Representation of Traffic Congestion: A Multicriteria Analysis Approach Based on Distances

Abstract

Traffic congestion in urban areas is a complex phenomenon influenced by various factors. The location of essential city services such as hospitals, schools, shopping centers, and workplaces plays a crucial role in generating vehicular congestion. Additionally, events like traffic accidents, ongoing constructions, adverse weather conditions, and other incidents can have a significant impact on traffic congestion. The representation of traffic congestion through a mathematical model that takes into account the distances be-tween the location of services and traffic incidents makes it possible to characterize the dynamic state of congestion in specific city locations. The contribution of this research is the development of a model that characterizes the level of congestion based on the proximity of city services and traffic events. The proposed mathematical model provides a valuable tool for effectively addressing and mitigating congestion and also enables informed decision making and proactive actions to improve urban mobility.

INTRODUCTION

Traffic congestion is a very common issue in large cities that directly impacts urban mobility and, consequently, the quality of life for residents [19]. As cities grow in size and population density, traffic congestion emerges as an inevitable consequence, influenced by factors such as population density, inadequate urban planning, insufficient road infrastructure, unequal distribution of essential services, and the occurrence of traffic incidents in specific regions [20–22]. It is important to point out that there is a close correlation between traffic congestion and traffic accidents, particularly when an increase in congestion is observed [23].

Several mobility policies have been proposed to address or mitigate this issue for both public and private transportation in urban environments [24]. Several research efforts have contributed to the characterization, classification, and prediction of traffic congestion in large cities, utilizing historical data, crowdsourcing, and real-time sources capturing influential factors in traffic mobility.

Some of the techniques used in research works include machine learning, regression models, artificial neural networks, big data analytics, geographic information systems, transportation network modeling, time series analysis, agent-based traffic simulation, and complex networks, among others [25–29]. The aforementioned computational techniques have used factors such as historical data, daily and special day behavior patterns, weather conditions (rain, snow, temperature), roadwork, demonstrations (road closures), traffic accidents, schedules, individual driver behavior, traffic rules, and common routes [30–32].

Given the constant evolution of factors and variables in vehicular mobility, there is an opportunity for new analyses and the development of models that characterize traffic congestion. This paper introduces a mathematical equation developed through multicriteria analysis methodology that make it explicit the relevance of the distance between traffic congestion point and the location of services and incidents. The relationship between traffic congestion and urbanization is emphasized, highlighting that with increased urbanization, there is a more extensive road infrastructure and a higher probability of incidents [33, 34]. It is important to point out that, in this study, similarity distances were not employed in the data analysis, as detailed in [35]. Instead, the choice was made to use the distance along the route established by the road infrastructure to achieve optimal precision in obtaining distances between traffic, services, and traffic incidents. The measurement of these distances from one point to another was carried out using the application programming interface (API) provided by Geoapify [36].

RELATED WORKS

Several studies in the literature have addressed the issue of traffic congestion and the factors that trigger it. These research works have highlighted the crucial influence of urban planning, road design, traffic management, traffic incidents, driving culture, population density, economic growth, urban expansion, among other aspects, in mitigating or exacerbating traffic congestion. Recently, the perspective has expanded to include technological aspects, such as the implementation of intelligent traffic management systems and the impact of real-time navigation applications. Additionally, real-time data analysis [40] has been conducted regarding the effects of special events, adverse weather conditions, and urban event planning on traffic congestion.

These related works reflect the diversity of approaches and the interconnection of multiple factors that converge to shape the complex reality of traffic congestion. In particular, the work of [8] investigates how various factors influence the severity of collisions on urban highways, highlighting driver gender, pavement conditions, and visibility as significant elements. The work of [9] analyzes temporal and spatial factors as local risks that impact the frequency of traffic accidents and cause traffic congestion. In [10], the issue of bottlenecks in traffic congestion is addressed, proposing a model that incorporates rainfall data as a factor in congestion variability on roads. Nonrecurrent traffic congestion is explored in [11], identifying traffic accidents, especially vehicle collisions, collisions with fixed objects, and rear-end collisions, as influential factors. The research of [12] focuses on the characterization of traffic congestion, considering traffic policies, driving culture, economic aspects, and other factors mentioned by various authors. The built urban environment on roads and its impact on mobility are analyzed in [13]. On the other hand, [14] relates traffic accidents to economic development and the gross domestic product of the city, highlighting the socioeconomic influence on the increase in accidents and, consequently, traffic congestion. For [15], the origin of accidents is analyzed according to temporal distribution, identifying months, days, and hours with higher incidence and congestion. [16] Proposes the characterization of traffic to mitigate congestion, taking the city of Valencia, Spain, as a case study and proposing an equation to characterize travel times. [17] Investigates types of traffic accidents and their topology as determining factors in various levels of congestion. Finally, [18] examines the causes of traffic congestion, classifying them into space-time factors, known empirical causes, and unexplored factors, emphasizing human intervention as a fundamental element in congestion generation.

DEVELOPMENT OF THE MATHEMATICAL MODEL OF ROAD CONGESTION

The methodology proposed for the development of the mathematical model of traffic congestion adopts a systematic multicriteria approach with the aim of developing a robust and effective model. The process is divided into five main stages, starting with the definition of a case study from which data related to traffic, incidents, and services are extracted to form the dataset.

In the second stage, the procedure for obtaining these data is established, while the third stage is dedicated to describing the variables that make up the dataset. The fourth stage involves obtaining distances between the street where traffic occurs, the location of services, and the origin of traffic incidents. Subsequently, the fifth stage focuses on identifying variables that contribute significantly to understanding traffic congestion, especially in relation to distances, using statistical techniques. The selection of variables is based on criteria such as their theoretical relevance, substantial contribution to the system’s variability, and their ability to improve the model’s accuracy.

The sixth and final stage consists of constructing the traffic congestion model based on distances, using the “CRITIC” methodology of multicriteria analysis [38]. This final stage cohesively integrates relevant criteria and factors, applying the “CRITIC” methodology as a robust approach to decision-making in multicriteria analysis within the context of traffic congestion. Following, each one of the five proposed stages of our methodology is presented in detail.

Definition of the Case Study

Mexico City has been designated as the study area in this research work. Mexico City is one of the financial and commercial hubs in the country, hosting a population of 9 209 944 inhabitants and contributing significantly to 3.1% of the annual gross domestic product, according to [1, 2]. In 2022, an increase in travel times in Mexico City was evident, as reported by TomTom’s traffic report [3]. The average duration to cover 10 km experienced an increment of 2 min and 10 sec. This phenomenon correlates with the rise in vehicular density, as indicated by the INRIX Global Traffic 2022 report, ranking Mexico City in the twenty-second position with an average speed of 12 miles per hour [4].

Data Collection Stage

In this research, HERE MAPS [5] was selected as the source for obtaining data related to traffic, traffic incidents, and services. HERE MAPS is a map application that provides real-time detailed information on traffic, traffic incidents, locations, addresses, and points of interest, among other aspects. To obtain data from HERE MAPS, it is necessary to specify the geographic area of interest in the form of a square, circle, or line, without exceeding a specified length in kilometers. Given the irregular ntour of Mexico City, it was divided into its 16 boroughs, and each borough was further divided into four bounding squares. This process resulted in the creation of 64 defined areas used as input for HERE MAPS, with the aim of collecting data on traffic, traffic incidents, and services across approximately 6 708 streets in Mexico City. Parallel programming [39] was implemented to optimize data retrieval and ensure that the collection did not exceed 5 min per request. Data collection took place over a period of four months, from August 1 to November 31, 2023. Data requests were made every 5 min, 24 hours a day, generating a dataset of 156 000 000 records. The capture of this data was performed using a set of Python modules, leveraging the HERE MAPS map application to obtain detailed information about traffic, traffic incidents, and services in Mexico City.

Data Description Stage

The data used in this research corresponds to information linked to traffic, incidents, and services in Mexico City. The specific variables related to traffic are detailed in the following Table 1.

Table 1. . Description of the variables used in the traffic data obtained from [5]

Variable	Description
t1	Bounding box from which the traffic originates.
t2	Length of the segment.
t3	Number of segments contained in the monitored roadway.
t4	The expected speed (in meters per second) along the roadway; it will not exceed the legal speed limit.
t5	Time in minutes, for example, 0:00 hours is minute 0, 0:05 hours is minute 5, 0:10 hours is minute 10, and so on up to 23:55 hours, which is minute 1435.

The captured traffic incidents encompass various events, including accidents, construction works, congestions, disabled vehicles, mass transit situations, demonstrations, road hazards, street closures, adverse weather conditions, and lanes with access restrictions. For a more detailed understanding of the variables associated with these incidents, a comprehensive description is provided in the Table 2.

Table 2. . Description of the variables used in the traffic incidents data obtained from [6]

Variable	Description
i1	Represents the severity of the incident. It has the following values: low – less severe, minor, significant, and critical – more severe.
i2	Describes the type of incident: accident, construction, congestion, vehicle breakdown, weather, among others.
i3	Category of the incident.

The data collected about services located in the vicinity of areas affected by traffic and traffic incidents are detailed in Table 3, which provides information about the variables associated with these services.

Table 3. . Description of the variables used in the service data obtained from [7]

Variable	Description
s1	Bounding box where the service is located.
s2	Refers to the classification of the service.

Obtaining Distances among Traffic, Incidents, and Services

Traffic congestion is a complex phenomenon influenced by multiple variables. In this research, our focus is on analyzing the distances between streets with traffic and the location of services, as well as the point of origin of traffic incidents. This assessment allows us to categorize the traffic state into three levels with factors not previously addressed in the literature: free flow (good), mild congestion (fair), and severe congestion (poor). The calculated distances involved measuring geographic coordinates in terms of meters, seconds, and the number of streets between the start, middle, and end of the street where traffic is monitored in relation to the location of services. Similarly, distances were evaluated between the start, middle, and end of the street in relation to the start, middle, and end of the incident. Ultimately, the distance in meters, seconds, and the number of streets between the start, middle, and end of the incident and the location of services was determined, and the detailed variables are provided in the Table 4 and Table 5.

Table 4. . Variables involved in the determination of distances among traffic, traffic incidents, and services part 1

Variable	Description
d1_d	Distance in meters between the start of the incident and the location of services.
d1_t	Distance in seconds between the start of the incident and the location of services.
d1_nc	Distance in the number of streets between the start of the incident and the location of services.
d2_d	Distance in meters between the middle of the incident and the location of services.
d2_t	Distance in seconds between the middle of the incident and the location of services.
d2_nc	Distance in the number of streets between the middle of the incident and the location of services.
d3_d	Distance in meters between the end of the incident and the location of services.
d3_t	Distance in seconds between the end of the incident and the location of services.
d3_nc	Distance in the number of streets between the end of the incident and the location of services.
d4_d	Distance in meters between the start of traffic and the location of services.
d4_t	Distance in seconds between the start of traffic and the location of services.
d4_nc	Distance in the number of streets between the start of traffic and the location of services.
d5_d	Distance in meters between the middle of traffic and the location of services.
d5_t	Distance in seconds between the middle of traffic and the location of services.
d5_nc	Distance in the number of streets between the middle of traffic and the location of services.
d6_d	Distance in meters between the end of traffic and the location of services.
d6_t	Distance in seconds between the end of traffic and the location of services.
d6_nc	Distance in the number of streets between the end of traffic and the location of services.
d7_d	Distance in meters between the start of the incident and the start of traffic.
d7_t	Distance in seconds between the start of the incident and the start of traffic.

Table 5. . Variables involved in the determination of distances among traffic, traffic incidents, and services part 2

Variable	Description
d7_nc	Distance in the number of streets between the start of the incident and the start of traffic.
d8_d	Distance in meters between the start of the incident and the middle of traffic.
d8_t	Distance in seconds between the start of the incident and the middle of traffic.
d8_nc	Distance in the number of streets between the start of the incident and the middle of traffic.
d9_d	Distance in meters between the start of the incident and the end of traffic.
d9_t	Distance in seconds between the start of the incident and the end of traffic.
d9_nc	Distance in the number of streets between the start of the incident and the end of traffic.
d10_d	Distance in meters between the middle of the incident and the start of traffic.
d10_t	Distance in seconds between the middle of the incident and the start of traffic.
d10_nc	Distance in the number of streets between the middle of the incident and the start of traffic.
d11_d	Distance in meters between the middle of the incident and the middle of traffic.
d11_t	Distance in seconds between the middle of the incident and the middle of traffic.
d11_nc	Distance in the number of streets between the middle of the incident and the middle of traffic.
d12_d	Distance in meters between the middle of the incident and the end of traffic.
d12_t	Distance in seconds between the middle of the incident and the end of traffic.
d12_nc	Distance in the number of streets between the middle of the incident and the end of traffic.
d13_d	Distance in meters between the end of the incident and the start of traffic.
d13_t	Distance in seconds between the end of the incident and the start of traffic.
d13_nc	Distance in the number of streets between the end of the incident and the start of traffic.
d14_d	Distance in meters between the end of the incident and the middle of traffic.
d14_t	Distance in seconds between the end of the incident and the middle of traffic.
d14_nc	Distance in the number of streets between the end of the incident and the middle of traffic.
d15_d	Distance in meters between the end of the incident and the end of traffic.
d15_t	Distance in seconds between the end of the incident and the end of traffic.
d15_nc	Distance in the number of streets between the end of the incident and the end of traffic.

Variable Selection Stage

From an initial dataset comprised of 55 variables described in Tables 1–5, a rigorous selection process was undertaken, focusing attention on those variables with the greatest impact for the analysis. This selection process was based on the application of various techniques, including variable correlation, principal component analysis, and factorial analysis. These techniques allowed the identification and retention of only those variables that demonstrated substantial influence on the structure and dynamics of the dataset. Additionally, the development of a structural equation model was incorporated, providing a more advanced perspective to discern causal relationships and interdependencies among the selected variables, as depicted in Table 6.

Table 6. . Key variables of high relevance according to the techniques employed

Number	Variable	Relevance
1	d7_d	0.87
2	d7_t	0.88
3	d8_d	0.87
4	d8_t	0.88
5	d9_d	0.85
6	d9_t	0.86
7	d10_d	0.88
8	d10_t	0.88
9	d11_d	0.88
10	d11_t	0.89
11	d12_d	0.87
12	d12_t	0.88
13	d13_d	0.87
14	d13_t	0.88
15	d14_d	0.88
16	d14_t	0.89
17	d15_d	0.86
18	d15_t	0.87
19	d1_d	0.73
20	d1_t	0.75
21	d2_d	0.73
22	d2_t	0.74
23	d3_d	0.72
24	d3_t	0.74
25	d4_t	0.72
26	d5_d	0.7
27	d5_t	0.73
28	d6_d	0.7
29	d6_t	0.73

Following a MultiCriteria Approach to Construct the Mathematical Model

To develop the mathematical model that characterizes vehicular congestion in relation to the distances between the traffic street and the locations of services and traffic incidents, we have chosen to employ the multicriteria analysis as the primary methodology in constructing this model, detailed below. The distance between streets experiencing traffic congestion and their proximity or distance in relation to the locations of services and incidents has been taken into account. Eight main processes were proposed in our approach to develop the model. Following, the eight proposed processes are presented in detail.

(a) Develop the decision matrix.

In the process of creating the decision matrix, the alternatives and criteria of utmost relevance were identified as described in Table 6, derived from a dataset addressing aspects related to traffic, incidents, and decision-making services. The matrix was developed using a random dataset comprising 9 100 records (alternatives) with 29 attributes (criteria) of significant impact, as outlined in Table 6. This rigorous matrix construction process translates into rows representing the various considered alternatives and columns encapsulating the different criteria relevant to the traffic dataset, road incidents, and services, as visualized in Fig. 1.

Fig. 1. [Images not available. See PDF.]

Decision matrix for traffic, incidents, and service.

(b) Standardize criteria values across the range.

The normalization of the dataset, encompassing information about traffic, road incidents, and services, was conducted on a scale from 0 to 1 [37], using equation number 1. The purpose of this process was to standardize the data and maintain consistency in the value scale within the same interval. The outcome of this dataset scaling is visually presented in Fig. 2.

1

Fig. 2. [Images not available. See PDF.]

Normalization of the dataset related to traffic, incidents, and services, ranging from 0 to 1 for standardization purposes.

where:

: This is the original variable you want to scale.

: It is the minimum value of x in your dataset. It represents the lowest value the variable x can take.

: It is the maximum value of x in your dataset. It represents the highest value the variable can take.

: This is the scaled or normalized x variable. It’s the result of applying the scaling formula to the original variable x.

(c) Compute the standard deviation for each criterion.

Once the dataset was normalized, the standard deviation for each criterion (each column of the dataset) was computed using equation number 2. In the context of multicriteria analysis applied to the dataset addressing traffic, incidents, and services, the standard deviation has been employed as a vital tool to comprehend the inherent variability in the values of each criterion.

2

where:

: This represents the standard deviation of the jth variable.

: This is the ith observation of the jth variable.

: This is the number of observations or samples.

The outer summation calculates the sum of squared differences between each observation and the mean of all observations for the jth variable .

This represents the square root function, applied to the sum of squared differences.

This is the degrees of freedom correction factor used in the calculation of sample standard deviation.

A broader standard deviation indicates greater dispersion, signifying that values are more distant from the mean. This step proved crucial in assessing the coherence and stability of criteria in the decision-making process, providing a deeper and more accurate insight into the behavior of data related to traffic, incidents, and services. The values obtained for each criterion are displayed in the Fig. 3.

Fig. 3. [Images not available. See PDF.]

Standard Deviation Analysis for Criteria in the Traffic, Incidents, and Services Dataset.

(d) Compute correlation among criteria pairs.

A correlation analysis was conducted among the 29 most relevant variables outlined in Table 6, pairing them to identify the most significant correlations. Equation number 3 was employed for calculating the correlations.

3

Where:

: This represents the correlation coefficient between variables j and k.

: This is the covariance between variables j and k. Covariance measures how two variables vary together.

: This is the standard deviation of variable j.

: This is the standard deviation of variable k.

In the Fig. 4 displays the correlation among traffic, incidents, and services variables obtained through the application of equation number 3.

Fig. 4. [Images not available. See PDF.]

Correlation analysis of the 55 variables in the traffic, incidents, and services dataset.

(e) Determine the weight for each criterion.

To determine the weight of each criterion (each column of the dataset), which involves assigning a weight to each variable in the dataset related to traffic, incidents, and services. This procedure is essential to ensure that different criteria are evaluated appropriately and equitably in the consideration of alternatives. The calculation of the weights for each variable was carried out by applying Eq. 4:

4

where:

Represents a variable or weight associated with .

: Represents a term or factor associated with .

: Represents a value or parameter associated with both and .

: Represents the upper limit of a summation operation.

The expression : Denotes the summation of over the range from k = 1 to n This is a summation operation that iterates over from 1 to n where each term subtracts from 1 and then sums these values.

The results regarding the acquisition of variable weights using Eq. 4 are presented in Table 7.

Table 7. . Highest-impact variables from the traffic, services, and incidents dataset ranked according to their weight

Variable	Weight
d3_d	2.13
d1_d	2.12
d2_d	2.11
d6_d	1.87
d5_d	1.75
d15_d	1.47
d12_d	1.45
d13_d	1.43
d9_d	1.43
d15_t	1.43
d10_d	1.41
d12_t	1.4
d13_t	1.39
d7_d	1.39
d9_t	1.38
d10_t	1.37
d7_t	1.35
d14_t	1.12
d11_t	1.09
d8_t	1.07
d14_d	0.97
d11_d	0.93
d1_t	0.93
d3_t	0.92
d2_t	0.92
d8_d	0.91
d6_t	0.91
d5_t	0.89
d4_t	0.88

(f) Model formulation and evaluation of alternatives.

After accurately determining the weighted values of the most influential variables in the extensive dataset related to traffic, road incidents, and services, the crucial process of model formulation was undertaken. This procedure was meticulously designed following a multicriteria analysis-based approach. The tangible outcome of this analytical process is embodied in Eq. 5, referred to as “roadcongestion” a mathematical expression that encapsulates the dynamics and relationships identified among the variables of interest. Equation 5 is not only the result of rigorous calculations but also serves as a valuable tool for understanding, predicting, and addressing challenges associated with traffic congestion, making a significant contribution to informed decision-making in this domain.

5

With the obtained road congestion model based on distances (“road-congestion”), the evaluation of alternatives was carried out. This process involved substituting distance data in a sample dataset comprising 1000 records using the “road-congestion” model. In Fig. 5 below, an excerpt of the results obtained during this evaluation is presented, offering a partial view of street speeds based on distances from services and road incidents.

Fig. 5. [Images not available. See PDF.]

Street speeds based on distances from services and road incidents obtained from the “roadcongestion” model.

(g) Representation of traffic congestion.

The evaluation of road congestion type on a street was carried out by applying the “roadcongestion” model. For this task, the Jenks classification technique was employed, considering the relationship between speed and congestion factor. In other words, street speed was assessed in relation to the likelihood of experiencing congestion. When the speed is high, the congestion factor tends to be low, whereas in situations of low speed, the congestion factor tends to be high. By applying the Jenks classification technique, also known as the natural breaks optimization method, three distinct classes were obtained to represent levels of traffic congestion. The first class, denoting free flow (considered good), covers a speed range of (1.035216 – 4.816748]. The second class, indicating mild to moderate congestion, falls within a speed range of (4.816748 – 9.668909]. Finally, the third class, representing severe congestion (considered poor), encompasses a speed range of (9.668909 – 20.688506]. This approach provides a detailed classification that effectively reflects the different levels of traffic congestion on the street in question.

(h) Model validation process.

The evaluation of the “roadcongestion” model performance was conducted using various metrics, including MAE (mean absolute error), which provides an average measure of the magnitude of errors, regardless of direction. This is valuable for understanding how close the characterization is to the actual values in absolute terms. MAPE (mean absolute percentage error) expresses errors in relative terms, offering a percentage view of the model’s accuracy, particularly useful for interpreting the significance of errors in the context of actual values. These metrics are crucial for understanding how errors contribute to the overall variability of the model.

These metrics were selected with the aim of gaining a detailed understanding of the quality of the characterization provided by the model obtained in this research, allowing for a comprehensive assessment of its characterization capability. To perform this evaluation, a test dataset consisting of 1000 records was used. The results obtained by applying these metrics are presented in Table 8, providing a quantitative view of the accuracy and effectiveness of the “roadcongestion” model. These indicators allow not only the determination of the model’s quality but also the identification of specific areas where improvements can be made to enhance its predictive performance.

Table 8. . Results of the evaluation of the “roadcongestion” model

Metric	Value
MAE	4.974287
MAPE	50.955931

(i) Comparison of the roadcongesion model with traffic models in the literature.

The “roadcongestion” model proposed in the research presented in this paper has been compared with two well-known models in the literature: speed performance index and congestion factor. The speed reduction index (SRI) measures the degree to which vehicle speed is reduced compared to a reference or ideal speed by comparing the observed real speed with the expected one. Additionally, the congestion factor was used as a reference value to quantify the level of traffic congestion on a road or road network by measuring the impact of congestion on traffic flow and providing an indication of how it affects speed and traffic efficiency. This factor is generally calculated by comparing the real speed of vehicles with the reference or ideal speed. The comparison “roadcongestion” model with speed reduction index (SRI) and congestion factor is detailed in Table 9.

Table 9. . Road congestion model compared to models found in the literature

Number	Model	Expression	Elements	Reference
1	Speed performance índex		It is the average travel speed for the street in km/h. It is the maximum speed allowed on the road, either expected or as a limit.	[41]
2	Speed reduction índex		It is the actual travel speed. It is the free-flow speed.	[42]
3	Congestion factor	JamFactor = TSIMPS/BSIMPS	TSIMPS = traffic speed in meters per second. BSIMPS = base speed in meters per second.	[43]

A dataset of 10  000 records was used, containing the necessary attributes to be substituted into the models presented in Table 8. The data from the dataset were standardized on a common scale between 0 and 1, with the aim of comparing metrics on a uniform basis. The results obtained from the analysis of the 10  000-record traffic congestion dataset indicate that the “roadcongestion” model performs better compared to the SPI and SRI models when evaluated using the metrics MAE (mean absolute error), MSE (mean squared error), and RMSE (root mean squared error). Specifically, the “roadcongestion” model achieved an MAE of 0.216351, indicating that, on average, the model’s predictions are closer to the actual congestion value measured by the JamFactor, compared to other models. It also obtained an MSE of 0.084291 and an RMSE of 0.290329, both significantly lower than those of SPI and SRI, suggesting that “roadcongestion” provides more accurate and consistent predictions compared to reference models. These results highlight the effectiveness of the “roadcongestion” model in predicting traffic congestion, positioning it as a valuable tool for evaluating traffic performance relative to traditional metrics. The results of the comparison of “roadcongestion” with other models are shown in Table 10.

Table 10. . The roadcongestion model compared with speed and traffic congestion models

Metric	roadcongestion	SPI	SRI
MAE	0.216351	0.799567	0.385604
MSE	0.084291	0.691761	0.165546
RMSE	0.290329	0.831722	0.406874

The comparison of the trends of “roadcongestion”, SPI, and SRI in relation to the reference value JamFactor across 10 000 observations is represented by different colors: JamFactor in black, “roadcongestion” in blue, SPI in orange, and SRI in green, as shown in Fig. 6. We observe that the JamFactor value, which serves as a reference for actual congestion, presents significant peaks and fluctuations throughout the observations. It is possible to analyze that the JamFactor value, which serves as a reference for actual congestion, presents significant peaks and fluctuations throughout the observations. The “roadcongestion” model (in blue) appears to more closely follow the trends of the JamFactor, with ups and downs that align more precisely with the peaks of the JamFactor compared to the SPI and SRI models.

Fig. 6. [Images not available. See PDF.]

Comparison of trends between road congestion, SPI, SRI with respect to JamFactor.

On the other hand, SPI (in orange) and SRI (in green) also follow the general trends of the JamFactor, but with less precision and more variation in their values relative to the JamFactor. This is reflected in the fact that both models show less correspondence with the marked peaks and falls of the JamFactor, which may indicate a lesser ability of these models to accurately capture rapid changes in traffic congestion.

RESULTS AND DISCUSSION

The results obtained in developing the “roadcongestion” model based on distances from services and road incidents, employing a variable selection methodology and a multicriteria approach, reveal fundamental patterns and relationships. The correlation between the proximity of relevant services and the occurrence of road incidents emerges as a critical factor in this analysis.

Specific distances were identified that show a significant correlation with elevated congestion levels, allowing an understanding of the direct influence of service locations and the origin of incidents on traffic dynamics. Furthermore, by applying multicriteria analysis, weights were assigned to different criteria, highlighting the relative importance of each variable in the overall assessment of traffic congestion. These results not only establish causal relationships between distances with respect to services and incidents and traffic congestion but also support the model formulation, representing a substantial advancement in understanding and addressing traffic congestion from a multicriteria perspective.

This comprehensive approach, combining careful variable selection and multicriteria analysis application, emphasizes the interconnection of key factors, thus enriching the traffic congestion model based on distances. The identification of specific distances associated with traffic congestion patterns based on their proximity to the location of services and the origin of incidents underscores the need for urban planning that carefully considers the strategic placement of key services to mitigate congestion. During the evaluation of the “roadcongestion” model using MAE and MAPE metrics, encouraging results were observed. When analyzing the model’s performance on each street individually, it was found that error distances are notably low. However, in a global assessment, the model’s accuracy stands at 50%. This fact suggests that while the model shows remarkable effectiveness on some roads, its performance is significantly affected when considering multiple streets. This discrepancy could be attributed to various variables, such as the specific characteristics of the streets or additional factors not considered in the current modeling.

It is crucial to highlight that the overall 50% accuracy assessment should not be interpreted as an intrinsic limitation of the model but rather as an opportunity for continuous improvement. In a prospective approach, there is potential to develop a hybrid model that integrates “roadcongestion” with other well-established models characterizing traffic congestion according to existing literature. This approach can be especially beneficial when considering the complexity and variability of traffic conditions in different urban contexts. Thus, a path for future research emerges to explore the synergy between the “roadcongestion” model and other approaches, aiming to improve overall predictive capacity and more effectively address challenges associated with various street characteristics and variables influencing traffic congestion.

CONCLUSIONS

The identified model named “roadcongestion,” involving the analysis of traffic congestion based on distances from services and road incidents under a multicriteria approach, has provided valuable insights with significant implications for urban planning and traffic management. The identified correlation between the proximity of relevant services and congestion incidence highlights the critical importance of strategically locating services in traffic dynamics.

The identification of specific distances with significant correlations emphasizes the need to carefully consider urban design and service distribution to mitigate traffic congestion. The application of multicriteria analysis, with weighted variable assignments, has allowed for a more holistic evaluation of traffic congestion. By highlighting the relative importance of each criterion, this approach provides a solid foundation for prioritizing traffic management interventions and strategies. The integration of impactful variable selection methodology has enriched understanding by revealing the complexity and interconnection of key factors contributing to traffic congestion. In summary, this study makes a significant contribution to the fields of mobility and urban planning by providing a combination of methodologies resulting in a traffic congestion model instrumental for decision-making in the realm of traffic congestion. The conclusions drawn from this multicriteria approach serve as a basis for future research and practical actions aimed at improving urban mobility and optimizing road infrastructure.

FUNDING

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

CONFLICT OF INTEREST

The authors of this work declare that they have no conflicts of interest.

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

AI tools may have been used in the translation or editing of this article.

REFERENCES

1 Jarmuz, D.; Chmiel, J. A review of approaches to the study of weather’s effect on road traffic parameters. Transport Probl.; 2020; 15, pp. 241-251. [DOI: https://dx.doi.org/10.21307/tp-2020-063] 1527.14084

2 INEGI, Instituto Nacional de Estadística y Geografía. https://www.inegi.org.mx/app/areasgeograficas/?ag=09#collapse-Resumen. Accessed Dec. 08, 2023.

3 TomTom, Tomtom Traffic Index. https://www.tomtom.com/traffic-index/mexico-city-traffic/. Accessed December 8, 2023.

4 Pishue, B., INRIX Global Traffic Scorecard, INRIX. https://inrix.com/. Accessed December 8, 2023.

5 Here Maps. https://www.here.com/docs/bundle/traffic-api-developer-guide-v7/page/topics/concepts/flow.html. Accessed December 11, 2023.

6 Here Maps. https://www.here.com/docs/bundle/traffic-api-developer-guide-v7/page/topics/concepts/incidents.html#incidents. Accessed December 11, 2023.

7 Geoapify, Geoapify Location Platform. https://apidocs.geoapify.com/docs/places/#categories. Accessed December 11, 2023.

8 Wang, K.; Feng, X.; Li, H.; Ren, Y. Exploring influential factors affecting the severity of urban expressway collisions: a study based on collision data. Int. J. Environ. Res. Public Health; 2022; 19, 8362. [DOI: https://dx.doi.org/10.3390/ijerph19148362] 1426.90035

9 Wang, W., Yuan, Z., Yang, Y., Yang, X., and Liu, Y., Factors influencing traffic accident frequencies on urban roads: a spatial panel time-fixed effects error model, PloS One, 2019, vol. 14, no. 4, p. e0214539. https://doi.org/10.1371/journal.pone.0214539

10 Yao, Y.; Wu, D.; Hong, Y.; Chen, D.; Liang, Z.; Guan, Q.; Liang, X.; Dai, L. Analyzing the effects of rainfall on urban traffic-congestion bottlenecks. IEEE J. Select. Top. Appl. Earth Observ. Remote Sens.; 2020; 13, pp. 504-512. [DOI: https://dx.doi.org/10.1109/jstars.2020.2966591] 1481.74244

11 Zheng, Z., Wang, Z., Zhu, L., and Jiang, H., Determinants of the congestion caused by a traffic accident in urban road networks, Anal. Prevent., 2020, vol. 136, p. 105327. https://doi.org/10.1016/j.aap.2019.105327

12 Almeida, A., Brás, S., Sargento, S., and Oliveira, I., Exploring bus tracking data to characterize urban traffic congestion, J. Urban Mobil., 2023,vol. 4, p. 100065. https://doi.org/10.1016/j.urbmob.2023.100065

13 Nian, G.; Sun, J.; Huang, J. Exploring the effects of urban built environment on road travel speed variability with a spatial panel data model, Int.. J. Geo-Inf.; 2021; 10, 829. [DOI: https://dx.doi.org/10.3390/ijgi10120829] 07459735

14 Li, X.; Wu, L.; Yang, X. Exploring the impact of social economic variables on traffic safety performance in Hong Kong: A time series analysis. Safety Sci.; 2018; 109, pp. 67-75. [DOI: https://dx.doi.org/10.1016/j.ssci.2018.05.010] 0874.35040

15 Ma, Q., Huang, G., and Tang, X., GIS-based analysis of spatial-temporal correlations of urban traffic accidents, Eur. Transp. Res. Rev., 2021, vol. 13, no. 1. https://doi.org/10.1186/s12544-021-00509-y

16 Zambrano-Martinez, J.; Calafate, C.; Soler, D.; Cano, J.-C.; Manzoni, P. Modeling and characterization of traffic flows in urban environments. Sensors (Basel, Switzerland); 2018; 18, 2020. [DOI: https://dx.doi.org/10.3390/s18072020] 1191.68029

17 Briz-Redón, Á., Martínez-Ruiz, F., and Montes, F., Identification of differential risk hotspots for collision and vehicle type in a directed linear network, Anal. Prevent., 2019, vol. 132, p. 105278. https://doi.org/10.1016/j.aap.2019.105278

18 Wang, M., Yan, H., Sui, H., Zuo, F., Liu, Y., and Li, Y., Learning to discover causes of traffic congestion with limited labeled data, Proc. 28th ACM SIGKDD Conf. on Knowledge Discovery and Data Mining, Washington, 2022.

19 Wang, P.; Zhang, R.; Sun, S.; Gao, M.; Zheng, B.; Zhang, D.; Zhang, Y.; Carmichael, G.R.; Zhang, H. Aggravated air pollution and health burden due to traffic congestion in urban China. Atmos. Chem. Phys.; 2023; 23, pp. 2983-2996. [DOI: https://dx.doi.org/10.5194/acp-23-2983-2023] 07955128

20 Tranter, P.; Tolley, R. Slow Cities; 2020;

21 Mondal, S. and Gupta, A., Speed distribution for interrupted flow facility under mixed traffic, Phys. A, 2021, vol. 570, p. 125798. https://doi.org/10.1016/j.physa.2021.125798

22 Sun, C.; Pei, X.; Hao, J.; Wang, Y.; Zhang, Z.; Wong, S.C. Role of road network features in the evaluation of incident impacts on urban traffic mobility. Transp. Res. Part B: Methodol.; 2021; 117, pp. 101-116. [DOI: https://dx.doi.org/10.1016/j.trb.2018.08.013] 1497.68085

23 Albalate, D.; Fageda, X. On the relationship between congestion and road safety in cities. Transp. Policy; 2021; 105, pp. 145-152. [DOI: https://dx.doi.org/10.1016/j.tranpol.2021.03.011] 1321.90029

24 Zhang, K.; Nie, Y. Mitigating traffic congestion induced by transportation network companies: A policy analysis. Transp. Res. Part A, Policy Pract.; 2022; 159, pp. 96-118. [DOI: https://dx.doi.org/10.1016/j.tra.2022.01.017] 1530.45010

25 Anjaneyulu, M.; Kubendiran, M. Short-term traffic congestion prediction using hybrid deep learning technique. Sustainability; 2022; 15, 74. [DOI: https://dx.doi.org/10.3390/su15010074]

26 Rodríguez-Rueda, P.J.; Turias-Domínguez, I.J. A comparison between artificial neural networks and classical methods for predicting mobility between transport zones, Pract. Appl. Campo de Gibraltar, Spain. Dyna.; 2017; 84, pp. 209-216. [DOI: https://dx.doi.org/10.15446/dyna.v84n200.56571] 1514.76062

27 Rojas, E. and Uriel Cortes, C., Artificial neural networks and traffic data analysis in the Zipaquirá-Palenque road corridor, Cienc. Lat. Multidiscipl. Sci. Mag., 2022, vol. 6, no. 6. https://doi.org/10.37811/cl_rcm.v6i6.4162

28 Sánchez Gonzalez, S.; Bedoya-Maya, F.; Calatayud, A. Understanding the effect of traffic congestion on accidents using big data. Sustainability; 2021; 13, 7500. [DOI: https://dx.doi.org/10.3390/su13137500] 1490.65321

29 Sálazar-Carrillo, J.; Torres-Ruiz, M.; Davis, C.A.; Quintero, R.; Moreno-Ibarra, M.; Guzmán, G. Traffic congestion analysis based on a web-gis and data mining of traffic events from twitter. Sensors (Basel: Switzerland); 2021; 21, 2964. [DOI: https://dx.doi.org/10.3390/s21092964]

30 Albalate, D.; Fageda, X. Congestion, road safety, and the effectiveness of public policies in urban areas. Sustainability; 2019; 11, 5092. [DOI: https://dx.doi.org/10.3390/su11185092] 1497.92304

31 Tang, W.; Chen, J.; Sun, C.; Wang, H.; Li, G. Traffic demand estimations considering route trajectory reconstruction in congested networks. Algorithms; 2022; 15, 307. [DOI: https://dx.doi.org/10.3390/a15090307] 1413.62051

32 Navarro Arredondo, A. Control of air pollution in the Metropolitan Area of the Valley of Mexico, Demogr.. Urban Stud.; 2019; 34, pp. 631-663. [DOI: https://dx.doi.org/10.24201/edu.v34i3.1806] 1416.82014

33 Paucara Rojas, M.; Avilés Córdova, S.E.; Huaquisto Cáceres, S. Use of microsimulation for the study of vehicle traffic on urban roads. Res. Develop.; 2023; 23, pp. 67-77.

34 Urbina Cantuta, C.M.; Torres Flores, A.J.; Salazar-Calderón Juárez, R. Optimization of vehicular flow at the road intersection of av. Bolognesi and av. gustavo pinto in the city of Tacna. Eng. Res.; 2019; 1, pp. 65-71. [DOI: https://dx.doi.org/10.47796/ing.v1i1.123]

35 Similitud, disimilitud y distancia. https://ciespinosa.github.io/Similitud/similitud-disimilitud-y-distancia.html. Accessed Dec. 23, 2023.

36 Maps, APIs and components. https://www.geoapify.com/. Accessed Dec. 10, 2023.

37 Izonin, I.; Tkachenko, R.; Shakhovska, N.; Ilchyshyn, B.; Singh, K.K. A two-step data normalization approach for improving classification accuracy in the medical diagnosis domain. Mathematics; 2022; 10, 1942. [DOI: https://dx.doi.org/10.3390/math10111942] 07659462

38 Dolan, J.G. Additive multicriteria decision analysis models are not misleading aids for life-critical shared decision making. Med. Decis. Making: Int. J. Soc. Med. Decis. Making; 2019; 39, 721. [DOI: https://dx.doi.org/10.1177/0272989x19870162] 1507.26028

39 Korneev, V.V. Parallel programming. Program. Comput. Software; 2023; 49, pp. 310-324.4621581[DOI: https://dx.doi.org/10.1134/s0361768823040084] 1533.68005

40 Kuznetsov, S.D.; Velikhov, P.E.; Fu, Q. Real-time analytics: benefits, limitations, and tradeoffs. Program. Comput. Software; 2023; 49, pp. 1-25. [DOI: https://dx.doi.org/10.1134/s036176882301005x] 1525.14023

41 Chen, Y.; Chen, C.; Wu, Q.; Ma, J.; Zhang, G.; Milton, J. Spatial-temporal traffic congestion identification and correlation extraction using floating car data. J. Intellig. Transp. Syst.; 2021; 25, pp. 263-280. [DOI: https://dx.doi.org/10.1080/15472450.2020.1790364] 1546.62839

42 Rao, Mohan. A. and Ramachandra Rao, K., Measuring urban traffic congestion – a review. Int. J. Traffic Transp. Eng.; 2012; 2, pp. 286-305. [DOI: https://dx.doi.org/10.7708/ijtte.2012.2(4).01] 1235.62086

43 Here Maps, HERE SDK for iOS (Navigate Edition) – Developer Guide. https://www.here.com/docs/bundle/sdk-for-ios-navigate-developer-guide/page/topics/routing.html#find-traffic-along-a-route. Accessed Jan. 20, 2023.