lane at one intersection), resulting in a lack of statistically significant results for U-turns, and further investigation in this area was abandoned. Three types of intersections were assessed, which are present in varying proportions in different cities. The lane width ranged from 2.75 to 5.25 m, with lane widths of 3.0 and 3.5 m being the most common. The studied approaches had two to five lanes (the study did not include small intersections with single-lane approaches). The lack of radius data shows vehicle movement in a straight-through relation.

4.1. Straight-Through Movements Only

The results of the Kruskal–Wallis test for dichotomous variables are presented in

Table 3. Kruskal–Wallis test results for two-category variables for the straight-through relation.

Variables	p-Value	Statistical Significance
signal type	<0.01	TRUE
channelized	<0.01	TRUE
tram crossing	<0.01	TRUE
buildings	<0.01	TRUE
other obstacles	0.03	TRUE

. All explanatory variables of this type used in the study exhibited a statistically significant effect on the speed of vehicles moving straight through the intersection.

The results of Dunn’s test for multi-category variables are presented in

Table 4. Dunn’s test results for the tested variables.

Comparison	Z	P.unadj	P.adj	Statistical Significance
Intersection type
I-2–I-3	11.78	<0.01	<0.01	TRUE
I-2–I-1	23.48	<0.01	<0.01	TRUE
I-3–I-1	6.66	<0.01	<0.01	TRUE
Lane width
(2.5, 3]–(3, 3.5]	2.10	0.04	0.11	FALSE
(2.5, 3]–(3.5, 4]	−20.32	<0.01	<0.01	TRUE
(3, 3.5]–(3.5, 4]	−20.42	<0.01	<0.01	TRUE
(2.5, 3]–(4.5, 5.25]	0.59	0.56	1	FALSE
(3, 3.5]–(4.5, 5.25]	0.39	0.7	0.7	FALSE
(3.5, 4]–(4.5, 5.25]	4.16	<0.01	<0.01	TRUE
Number of lanes
2–3	−22.05	<0.01	<0.01	TRUE
2–4	−2.79	0.01	0.01	TRUE
3–4	20.10	<0.01	<0.01	TRUE
2–5	8.20	<0.01	<0.01	TRUE
3–5	16.48	<0.01	<0.01	TRUE
4–5	9.42	<0.01	<0.01	TRUE
Cross-section entry type (number of roads/number of lanes)
(1/2)–(1/4)	−9.47	<0.01	<0.01	TRUE
(1/2)–(2/2)	−13.86	<0.01	<0.01	TRUE
(1/4)–(2/2)	4.29	<0.01	<0.01	TRUE
(1/2)–(2/3)	−23.96	<0.01	<0.01	TRUE
(1/4)–(2/3)	0.61	0.55	0.55	FALSE
(2/2)–(2/3)	−12.16	<0.01	<0.01	TRUE
Approach width
(0, 6]–(12, 15]	−14.07	<0.01	<0.01	TRUE
(0, 6]–(6, 9]	−26.69	<0.01	<0.01	TRUE
(12, 15]–(6, 9]	−16.01	<0.01	<0.01	TRUE
(0, 6]–(9, 12]	−21.56	<0.01	<0.01	TRUE
(12, 15]–(9, 12]	−9.11	<0.01	<0.01	TRUE
(6, 9]–(9, 12]	7.47	<0.01	<0.01	TRUE
Longitudinal slope at approach
(−0.5, 0.5]–(−1.5, −0.5]	17.86	<0.01	<0.01	TRUE
(−0.5, 0.5]–(−2.5, −1.5]	−15.19	<0.01	<0.01	TRUE
(−1.5, −0.5]–(−2.5, −1.5]	−23.73	<0.01	<0.01	TRUE
(−0.5, 0.5]–(−3.5, −2.5]	−0.39	0.69	0.69	FALSE
(−1.5, −0.5]–(−3.5, −2.5]	−2.41	0.02	0.1	FALSE
(−2.5, −1.5]–(−3.5, −2.5]	2.68	0.01	0.05	FALSE
(−0.5, 0.5]–(0.5, 1.5]	8.66	<0.01	<0.01	TRUE
(−1.5, −0.5]–(0.5, 1.5]	−3.07	<0.01	0.02	TRUE
(−2.5, −1.5]–(0.5, 1.5]	18.30	<0.01	<0.01	TRUE
(−3.5, −2.5]–(0.5, 1.5]	1.84	0.07	0.2	FALSE
(−0.5, 0.5]–(1.5, 2.5]	−1.91	0.06	0.22	FALSE
(−1.5, −0.5]–(1.5, 2.5]	−6.48	<0.01	<0.01	TRUE
(−2.5, −1.5]–(1.5, 2.5]	4.82	<0.01	<0.01	TRUE
(−3.5, −2.5]–(1.5, 2.5]	−0.41	0.68	1	FALSE
(0.5, 1.5]–(1.5, 2.5]	−5.01	<0.01	<0.01	TRUE
(−0.5, 0.5]–(2.5, 3.5]	9.47	<0.01	<0.01	TRUE
(−1.5, −0.5]–(2.5, 3.5]	2.03	0.04	0.21	FALSE
(−2.5, −1.5]–(2.5, 3.5]	17.28	<0.01	<0.01	TRUE
(−3.5, −2.5]–(2.5, 3.5]	2.90	<0.01	0.03	TRUE
(0.5, 1.5]–(2.5, 3.5]	3.67	<0.01	<0.01	TRUE
(1.5, 2.5]–(2.5, 3.5]	6.77	<0.01	<0.01	TRUE
Traffic organization signs at approach
B-1–B-1/D-3	−12.92	<0.01	<0.01	TRUE
B-1–B-2	3.40	<0.01	<0.01	TRUE
B-1/D-3–B-2	9.15	<0.01	<0.01	TRUE
B-1–B-3	−41.85	<0.01	<0.01	TRUE
B-1/D-3–B-3	−14.87	<0.01	<0.01	TRUE
B-2–B-3	−16.30	<0.01	<0.01	TRUE
B-1–B-3/H-8	7.62	<0.01	<0.01	TRUE
B-1/D-3–B-3/H-8	13.11	<0.01	<0.01	TRUE
B-2–B-3/H-8	3.16	<0.01	<0.01	TRUE
B-3–B-3/H-8	20.41	<0.01	<0.01	TRUE
Pedestrian crossing presence
both–approach only	−13.63	<0.01	<0.01	TRUE
both–exit only	−12.23	<0.01	<0.01	TRUE
approach only–exit only	1.27	0.2	0.2	FALSE
Bicycle crossing presence
none–both	−7.29	<0.01	<0.01	TRUE
none–approach only	−20.36	<0.01	<0.01	TRUE
both–approach only	−15.28	<0.01	<0.01	TRUE
none–exit only	−12.53	<0.01	<0.01	TRUE
both–exit only	−7.78	<0.01	<0.01	TRUE
approach only–exit only	5.95	<0.01	<0.01	TRUE

. The results include the compared pair of categories, the Z-test statistic value, and the p-value considering multiple comparisons. The last column shows whether there is a statistically significant difference between the data groups.

For the speed model of the straight-through relation only, a rather poor fit to the empirical results was obtained. The small p-value shows that the model is statistically significant. However, the R² value of 0.433 suggests that factors influencing vehicle speed in straight-through relations are not fully accounted for in this model.

4.2. Turning Movements Only

Analogous statistical analyses were performed for this case. The p-value shows that the model is statistically significant. The R² value of 0.617 suggests that the model based on the analyzed variables explains a larger part of the variance in vehicle speeds than the straight-through model.

In the case of turning relations, the model holding more variables explains the dependency of free-flow speed much better than the model holding only the radius dependency. The more complex model has a significantly higher R² value and a lower AIC value. Data for the model based solely on the turning radius value are presented in

Table 5. Summary of speed model dependent only on trajectory radius.

	0.15 Quantile			Mean			0.85 Quantile
Variable	Coeff	95% CI 1	p-Value	Coeff	95% CI 1	p-Value	Coeff	95% CI 1	p-Value
(Intercept)	−3.2	−3.5, −2.8	<0.001	0.38	−0.29, 1.0	0.3	3.9	3.5, 4.2	<0.001
log(radius)	8.1	7.9, 8.2	<0.001	8.0	7.8, 8.3	<0.001	8.0	7.9, 8.2	<0.001

¹ CI = Confidence Interval, bolded p-Values are statistically significant

, with the prediction course and confidence interval shown in Figure 3. This model achieved an R² value of 0.489, and an AIC level of 28,636 for p-value < 0.001. Additionally, calculations for the 0.15 and 0.85 quantiles were included along with the regression model and confidence intervals (Table 5).

4.3. Results for All Relations Model

Additional statistical analyses demonstrated that we achieved a significantly better model fit by employing linear regression dependent on the movement relation through the intersection (straight, left turn, right turn) without incorporating turning radius data. It was found that modeling the speeds of vehicles traversing the intersection based on the type of movement and multiple geometric factors yields better results than models that include the turning radius.

Based on the obtained data regarding the statistical significance of individual variables, the following road infrastructure factors influencing vehicle speed were ultimately selected for further analysis:

• Type of movement at the intersection (straight-through, left turn, right turn);
• Type of intersection and traffic organization at the analyzed approach;
• Type of signal indication provided by the traffic signal (general/permissive or directional/protected) for the given movement;
• Number of traffic lanes at the analyzed approach;
• Type of cross-section of the intersecting road at the analyzed approach;
• Longitudinal slope at analyzed approach;
• Presence and type of a channelizing island for the analyzed movement;
• Presence of bicycle crossings;
• Presence of tram crossings;
• Presence of buildings within less than 10 m from the edge of the roadway at the analyzed approach;
• Presence of other obstacles on the left or right side of the analyzed traffic lane (such as fences, road barriers, trees, or shrubs at the road edge).

All the results of the statistical analysis for the tested model are presented in

Table 6. Summary statistics for model (1) with all relations.

Variable	Coeff	95% CI 1	p-Value
(Intercept)	34	33, 35	<0.001
Type of movement at the intersection
straight-through	0.00	—
left turn	−12	−12, −11	<0.001
right turn	−18	−18, −18	<0.001
Type of intersection and traffic organization
I-1_B-1	0.00	—
I-1_B-2	−0.91	−2.6, 0.74	0.3
I-1_B-3	4.4	3.5, 5.3	<0.001
I-1_B-3/H-8	−1.7	−2.9, −0.56	0.004
I-2_B-1	5.8	4.8, 6.7	<0.001
I-2_B-3	12	11, 13	<0.001
I-3_B-1	3.5	2.0, 5.0	<0.001
I-3_B-1/D-3	13	12, 14	<0.001
I-3_B-3	8.4	6.8, 9.9	<0.001
Signal type
direction-only	0.00	—
general	0.61	0.04, 1.2	0.035
Number of lanes
2	0.00	—
3	0.54	0.05, 1.0	0.030
4	−4.0	−4.6, −3.5	<0.001
5	−6.4	−7.4, −5.4	<0.001
Cross-section entry type
(1/2)	0.00	—
(1/4)	8.4	7.1, 9.7	<0.001
(2/2)	−0.69	−1.4, −0.01	0.047
(2/3)	3.4	2.8, 4.1	<0.001
Longitudinal slope at approach
(−3.5, −1.5]	0.00	—
(−1.5, 1.5]	−2.4	−3.3, −1.5	<0.001
(1.5, 3.5]	−3.1	−4.3, −2.0	<0.001
Channelized type
none	0.00	—
horizontal marking	2.5	−0.29, 5.3	0.079
island with curb	3.4	2.2, 4.7	<0.001
Bicycle crossing presence
none	0.00	—
both	1.9	1.3, 2.4	<0.001
approach only	6.7	6.0, 7.3	<0.001
exit only	4.4	3.8, 5.1	<0.001
Tram crossing presence
no	0.00	—
yes	−1.7	−2.1, −1.3	<0.001
Buildings presence
no	0.00	—
yes	−1.6	−2.1, −1.2	<0.001
Other obstacles presence
no	0.00	—
yes	−2.2	−2.6, −1.8	<0.001

¹ CI = Confidence Interval, R² = 0.647; AIC = 89,458; p-value ≤ 0.001, bolded p-Values are statistically significant.

.

5. Discussion

5.1. Speed Modeling Results

The cities selected for this study vary in size. Warsaw, the capital and largest city in Poland, has over 1.8 million residents. Toruń and Bydgoszcz are medium-sized provincial cities, with populations of approximately 330,000 and 195,000, respectively. These cities also differ in terms of socio-economic development. The study showed variations in the implementation of traffic solutions among these cities. However, statistical tests for individual factors were conducted without distinguishing between cities. This approach aims to obtain results applicable to traffic signal design across the entire country. The influence of a city’s size or the nature of its land use, and perhaps even its degree of socioeconomic development, is a necessary direction for further research. Figure 4 illustrates the differences in speed results for different turning radii classes and for through movements at intersections. The results were analyzed using statistical methods and visualizations of selected speed distribution functions.

The fastest movements at intersections with traffic lights is to drive in a straight-through relation. Left-turning vehicles travel significantly faster than right-turning vehicles, by an average of about 6 km/h. It was further confirmed that this occurs not only because the turning radius for left turns is usually larger (right-hand traffic in Poland), but also because, for the same radius, left-turning vehicles move faster. This is likely due to the wider available maneuvering corridor for left turns, whereas right turns are constrained by the curb along the entire curved section.

For statistical analyses, variables related to intersection type and entry lane signs (traffic organization) were combined as they were interdependent. The reference value was a standard intersection with a minor approach. The highest speed increase occurs at channelized intersections with priority approach and at rotary intersections (up to 12–13 km/h on average). Given the statistically insignificant result of minor intersection approaches with a “stop” sign (B-2), its effect on speed can be ignored. Combining the variables related to intersection type and traffic organization also allowed us to draw further conclusions. Interestingly, higher operational speeds (85th percentile) for straight-through movements are observed at standard intersections compared to those with a central island. Left-turn speeds are highest at channelized intersections (I-2), and right-turn speeds are highest at intersections with a central island (I-3). This is likely due to the “open space” for drivers at channelized intersections, allowing a broader range of turning radii and higher speeds. At large intersections with central islands, right turns follow a relatively large turning radius, resulting in higher speeds. The relationships discussed can be read from Figure 5.

Vehicles move faster during general signal phases compared to protected phases. This may be because general signal phases last longer, allowing vehicles to accelerate and disperse more. Protected signals are often used at geometrically complex intersections with less intuitive traffic organization, prompting slower traversal. This phenomenon was only observed in Bydgoszcz for straight-through movements controlled by directional-only signals.

The number of lanes at an intersection approach and their width also affects the speed selection of drivers (Figure 6 and Figure 7). The research has shown that, relative to two-lane intersection approaches, when drivers travel on an approach with three lanes, they drive slightly faster (for the straight-through relation in particular). In contrast, drivers drive slower on approaches with more than three lanes. It is presumed that this is most likely caused by the greater complexity of traffic organization at the intersection approach (including multi-phase control), which reduces its legibility. Moreover, it is believed that the decrease in speed in the straight-thought movement in cities with such large widths of intersection approaches may be related to the slow movement of vehicle columns near the edge of the roadway, or their stopping and drivers waiting for the green signal in a separate signal phase. The impact may therefore be similar to drivers moving on infrastructure with closely located side obstacles (such as trees, lampposts, buildings, etc.).

The highest speeds were recorded for cross-section (1/4)—an increase of as much as 8 km/h compared to cross-section (1/2). This is the least safe street cross-section, devoid of any separation between opposing streams of vehicles. It has not been used on designed roads for many years, but in cities there are still streets with this geometry. The results of the study also prove that drivers enter an intersection with traffic lights faster from a road with a 2/3 cross-section. On the other hand, it should be noted that the result of comparing the 1/2 road cross-section with the 2/2 cross-section and their effect on the speed of vehicles that enter the intersection approach with traffic lights is inconclusive. However, by making a comparison of speed distributions, it is shown that drivers perform the turning maneuver differently at these analyzed cross-sections of the intersecting road. It seems that this may have to do with the geometric compactness of the intersection surface.

The presence of channelizing islands at the approaches leads to an increase in the speed of moving vehicles. This phenomenon is significantly stronger for through movements (an increase of an average of 3 km/h). This is an unexpected relationship, as it was generally anticipated that the presence of an obstacle close to the lane (in the form of a curb) would encourage drivers to reduce their speed. Perhaps the channelizing island, which enhances clarity and comprehension in trajectory selection for drivers, facilitates movement within the main intersection area to such an extent that the perceived improvement in comfort leads to executing the maneuver through the intersection at higher speeds. For traffic organization using channelizing islands marked solely by pavement markings, as expected, this measure does not contribute to a reduction in the speed of vehicles. This may be attributed, for example, to the lack of consequences for drivers making improper turning maneuvers and driving over the marked surface. This results in increased driver confidence during the turning maneuver, leading to a larger radius of the horizontal arc and, consequently, higher speeds. For drivers going straight-through, invading the horizontal markings has no consequences and at the same time is associated with widening the space available for the driver to pass the intersection. The variable describing channelization type is not significantly related to the organization of traffic at the approach and intersection type.

The analysis omits a division into intersections with the presence of pedestrian crossings. This is because, in cities, many intersections with traffic lights have pedestrian crossings. On the other hand, the study sample represented only one case of analysis (left turn relationship), when drivers did not cross any pedestrian crossings.

In contrast, the situation in Poland is different when it comes to the presence of bicycle crossings. Figure 8 illustrates the distribution of travel speeds through the intersection based on the presence of bicycle crossings. The presence of bicycle crossings, unexpectedly, leads to an increase in speed. This may be related to greater obstacle-free space when there is a bicycle path alongside the roadway or to better pavement quality (a factor not examined) at renovated intersections with bicycle infrastructure. It is noted that bicycle infrastructure in Poland is relatively new, and its introduction is almost always associated with the modernization of the main intersection area. This influences their geometric parameters and the choice of movement trajectories by drivers. Additionally, the presence of a bicycle crossing only at the intersection approach may give drivers greater confidence when passing through the intersection, as they execute the maneuver at higher speeds with no bicycle collisions in the signal phase. This is particularly noticeable for right turns. Such a pronounced effect is not observed when passing through the intersection for left turns. This may be due to the complexity of performing this maneuver. Drivers have a longer approach to the exit and must observe more factors during this approach, including vehicles from the opposing entry. It is also noted that this phenomenon occurs among the fastest-moving drivers (i.e., the 85th percentile of the speed distribution). An interesting observation is that, for turning movements at signalized intersections without bicycle crossings, lower speeds are observed compared to when these road infrastructure elements are present. The authors did not definitively identify the factor responsible for influencing such driver behavior. It was rather expected that in such cases, vehicle speeds would be highest. Perhaps it has to do with the atypical land use around the intersection, which differs from current design standards and current city transportation policies that consider the need to route bicycle paths.

A comparison was made of speeds at the studied intersections depending on the value of the longitudinal gradient. The obtained result in the model shows that drivers on relatively flat terrain drive about 2.5 km/h slower than on a gradient. When driving uphill, the speed drops to about 3 km/h.

Drivers crossing the tram track perform this maneuver at a slower rate of almost 2 km/h. Thus, this phenomenon has been confirmed, as this fact is commonly considered in capacity calculations of intersections with traffic lights.

The presence of buildings close to the road edge (with a boundary assumed at a distance of 10 m from the edge of the outer lane) caused a slight decrease in speed for each movement (by an average of 1.6 km/h). The presence of other obstacles caused a slight reduction in vehicle speeds for through movements (a decrease of 0.82 km/h), and for turning movements, the impact was slightly more noticeable, though still relatively small (a decrease of 1.7 km/h). This situation is illustrated in Figure 9.

5.2. Comparison of Intergreen Time Calculations

Based on the analysis of the developed speed model for all relations (Equation 1), the last step examined its impact on the calculation of intergreen times in Poland. For this purpose, six randomly selected approved traffic signalization projects were used (two intersections for each established intersection type: I-1, I-2, and I-3). These intersections were in the following cities: Chorzów, Gliwice, Łódź, Strawczyn, and Jastrzębie-Zdrój.

For the comparative analysis, the national method of calculating intergreen times was selected, as per [1]. All intergreen time calculation results were compared based on the selection of speed parameters according to the national method and the developed model (1). The national method involves selecting speed values in urban areas equal to the permissible speed limit (typically 50 km/h). This speed is not dependent on geometric features or turning maneuvers.

Table 7. Comparison of the results of the calculations of the intergreen times using the Polish method [1] using the fixed value of the speed limit and the determined value by the model (1).

National Model						Proposed Model
Basic Statistic; N = 980
Min.	1st Qu.	Med.	Mean	3rd Qu	Max.	Min.	1st Qu.	Med.	Mean	3rd Qu	Max.
−4.664	2.176	3.470	3.737	5.143	12.469	−6.454	1.797	4.164	4.267	6.641	16.887
Shapiro-Wilk normality test
W statistic			p-value			W statistic			p-value
0.97023			<0.001			0.99524			0.004
Wilcoxon signed rank test with continuity correction
Tested probe				V statistic				p-value
all intersection types				184,569				<0.001
I-1				667				<0.001
I-2				14,092				0.018
I-3				81,026				0.001
Intraclass Correlation Coefficient
Tested probe				ICC statistic [95% CI1]; F statistic				p-value
all intersection types				0.685 [0.640; 0.724]; 5.55				<0.001
I-1				0.612 [0.367; 0.762]; 4.96				<0.001
I-2				0.719 [0.654; 0.773]; 6.26				<0.001
I-3				0.679 [0.629; 0.722]; 5.38				<0.001
Pearson’s product-moment correlation
Tested probe				R statistic [95% CI1]; t value				p-value
all intersection types				0.722 [0.691; 0.751]; 32.644				<0.001
I-1				0.666 [0.513; 0.778]; 7.467				<0.001
I-2				0.768 [0.714; 0.813]; 19.676				<0.001
I-3				0.714 [0.674; 0.750]; 25.669				<0.001
Spearman’s rank correlation rho
Tested probe				Ρ statistic; S statistic				p-value
all intersection types				0.700; 47,102,835				<0.001
I-1				0.697; 18,874				<0.001
I-2				0.729; 898,333				<0.001
I-3				0.694; 13,062,598				<0.001
Root Mean Squared Error RMSE [s]
all intersection types			I-1			I-2			I-3
2.53			2.67			2.49			2.52

¹ CI = Confidence Interval, bolded p-Values are statistically significant.

presents the results of the statistical significance analysis compared with the calculations using the national method. For this purpose, the Wilcoxon signed-rank test was employed because the data do not follow a normal distribution. Additional analyses were performed by calculating the correlation coefficient, intraclass correlation coefficient, and the root mean square error (RMSE) of the obtained differences. Figure 10 illustrates the analysis results using a Bland–Altman plot with a marked interval of ±1.96 standard deviation values.

Based on the conducted statistical analysis, the following conclusions can be drawn. First, the compared calculation results that used the same method but with different approaches to adopting speed values differed from each other in a statistically significant manner. Second, regardless of the selected intersection type, as well as for the entire sample, approximate values of correlation coefficients were obtained, indicating that the calculation results are similar. Third, the intraclass correlation coefficients indicate good or moderate agreement between both methods for the same phenomenon, despite using different speed parameters. The calculation results are therefore similar but not consistent.

Finally, it is worth noting the mean difference values in the compared calculation results. A value of approximately 2.5 s indicates a large average deviation. This result implies that selecting speeds based on the developed model results in estimating intergreen times on average over 2 s longer. This can also be observed by analyzing the data presented in Figure 10. There are more points in the central part of the graph, where the differences are minimal. Larger differences occur at the extremes, suggesting that the methods are less consistent at higher values of approach and clearance distances of mutually conflicting streams. The difference values in most cases oscillate around zero, suggesting a lack of systematic bias between these methods.

Since this approach is based on observing vehicle speeds at signalized intersections, it may have significant implications for road traffic safety. Therefore, the results may have substantial practical importance.

6. Conclusions

A limitation of the study is that the measurements were conducted on a non-representative group of intersections. The tests were conducted at the training ground with the highest accident rate. In Warsaw, where there are 900 traffic lights, these are particularly above-average intersections, especially when it comes to simple intersections. In Bydgoszcz and Toruń, the relations of turning left, right, and driving straight-through are in quite similar proportions, while in Warsaw as many as 90% of journeys in the study drove straight-through. This is due to both the directional structure of traffic at an intersection and the fact that only vehicles in free traffic were analyzed. Turning maneuvers in Warsaw usually take place with a stop due to very heavy pedestrian or cyclist traffic. Also, the proportion of types of intersections was distorted between cities or by the use of a directional signal (e.g., in Warsaw it is used less frequently). Despite this, interesting results were obtained regarding the dependence of speed on road infrastructure factors. Hence, when conducting further research, it is advisable to include a larger number of cities in the study, a representative sample of intersections, and to ensure that individual features are balanced in the research sample.

Our results are intended to confirm the hypothesis that the selection of a permissible, operational, or design-fixed value of speed as a key parameter for designing a traffic light program may be incorrect. The argument for this approach is informed by the complexity of traffic organization at the approaches of city intersections, which, in the vast majority of cases in Poland, are the most dangerous intersections are not solved by typical and recurring solutions [48,49,50]. In particular, this applies to the disproportion between the speeds of the slowest and fastest moving vehicles. Obviously, the discussed behaviors shown in the set of distributions occurred in the context of crossing the intersection in the straight-through direction. Nevertheless, significant differences in the speed of intersection crossing were also recorded in turning relations. Hence, the evidence resulting from the works of [37,38,39] is confirmed. It is therefore recommended that the design of intergreen times in traffic light programs be conducted with great caution, including depending on road infrastructure factors. This is evidenced by the results of a comparative analysis for the selected six intersections in Poland, from which there can clearly be seen to be a significant difference in the estimation of the final value of the intergreen time using the value of speed depending on the characteristics of the road infrastructure. Thus, both hypotheses from Chapter 2 were confirmed.

In general, it was confirmed that the type of intersection chosen in connection with traffic organization has a significant impact on the choice of driver speed. If a driver is moving along the road with the right of way, he is moving faster. The available space for the driver also has an impact on the increase in speed, both in terms of the number of lanes, the width of the approach, or the type of road cross-section. It is interesting that the increase in speed was also dictated by the presence of a bicycle crossing. On the other hand, the presence of side obstacles next to the road and buildings also have a major impact on the speed reduction values of vehicles both passing through the intersection straight-through and in turning relations.

When designing intersections and signaling programs, it is not possible to consider all of characteristics of vehicles, the psychophysical factors of drivers, or their motivation for travelling. It is necessary to consider the correct average speed value with the required probability which will ensure traffic safety for all users of an intersection with traffic lights. According to the authors, this applies to critical periods of traffic control, i.e., the times of transitions between phases—mainly outside traffic peaks. Therefore, it is suggested to undertake a large research grant to determine the speed of evacuation and access from the potential collision area of streams with unacceptable simultaneous traffic permits.