Dynamic congestion pricing for traffic management and air quality in a real world Italian road corridor

Abstract

Dynamic congestion pricing is emerging as a potential approach to contemporarily manage traffic congestion and air quality. However, most toll road pricing strategies tend to rely on traditional solutions such as fixed or variable pricing, leading to suboptimal results in terms of traffic demand or pollution. In this paper, we propose a dynamic congestion pricing algorithm enabling to deal with both traffic congestion and PM2.5 levels reduction. Through a case study based on the SS36 road corridor connecting Milan to Bormio, we show that the proposed approach activates an extra toll fee on 28.26% of observations in 2022, leading to a total charge cost of 14.9€ million. This approach determines a reduction in road traffic density equal to 11.2%, contributing to a percentage drop of PM2.5 levels equal to 0.01%. The results remain robust across alternative specifications, including sensitivity analyses on air quality and traffic speed thresholds, as well as demand price elasticity assumptions. Overall, the paper shows that the dynamic congestion pricing strategy may provide insights for policymakers aiming to target both air quality and traffic management issues.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-56655-7.

Introduction

In the contemporary landscape, traffic congestion has emerged as a paramount problem not only for travel efficiency but also for environmental sustainability and urban livability. Occurring when the volume of vehicles surpasses the route’s capacity, leading to reduced flow speed and increased crowding, traffic congestion represents a significant burden with relevant socio-economic and environmental impacts: increased greenhouse gas emissions, deterioration of air quality with a consequent rise in disease incidence, and greater travel time and uncertainty, affecting both individual mobility and freight transportation^{1, 1, 2, 3, 4}. Additionally, traffic is often associated with a higher risk of accidents than free-flow traffic⁵.

Among the various strategies proposed to tackle traffic congestion and its related externalities, congestion pricing has emerged as a promising tool within the broader framework of sustainable and integrated transport planning. It consists of a set of mechanisms designed to influence drivers’ behaviors by imposing fees for the use of road infrastructure. Congestion pricing aims to reduce traffic congestion by diverting drivers towards less crowded routes or promoting alternative more sustainable modes of transportation, like public transit or bicycles, aligning with transformative innovations in transport management¹. Several studies have contributed to discussing alternative technologies and methodologies to optimize congestion pricing and mitigate traffic bottlenecks^{6, 7, 8, 9, 10}. At the same time, such theoretical approaches have been tested through real-world applications proliferating across different countries during the last few years. Notable examples include the London Congestion Charge (LCC), Milan’s Area C, Singapore’s Electronic Road Pricing (ERP), the United States’ Managed Lanes, and the Stockholm Congestion Charge^{11, 12, 13, 14, 15, 16, 17}.

Fixed and variable pricing strategies have initially emerged as the main approaches to managing traffic congestion. More recently, the possibility to retrieve and exploit real-time data about traffic has driven the emergence of innovative and more advanced congestion pricing strategies like dynamic pricing, which leverages big data to apply real-time toll adjustments in response to traffic conditions¹⁸. However, existing applications, relying on dynamic pricing strategies, are still not widely implemented due to complex algorithm development^{19, 20, 21, 22}. Consequently, most extant studies tend to rely on fixed or variable pricing techniques, that are easier to implement, as they rely on constant tolls, or fees changing in a predefined way, although they may imply suboptimal results in terms of traffic management²³.

In addition, in terms of tolling system design for congestion pricing policy, existing contributions have mainly focused on the optimization of traffic variables, without taking into account the impact that such approaches may also have in terms of traffic-related environmental externalities concerning the reduction of air pollutants concentration^{24, 25}. Therefore, additional research seems required to integrate environmental variables in the congestion pricing process and design solutions, aiming to achieve an optimal trade-off between traffic management and environmental outcomes in terms of air pollution.

Against this background, this paper aims to fill these gaps and to contribute to the ongoing debate on sustainable urban mobility by investigating the feasibility of exploiting dynamic pricing for integrating an environmental management component into traffic-optimizing congestion toll pricing. In particular, the paper aims to answer two research questions:

• RQ1: Can a congestion pricing strategy dynamically respond to both traffic and environmental triggers?

• RQ2: What is the impact of such a pricing strategy in terms of traffic flow and air quality optimization?

To explore the congestion pricing approach, our study focuses on the Italian context and, in particular, on the SS36 road corridor, that links Milano to relevant industrial districts, such as Monza and Lecco, and highly touristic places, like Como Lake and Bormio. More specifically, we focus on the segment from Sesto San Giovanni to Carate/Verano Brianza, as it represents a vital link for the Winter Olympic Games “Milano-Cortina 2026”. This application represents a pilot study on a limited road segment, aimed at testing the feasibility of the proposed framework. This area is already facing congestion and air quality issues which are likely to further increase, due to the expected increase in volume of users. Hence, it provides a relevant setting to test congestion pricing techniques integrating traffic management and environmental variables.

To assess the effectiveness of the proposed strategy, we compare a scenario simulating traffic levels and air quality after the implementation of our congestion pricing approach with the as is scenario, based on real observed data in 2022 when congestion pricing was not applied. The no-congestion pricing scenario revealed significant challenges in the area. A noteworthy percentage of observations (38.7%) surpassed the PM2.5 EU imposed threshold, underscoring the urgent need for environmental intervention, especially in the context of the European Commission’s 2030 PM2.5 reduction goals²⁶. Simultaneously, traffic speed falls below the set threshold equal to 75 km/h (13.55% of total observations), suggesting a frequent saturation of the SS36 road in terms of traffic flows.

In the simulated scenario, tolling was active for 28.26% of the analyzed period, triggered by both environmental and traffic conditions. The average charge over the entire observation horizon was approximately €1.2; however, when considering only the time intervals in which the toll was effectively applied, the average charge increased to €4. This resulted in a Total Charge Cost (TCC) of €14.9 million, where TCC represents the actual cost borne by citizens for the use of the road infrastructure over the considered time horizon. The results indicate that the dynamic pricing mechanism activates charges conditionally on observed traffic and environmental thresholds, thereby potentially reducing the likelihood of applying charges during low-demand periods compared with fixed or variable pricing strategies. For instance, the month of August, marked by improved air quality due to business closures for summer holidays and lower traffic intensity resulting from fewer daily commuters, did not experience any active charging. Additionally, the reduction in road density averaged 11.2% over the entire observation period; however, when considering only the intervals in which the toll was active, the reduction increased to 38%. This decrease in traffic density corresponded to an average reduction in PM2.5 concentrations of 0.01% across all periods, rising to 0.04% when limited to tolling periods only. In addition, we test the robustness of the proposed framework through sensitivity analyses on key policy parameters, including air quality thresholds, traffic speed targets, and traffic demand elasticity to pricing.

Overall, this study contributes to the literature by providing a data-driven simulation of a dynamic congestion pricing scheme that incorporates an environmental management component within a framework traditionally focused on traffic variables. While the estimated environmental effects are modest in magnitude, the proposed approach illustrates how environmental indicators can be structurally integrated into congestion pricing mechanisms. In this sense, it may inform the design of policy tools aimed at jointly addressing traffic management and air quality concerns. This is particularly relevant in the context of the European Union’s more stringent PM2.5 regulations, and considering the United Nations’ 11th Sustainable Development Goal, which focuses on building sustainable cities.

This paper is structured as follows: “Research background” frames our case study within extant literature on congestion pricing models. “The congestion pricing model” describes the data and methods that we use in our empirical analysis. “Data” shows our main results, while the paper concludes by highlighting the main value-added of this research.

Research background

Congestion pricing strategies tend to differ in terms of policy objectives^{13, 24} and pricing strategy^{6, 24}. Congestion pricing strategies could also be different in terms of the scheme structural conformation, referring to the type of geographical area that is under investigation for the application of the congestion pricing policy. Current literature distinguishes between facility-based, cordon, and zonal pricing schemes. Considering that the selected structural conformation strictly depends on the geography, location, and road infrastructure of the area where the toll is to be imposed, and is not a key element directly decided by the policy maker, in our paper we focus on the optimization of the congestion pricing policy in terms of policy objectives (aiming to integrate both traffic management and environmental targets) and pricing strategies (pointing to implement the most advanced approach, e.g., dynamic pricing).

First, policy objectives refer to the expected outcomes of the policy, which in the case of congestion policies are generally related to traffic management and environmental impact reduction. However, traffic management is a policy objective often directly addressed, with traffic levels acting as fee-triggering, and charges reflecting traffic behavior. Conversely, environmental impacts tend to be considered only indirectly, as a result of the reduction of traffic level, without the explicit inclusion of environmental-related variables in the majority of congestion pricing models^{27, 24, 25}.

The pricing strategy constitutes the logic adopted to change the toll price to reduce traffic congestion. Fixed, variable, and dynamic pricing strategies could be developed⁶. The pricing strategy is defined by the policy maker, consistently with the specific contextual background and targeted policy objectives. Indeed, the choice of pricing strategy determines the fee-triggering process and, thus, how the policy copes with external factors to reach its objectives.

A fixed pricing strategy consists of charging a constant toll throughout the designated charging periods. It is cost-effective due to the minimal algorithmic development time, but it can lead to inefficiencies in terms of traffic management^{28, 29, 30}. A variable pricing strategy involves tolls varying in a predefined way over the charging time spans. This method efficiently deals with predictable traffic behavior but requires in-depth traffic studies^{31, 30}. However, it is not optimal when confronted with unpredictable traffic dynamics, e.g., incidents²⁴. Finally, a dynamic pricing strategy adapts tolls in real-time, or almost real-time, based on current conditions. It can capture both predictable and unpredictable traffic behavior⁶, making it the most efficient strategy^{22, 32}. Nonetheless, due to implementation challenges related to complex and costly algorithm design and time-consuming implementation, it is not widely adopted, yet.

In this paper, we focus on congestion policies that explicitly aim at pursuing both traffic management and environmental outcome targets, calling for the direct inclusion of environmental variables as triggers in the congestion pricing strategy³³. This requires a coherent design of the other policy elements³⁴. In particular, in fixed and variable pricing strategies, environmental variables cannot play the same fee-triggering role as traffic variables. Although traffic behavior is partially characterized by a predictable component (e.g., daily peak hours), environmental variables, (e.g., air quality) cannot be forecasted with the same certainty as many exogenous factors (e.g., weather, wind, and global radiation, and their fast-changing rate) influence environmental variables. Conversely, the responsive nature of dynamic pricing allows the design of congestion pricing strategies that incorporate both traffic and environmental variables in the fee-triggering process.

In the next sections, we propose a congestion pricing model aiming to integrate both traffic management and environmental variables. The model is then applied to a case study referred to as the SS36 road (facility-based structural conformation) in Lombardy. In this way, we aim to fill a gap in the Italian research landscape that is still lacking real-world studies on dynamic congestion pricing policies taking into account both traffic management and environmental targets.

The congestion pricing model

The proposed model aims to describe the logic adopted to compute the road toll in real-time as a function of the current level of PM2.5 and traffic flow speed as shown in Fig. 1.

Fig. 1.

The congestion pricing algorithm logic.

The pricing strategy first requires establishing baseline thresholds for traffic and environmental metrics. In this application, the environmental threshold is set equal to the limit imposed by the European Commission: 25 µg/m³. The 85th percentile speed, commonly referenced in literature as the safe operating speed^{35, 36}, is used as a traffic threshold equal to 75 km/h. This provides flexibility to adjust the traffic threshold in response to environmental requirements. Additionally, it prevents the establishment of an overly low traffic baseline, which could compromise throughput efficiency.

The road toll is determined based on the following algorithm:

• Environmental threshold comparison: The first step consists of comparing the level of PM2.5 measured in the period t − 1 with the environmental threshold. This step serves to set the traffic threshold for the period t. If PM2.5_t−1 ≤ 25 µg/m³, there is no need for environmental management in the following period and the speed threshold remains aligned to the baseline one (75 km/h). Conversely, if PM2.5_t−1 > 25 µg/m³, a new traffic threshold is computed based on the Environmental Congestion Pricing Effect Forecasting Model (ECPEFM, see Sect.  3.1.1 for further details).

• Traffic threshold comparison: The traffic threshold for period t should be compared with the average flow speed in period t − 1. If the threshold is below the current speed, no charge is applied. Instead, if it is above, the necessary decrease in road density to reach the desired flow speed is computed through the Traffic Behavior Model (TBM, see Sect.  3.1.2 for further details). This method is based on the critical assumption that traffic demand remains constant over small, discrete time intervals unless targeted measures are implemented. Thus, the previous period’s demand is used to determine the desired change in traffic.

• Tolling charge computation: Finally, the desired percentage reduction in road density is compared with the Price Elasticity Table (PET, see Sect.  3.1.3 for further details) to identify the charge to be applied in period t. Furthermore, a constraint of ±€1.5 is imposed on charges between two consecutive periods. This restriction relies on the idea that the pricing to be influential towards travelers’ choices must be known in advance. This limitation serves to mitigate the level of volatility between consecutive periods, providing drivers with a reasonably accurate estimate of the impending charges. However, if the previous period had a charge equal to zero, then no inferior boundary exists, while the superior equals €3.5. This number comes from summing €1.5 to the minimum acceptable charge, namely €2. The minimum charge of €2 was defined in relation to existing public transport fares within the area of study. As of September 2023, comparable trips, such as a train ride from Sesto San Giovanni to Carate Brianza or a bus ride from Monza to Milan, cost €2.60, while shorter extra-urban trips within Monza were priced at €2.20. In addition, alternative modes of transport (e.g., private car use) entail further costs like fuel and parking, often exceeding €2.50 per trip on average. A €2 charge therefore remains competitive while still reflecting a realistic lower bound of user costs.

These steps are to be performed at the beginning of each period to determine the tolling price. To conclude, a pseudocode is reported to enhance understandability.

The congestion pricing policy input models

In this section, we describe the ECPEFM, TBM, and PET which are models providing key inputs for the congestion pricing policy.

The environmental congestion pricing effect forecasting model

The Environmental Congestion Pricing Effect Forecasting Model aims at determining the level of PM2.5 associated with a certain level of traffic speed, based on a Multiple Linear Regression model (MLR):

1

is the observed level of pollutant concentration at time t, is the average traffic speed at time t, and is a vector accounting for a set of control variables that may affect the PM2.5 level. First, the control variables include certain meteorological factors, i.e., wind intensity^{37, 38}, relative humidity^{39, 40, 38} cumulative precipitation^{41, 42}, and hydrometric level⁴³. Second, the level of PM2.5 might be affected by the presence of other pollutants^{44, 38} and by its past levels, due to the persistence of emissions in the atmosphere depending on many variables like the size of street buildings, the amount of landscaping⁴⁵. For this reason, the control variables include the lagged values of NO2, NOx, CO, and PM2.5. Third, the level of PM2.5 might be influenced by cycles related to seasonality patterns^{46, 47, 48}. Consequently, time categorical variables representing the month to which each observation is referring are considered.

To assess the robustness of the ECPEFM, we also estimated alternative model specifications including non-linear terms, extended lag structures, and interaction effects between traffic speed and the wind speed. The comparison across these alternative formulations was conducted by jointly considering goodness-of-fit and model parsimony indicators, namely the adjusted , Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC).

Traffic behavior model

The Traffic Behavior Model assesses the relationship between traffic speed and traffic density (representing a proxy of road infrastructure demand) through a time-invariant function based on Greenshield’s Macroscopic Stream Model. Assuming homogeneous vehicle dimensions, the generalized model equation is:

2

where is the free flow speed, and is the jam density, meaning the number of vehicles per spatial unit such that the flow speed is zero.

The Traffic Behaviour Model allows us to estimate the traffic density that is necessary to achieve the desired level of traffic speed that is necessary to comply with environmental targets obtained through the ECPEFM described in “The environmental congestion pricing effect forecasting model”.

Price elastic function

The design of the congestion pricing strategy involved an additional input, related to the need to identify a viable price elasticity function associating the road toll change to each variation of traffic density required to comply with traffic management and environmental targets.

The price elasticity function was built based on data observed nine months after the implementation of the Milan EcoPass Area in 2008 and consistently with values available in the literature⁴⁹. Table 1 reports the resulting price elasticity table adapted to the chosen toll boundaries.

Table 1.

The table shows the price elasticity function adopted in our study. It highlights the charge required to achieve a specific traffic density reduction range.

Begin Interval (%)	End Interval (%)	€
0	29.338	2.0
29.338	32.676	2.5
32.676	35.455	3.0
35.455	37.835	3.5
37.835	39.918	4.0
39.918	41.768	4.5
41.768	Inf	5.0

Data

This paper aims to apply congestion pricing policies to the initial segment of the 2026 Milan-Bormio Olympic route. It consists of approximately 15 km spanning from Sesto San Giovanni to Carate/Verano Brianza (see Fig. 2), featuring three lanes in each direction. To account for both traffic management and environmental targets, we rely on data related to traffic and PM2.5 levels in the analyzed route with air quality data sourced from the monitoring station located in Monza, a central city along the corridor.

Fig. 2.

We show the analysed road and the related geographical context.

Specifically, the former has been estimated by Motion Analytica leveraging on mobile network data provided by Vodafone Business Italia and made available to the authors by Polis, the institute supporting policy design of Regione Lombardia, the regional government of Lombardy. The use of mobile network data to approximate traffic flows is now well-established in the literature: mobile data can reliably capture spatial and temporal mobility patterns and are increasingly used for traffic demand estimation and congestion analysis^{50, 51}.

The available data disclose the total number of vehicles on the considered road route and the average travel time for all days of the year 2022, organized with a four-hour time granularity. In particular, the average number of vehicles passing through was equal to 11,749, with a maximum peak of 70,660, and a minimum of 457. Moreover, the average travel time accounted for 11.3 min.

To assess whether the adopted four-hour time granularity is sufficient to capture relevant congestion dynamics, we performed a descriptive analysis of traffic patterns across time slots. Figure 3 reports the distribution and average values of traffic density and speed, together with a comparison between weekdays and weekends. It is important to note that the variables are expressed in standardized form, allowing for a consistent comparison across time intervals.

Fig. 3.

Traffic density and speed patterns across time slots. Panels A–C report the distribution, average values, and weekday–weekend comparison for traffic density, while panels D–F show the corresponding results for average speed. Variables are expressed in standardized form.

The results highlight a clear differentiation between low-traffic and high-traffic periods. Night-time intervals (01:00–04:59) are associated with substantially lower traffic density, while significantly higher values are observed during daytime and late-afternoon intervals, with peaks occurring between 09:00–20:59.

The analysis by day type further confirms the presence of structured temporal patterns. On weekdays, traffic density increases progressively during the day and reaches its highest levels in the central and late-afternoon time slots. Importantly, these intervals correspond to lower average speed levels, indicating that higher traffic density effectively translates into congestion conditions.

Overall, despite the use of four-hour aggregation intervals, the dataset preserves the main temporal structure of traffic dynamics⁵². While finer temporal granularity would allow for a more detailed representation of intra-period fluctuations, the adopted time resolution is sufficient to identify the most relevant congestion patterns and to support the proposed dynamic pricing framework.

Environmental outcomes have been measured based on PM2.5 concentration levels, given its strong policy relevance, its well-established link with adverse health outcomes, and its suitability for local-scale analysis. In particular, PM2.5 is one of the key indicators monitored within international sustainability frameworks, including those related to Sustainable Development Goal 11, making it directly relevant for policy-oriented studies⁵³. At the same time, it represents one of the primary environmental determinants of mortality, thus providing a meaningful benchmark for assessing the societal impact of air quality interventions⁵⁴. Finally, compared to more dispersive pollutants, PM2.5 is more strongly influenced by local emission sources and meteorological conditions, making it particularly appropriate for evaluating the environmental effects of localized policies such as dynamic pricing applied to a specific road segment^{45, 55}. PM2.5 data were sourced from ARPA Lombardia, the Regional Agency for Environmental Protection.

Over the considered period, the analyzed area experienced a daily average PM2.5 level equal to 25.3 µg/m³. Such value confirms how the Milan metropolitan area faces persistent air quality challenges due to industrialization and difficulties in managing airborne pollutants⁴⁶. Table 2 exhibits descriptive statistics for our dependent and explanatory variables.

Table 2.

We show the descriptive statistics for the dependent and explanatory variables used in our models supporting the design of a dynamic congestion pricing strategy.

Variable	Q1	Q3	Mean	median	std	Time Granularity
Speed (km/h)	78.33	83.61	80.31	80.90	4.90	4 h
Density (car/km)	249.80	1099.40	786.50	804.60	577.50	4 h
Wind speed (m/s)	0.87	1.56	1.26	1.21	0.55	hourly
Cumulated precipitation (mm)	0.00	0.20	1.24	0.00	3.84	hourly
Hydrometric level (cm)	-6.00	0.20	-1.83	-3.0	6.17	hourly
Lagged PM2.5 (µg/m3)	13.00	35.00	25.27	19.00	16.39	daily
Lagged CO	0.23	0.53	0.40	0.33	0.24	hourly
Lagged NO2	20.20	46.53	35.62	30.26	20.00	hourly
Lagged NOx	24.82	62.14	49.90	37.07	36.03	hourly
PM2.5	13.00	35.00	25.26	19.00	16.38	daily

Results

The effectiveness of the proposed pricing strategy was assessed through a comparison of two scenarios: the simulation of congestion and environmental-based dynamic pricing strategy versus a scenario with no congestion pricing. The assessment involved confronting a dataset representing the as is scenario with one simulating traffic and environmental conditions post-implementation. The dataset comprised 1564 observations from the year 2022, with a reorganized detailed temporal resolution of four hours.

Traffic behavior model

The final equation of the Traffic Behavior Model describing traffic dynamics on the San Giovanni- Verano Brianza segment of the 2026 Milano-Bormio Olympic route is the following (obtained through an OLS model):

3

The derived equation relates flow speed to road density. Figure 4 plots its representation.

Fig. 4.

Traffic behavior model.

The suitability of the Greenshields’ model for this corridor was assessed by comparing the theoretical speed-density relationship with the observed data: the scatter plot displaying the relationship between traffic density and flow speed exhibits a pattern consistent with the linear formulation⁵⁶, supporting the adoption of this specification over alternative macroscopic models.

The model indicates that on the selected route, measuring over a four hour period, an increase of 1000 cars results in an average speed decrease of 1.9 km/h. The model’s intercept indicates a free-flow speed of approximately 81 km/h, providing critical insights for managing congestion effectively.

Environmental congestion pricing effect forecasting model

Table 3 reports the results of the Environmental Congestion Pricing Effect Forecasting Model. The R² and adjusted-R² values of the baseline model are 0.766 and 0.762, respectively, suggesting that the model explains approximately 76% of the variance in PM2.5 levels. The coefficient for average speed is –0.0614, suggesting that a 1 km/h increase in average speed corresponds to a significant reduction of approximately − 0.205 µg/m³ in PM2.5 levels. The reduction in PM2.5 is quantified, taking into account that variables employed in the regression are normalized. This means that an increase of one standard deviation of the average speed (4.9 km/h) leads to a PM2.5 reduction of 0.0614 standard deviations of PM2.5 (16.38 µg/m³). Therefore, the actual PM2.5 drop per a 1 km/h increase is given by 0.0614*16.38/4.9 = 0.205 µg/m³*h/km. Moreover, the relationships between PM2.5 values and the control variables are in line with the literature. Indeed, higher wind speed^{34, 38} and larger values of cumulated precipitation^{41, 42}, as well as hydrometric levels⁴³ are associated with better air quality. Moreover, a stronger concentration of past levels of alternative chemicals tends to lead to higher PM2.5 values, suggesting the persistence of pollutants in the atmosphere^{44, 38}.

Table 3.

We report the results of the ECPEFM.

Dependent variable: PM2.5	m1 (Baseline)	m2 (Quadratic)	m3 (Dynamic)	m4 (Interaction)
Traffic speed	–0.061***	–0.064***	–0.061***	–0.067***
	(0.012)	(0.013)	(0.012)	(0.013)
Traffic speed²		–0.009
		(0.009)
Wind speed	–1.994***	–2.016***	–1.994***	–1.919***
	(0.253)	(0.254)	(0.253)	(0.258)
Cumulated precipitation	–0.029**	–0.028**	–0.029**	–0.029**
	(0.012)	(0.012)	(0.012)	(0.012)
Hydrometric level	–0.091***	–0.091***	–0.091***	–0.091***
	(0.016)	(0.016)	(0.016)	(0.016)
Lagged PM2.5	0.374***	0.374***	0.400***	0.374***
	(0.018)	(0.018)	(0.040)	(0.018)
Lagged PM2.5 (t − 2)			–0.029
			(0.039)
Lagged CO	0.120***	0.120***	0.120***	0.123***
	(0.021)	(0.021)	(0.021)	(0.021)
Lagged NO2	0.156***	0.157***	0.155***	0.157***
	(0.022)	(0.022)	(0.022)	(0.022)
Lagged NOx	0.082***	0.081***	0.082***	0.080***
	(0.022)	(0.022)	(0.022)	(0.022)
Traffic speed × wind speed				0.327
				(0.231)
Constant	0.392***	0.399***	0.399***	0.390***
	(0.055)	(0.056)	(0.056)	(0.055)
N. Observations	1564	1564	1564	1564
R²	0.766	0.766	0.766	0.766
R²-Adjusted	0.762	0.761	0.760	0.761
AIC	1855.32	1858.37	1858.77	1857.29
BIC	1969.77	1976.18	1976.58	1975.10

*p-value < 0.1; **p-value < 0.05; ***p-value < 0.01.

Across all alternative specifications reported in Table 3, the estimated relationship between traffic speed and PM2.5 levels proves to be highly stable. The coefficient associated with traffic speed remains consistently negative, statistically significant at the 1% level, and remarkably similar in magnitude across all models, ranging from − 0.061 to − 0.067. This evidence indicates that the core finding of the ECPEFM, namely, that higher traffic speed is associated with lower PM2.5 concentrations, is not sensitive to reasonable variations in model specification.

The introduction of non-linear terms does not provide evidence of significant departures from linearity, as the quadratic term is not statistically significant. Similarly, extending the dynamic structure of the model by including an additional lag of PM2.5 does not improve explanatory power, nor does it substantially alter the estimated coefficients. Finally, the interaction between traffic speed and wind speed is not statistically significant, suggesting that the impact of traffic speed on PM2.5 is relatively stable across different meteorological contexts.

Given the absence of meaningful improvements in model fit, we retain the baseline model (m1) as our preferred specification, due to the slightly higher R² adjusted and lower values of AIC and BIC. This choice is also motivated by its parsimony and interpretability, as it captures the key relationship of interest without introducing unnecessary complexity. Importantly, the use of alternative specifications would not affect the subsequent simulation results, since the estimated effect of traffic speed on PM2.5 remains virtually unchanged across models. This further supports the robustness of the proposed framework and strengthens the validity of the policy analysis based on the baseline ECPEFM.

Congestion and environmental-based dynamic pricing strategy and performance assessment

The implementation of the innovative congestion pricing strategy resulted in charging an active toll in 442 observations, approximately 28.26% of the simulated post-implementation dataset, thus suggesting the frequent need to rely on the proposed algorithm to meet both environmental and traffic targets.

The average charge along all the analyzed time frame is approximately €1.24, resulting in a Total Charge Cost of 14.9 million €, as shown in Fig. 5 (top-left panel). If, instead, we were to consider only those periods in which a toll was charged, the value would be €4.

Fig. 5.

We show the impact of the dynamic charging in terms of additional charge, traffic density reduction, speed increase as well as PM2.5 reduction.

The results suggest that the algorithm activates charges conditionally on the defined traffic and environmental thresholds, potentially limiting the application of tolls during low-demand periods. For instance, in August, marked by improved air quality due to business closures for summer holidays, and lower traffic intensity resulting from fewer daily commuters, no toll charges were applied. This feature is inherently linked to the conditional nature of dynamic pricing. By contrast, fixed or predefined variable pricing schemes would apply charges according to predetermined schedules, potentially resulting in tolls being imposed even during periods of relatively low traffic or environmental pressure. The analysis of traffic management showed an average reduction in traffic density of 11.2% over the year analyzed. Such a figure would be equal to 38.0% in case we just focus on periods during which a toll was charged (top right panel in Fig. 5).

The algorithm’s capability to reduce the density of road infrastructure is also linked to an average traffic speed growth of 0.02%, equivalent to 0.016 km/h (see bottom-left panel in Fig. 5). The reduced congestion along the analyzed toll road is also associated with a decrease in PM2.5 levels within the surrounding area of the 15 km road segment under consideration with an average contraction of PM2.5 values equal to 0.01% (see bottom-right panel in Fig. 5). This value would rise to 0.04% in case we just account for periods when the dynamic pricing algorithm is activated. This relatively modest reduction in PM2.5 is consistent with our framework of analysis. First, the proposed application should be interpreted as a pilot intervention on a single 15-km road corridor, rather than as a system-wide policy applied to the entire urban transport network; accordingly, the environmental effect is necessarily local and limited in scale. Second, PM2.5 is a multi-source pollutant, generated by several anthropogenic activities beyond transport, including residential heating, industry, energy production, and agriculture, so that traffic-related improvements affect only one component of the overall particulate burden. In this respect, empirical evidence for Western Europe indicates that transport accounts for only a limited share of total PM2.5 compared with other sectors⁵⁷. Third, the magnitude of the estimated effect is also coherent with the broader environmental policy literature, where annual country-level emission reductions on the order of 1–2% are generally considered meaningful progress toward long-term targets⁵⁸. The PM2.5 result should therefore be interpreted as a plausible and conservative outcome of a localized pilot intervention, rather than as the full environmental potential of a broader pricing reform.

Sensitivity analysis

To assess the robustness of the proposed dynamic congestion pricing algorithm and to better understand the trade-offs between environmental and traffic objectives, we performed a sensitivity analysis by systematically varying the key policy parameters, namely the environmental threshold (PM2.5) and the traffic speed threshold. In particular, starting from the baseline configuration (PM2.5 threshold = 25 µg/m³; speed threshold = 75 km/h), we simulated six alternative scenarios by independently modifying each threshold (PM2.5 = 20 and 30 µg/m³; speed = 70 and 80 km/h), as well as two combined extreme cases (PM2.5 = 20 with speed = 80; PM2.5 = 30 with speed = 70). The objective of this analysis is to evaluate how different policy stringency levels influence the activation frequency of the tolling mechanism and its overall effectiveness in reducing traffic congestion and air pollution.

Results, reported in Table 4, highlight a clear and consistent pattern. First, increasing policy stringency, either by lowering the environmental threshold or raising the traffic speed threshold, leads to a higher activation rate of the pricing mechanism. For instance, the activation share increases from 28.2% in the baseline scenario to 45.5% in the most stringent configuration (PM2.5 = 20 µg/m³; speed = 80 km/h). Conversely, more permissive configurations (PM2.5 = 30 µg/m³; speed = 70 km/h) significantly reduce the frequency of intervention, with activation rates dropping to 16.6%.

Table 4.

Sensitivity analysis of the dynamic congestion pricing model under alternative environmental (PM2.5) and traffic speed thresholds, reporting policy activation rate, average charge, and resulting impacts on traffic density, speed, and PM2.5 levels.

Scenario	% Activation	Avg charge (€)	Traffic Δ (%)	Speed Δ (%)	PM2.5 Δ (%)
PM2.5_T = 25; Speed_T = 75	28.2%	1.23	11.17	0.021	0.012
PM2.5_T = 20; Speed_T = 75	32.0%	1.40	12.69	0.024	0.013
PM2.5_T = 30; Speed_T = 75	24.0%	1.02	9.40	0.018	0.010
PM2.5_T = 25; Speed_T = 70	21.8%	0.95	8.64	0.016	0.007
PM2.5_T = 25; Speed_T = 80	43.6%	1.94	17.40	0.033	0.022
PM2.5_T = 30; Speed_T = 70	16.6%	0.72	6.55	0.012	0.005
PM2.5_T = 20; Speed_T = 80	45.5%	2.03	18.16	0.034	0.023

Second, the intensity of the policy, measured through the average charge, follows a similar pattern. Stricter scenarios require higher average toll levels (up to €2.03), reflecting the greater effort needed to induce behavioral changes in traffic demand. In contrast, less stringent configurations lead to lower average charges (down to €0.72), indicating a reduced need for corrective interventions.

Most importantly, the sensitivity analysis reveals a strong and monotonic relationship between policy stringency and system performance. More stringent scenarios generate substantially higher reductions in traffic density (up to 18.16%) and corresponding increases in average speed (up to 0.034%). These traffic improvements translate into more significant environmental benefits, with PM2.5 reductions reaching up to 0.023% in the most aggressive scenario. On the contrary, more relaxed configurations produce limited effects across all dimensions, with traffic density reductions as low as 6.55% and PM2.5 improvements of only 0.005%.

Overall, these findings highlight a fundamental trade-off embedded in the design of congestion pricing policies. While stricter thresholds enhance both traffic and environmental outcomes, they also imply a higher economic burden for users due to more frequent and higher tolls. Conversely, less stringent policies reduce the financial impact on users but at the cost of significantly lower effectiveness.

In addition, to assess the robustness of the proposed dynamic congestion pricing model with respect to the underlying behavioral assumptions, we conducted a sensitivity analysis on the price elasticity of demand. Given that the elasticity table is derived from prior empirical evidence, this exercise aims to evaluate how uncertainty in users’ responsiveness to pricing may influence the model’s outcomes. In particular, we constructed alternative elasticity scenarios by proportionally varying the demand reduction intervals associated with each price level by ± 5% and ± 10%, while keeping the set of toll levels unchanged. This approach allows us to isolate the effect of behavioral variability without altering the policy design, thereby ensuring that the simulated tolls remain within a realistic and policy-relevant range.

The results, reported in Table 5, reveal a clear and consistent pattern. Variations in elasticity primarily affect the magnitude of traffic demand reduction, as reflected in the progressive change in traffic density reduction, which ranges from 10.05% in the low-elasticity scenario (− 10%) to 12.28% in the high-elasticity scenario (+ 10%). This monotonic trend confirms that higher user responsiveness to pricing leads to stronger traffic mitigation effects. These changes propagate to the subsequent variables in the model, producing corresponding, albeit limited, increases in average speed and reductions in PM2.5 levels.

Table 5.

Sensitivity analysis of main model outcomes to variations in demand price elasticity (± 5% and ± 10%).

Scenario	Traffic Δ (%)	Speed Δ (%)	PM2.5 Δ (%)
Elasticity − 10%	10.05	0.0191	0.0104
Elasticity − 5%	10.61	0.0202	0.0110
Baseline elasticity	11.17	0.0212	0.0115
Elasticity + 5%	11.73	0.0223	0.0121
Elasticity + 10%	12.28	0.0233	0.0127

However, the overall impact on system performance remains relatively modest, suggesting that the proposed dynamic pricing mechanism is robust to moderate variations in the assumed price elasticity of demand.

Conclusions

In this paper, we design and simulate a dynamic pricing strategy for the 2026 Milan-Bormio Olympic road corridor from Sesto San Giovanni to Carate/Verano Brianza, with the goal of contributing to a smarter and more sustainable mobility system. By integrating real-time traffic density and air quality indicators, the proposed approach offers insight into how dynamic pricing could be structured to jointly address traffic and environmental objectives. The simulation results suggest that the algorithm is technically capable of responding to both traffic and environmental triggers, indicating that the integration of environmental management within congestion charging through dynamic pricing may represent a feasible policy option.

Simulations on the implementation of our dynamic pricing strategy show that an active toll is charged in 28.26% of the analyzed periods, leading to an average fee of 1.2€ and a cumulative total cost of 14.9€ million. The minimum charge of €2 was calibrated against local public transport fares in the area of study, which ranged between €2.20 and €2.60 for comparable trips as of September 2023, ensuring that the toll remains within a range where alternative modes represent a financially viable option for users. Equity implications, including distributional effects across income groups and spatial accessibility to alternatives, constitute an important avenue for future research.

We observe a decrease in traffic density of 11.2% in line with previous research by Cipriani et al.²⁷, Croci et al.⁴⁹, and Richardson et al.⁵⁹, obtaining a contraction of road density between 12% and 25% in applications in the cities of London, Milan, Rome, and Stockholm. From an environmental perspective, established schemes such as Milan’s EcoPass and the Stockholm Congestion Charge achieved reductions of 14–19% for key air pollutants and between 8.5 and 13% for NOx and PM10, respectively⁴⁹. However, these estimates typically refer to reductions in emissions from transport sources specifically. By contrast, our analysis captures changes in overall ambient air quality, where PM2.5 concentrations are influenced by multiple concurrent sources (e.g., residential heating, industrial activities, and background pollution). As a result, the estimated PM2.5 reduction of 0.01% appears more modest, but this is consistent both with the broader measurement scope and with the localized, pilot-scale nature of the intervention, which targets a single 15-km corridor rather than a wider urban area.

The practical deployment of the proposed algorithm would require addressing challenges across technological, institutional, and behavioral dimensions. On the behavioral side, dynamic pricing schemes face greater public opposition than fixed-rate alternatives due to the perceived unpredictability of toll levels^{6, 24}. The ±€1.5 constraint embedded in the algorithm is explicitly designed to limit inter-period volatility and improve predictability for users. On the institutional side, implementation on a national road corridor would require coordination among multiple public authorities and a regulatory framework enabling real-time toll adjustment. The revenues generated by the mechanism could in principle be reinvested in public transport improvements, as in the case of the London Congestion Charge¹¹, thereby strengthening both modal alternatives and public acceptability.

Concerning the technological dimension, a robust infrastructure is required to support real-time data collection, processing, and toll computation. The literature identifies Vehicle Positioning Systems (VPS) relying on satellite-location technology (typically GPS) as the most suitable infrastructure for future dynamic pricing schemes, given their flexibility in toll adjustment. However, current unit costs of on-board VPS equipment remain significant. More widely deployed alternatives, such as Image-based Tolling via Automatic License Plate Recognition (ALPR), raise concerns around data privacy that may affect public acceptability. Furthermore, the effectiveness of dynamic pricing is contingent on travellers being informed about charges sufficiently in advance to adjust their behavior⁶, which requires investment in real-time communication infrastructure.

Overall, our approach complements extant studies, by explicitly dealing with congestion issues and pollution reduction in the pricing strategy. In particular, we offer valuable insights for policymakers and researchers considering increasing concerns over the health impacts of poor air quality and the progressively stricter EU thresholds for acceptable PM2.5 levels, aiming for enhanced restrictions by 2030 in alignment with the United Nations’ 11th Sustainable Development Goal for sustainable cities^{60, 61, 62, 63, 64, 65, 57}. The proposed dynamic pricing strategy may represent a potentially useful instrument for regulators aiming to support low-carbon economy targets.

This study is subject to several limitations that should be acknowledged when interpreting the results. First, mobile-network-derived traffic data may be affected by provider coverage and market-share bias, and may therefore not fully represent the entire population of road users. In addition, the aggregation and modelling procedures required to transform mobile-network signals into traffic indicators may smooth short-term fluctuations and introduce uncertainty in vehicle-count, travel-time, and density estimates. Accordingly, traffic variables should be interpreted as aggregated proxies of road demand rather than direct measurements of all vehicles. Future work could validate these estimates against independent traffic-monitoring sources.

Second, the analysis is based on a simulated post-implementation scenario rather than on observed behavioral responses to an actual toll introduction. Consequently, the estimated traffic and environmental effects depend on the assumed price elasticity function and model specifications, and may not fully capture real-world adaptation mechanisms or longer-term behavioral adjustments, such as route switching, modal shift, or changes in travel habits over time⁶. A related limitation concerns potential spillover effects: as a facility-based scheme, the proposed policy may induce traffic diversion toward nearby routes not subject to tolling, which are not captured in the current single-corridor framework⁶. Furthermore, no comparison with observed post-implementation data was possible, as the algorithm has not yet been deployed in practice on the SS36 corridor. The performance assessment is therefore limited to a counterfactual simulation based on 2022 observed data.

Third, the use of a four-hour time granularity, while sufficient to capture the main temporal structure of traffic demand and congestion patterns, may smooth short-term fluctuations and peak-hour dynamics, thus limiting the precision of the estimated effects. The availability of higher-frequency data (e.g., hourly or real-time observations) would allow a more accurate identification of critical congestion intervals and a more responsive calibration of the pricing mechanism.

Fourth, the estimated reduction in PM2.5 is modest in magnitude, reflecting the fact that congestion pricing affects only one of several emission sources contributing to air pollution. This suggests that, in the short term, congestion pricing alone may have limited effects on air quality and should therefore be interpreted as a complementary instrument within a broader environmental policy mix rather than as a standalone solution.

In addition, the demand response is modelled through a price elasticity function calibrated using historical evidence and adapted values from the literature. While this ensures consistency with prior studies, it may not fully reflect current behavioral patterns. Future research could improve robustness by exploiting updated revealed-preference data or quasi-experimental evidence from real-world toll implementations.

Moreover, the Environmental Congestion Pricing Effect Forecasting Model (ECPEFM) relies on a parsimonious regression framework linking air quality to traffic and environmental variables. Although the robustness analysis confirms the stability of the estimated relationships, further work could explore more advanced modelling approaches, including time-series or data-driven methods, to better capture the dynamic interactions between traffic and air pollution. Finally, the results refer to a specific corridor in Northern Italy and may not be directly generalizable to other geographic, infrastructural, or regulatory contexts. Extending the analysis to different road typologies and urban settings would allow a broader assessment of the external validity of the proposed approach. In this respect, the modular nature of the framework’s data inputs, mobile network data increasingly available across different geographical settings⁵⁰ and environmental monitoring data accessible through equivalent regional agencies in most European countries, support its technical transferability, contingent on local re-calibration of the supporting models.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

AJC: conceptualization, methodology, software, data curation, writing—original draft preparation. FS: conceptualization, methodology, software, data curation, writing—original draft preparation. MA: conceptualization, supervision, writing—review & editing. GA: conceptualization, supervision.

Funding

This study was funded by the European Union - NextGenerationEU, Mission 4, Component 2, in the framework of the GRINS -Growing Resilient, INclusive and Sustainable project (GRINS PE00000018 – CUP D43C22003110001). The views and opinions expressed are solely those of the authors and do not necessarily reflect those of the European Union, nor can the European Union be held responsible for them.

Data availability

All environmental variables have been collected from the Italian National Institute of Statistics (ISTAT, http://dati.istat.it/) or from the Italian Institute for Environmental Protection and Research (ISPRA, https://www.isprambiente.gov.it/it/banche-dati), or from the Open Data Lombardia platform (https:/www.dati.lombardia.it).Data describing the traffic flows have been provided under an academic license agreement by Motion Analytica leveraging on mobile network data gathered by Vodafone Business Italia and made available to the authors by Polis, the institute supporting policy design of Regione Lombardia, the regional government of Lombardy (available at the link: (https:/www.motionanalytica.com). To enhance transparency and reproducibility, a synthetic version of the dataset is also made available as supplementary material. This dataset has been generated through a stratified random sampling procedure designed to preserve the main statistical properties of the original data, including the joint distribution across temporal dimensions (months, time-of-day intervals, and day type) and the key variables used in the analysis, such as traffic density and average speed, while fully complying with confidentiality and licensing constraints. This study does not involve human participants, human biological material, or the collection of identifiable personal data. The analyses rely on aggregated traffic-flow indicators (e.g., vehicle counts, average travel time/speed) computed over four-hour time windows for a predefined road segment, and on publicly available air-quality measurements from an environmental monitoring station. No information is available at the level of individual persons, devices, or vehicles, and no attempt was made to identify, track, or infer the behavior of specific individuals. The traffic dataset was provided in anonymized and aggregated form by the data provider and processed in accordance with applicable privacy and data-protection protocols. On this basis, an ethics statement and informed consent procedures were not required for this work. All traffic data were handled exclusively in anonymized, aggregated form. The dataset does not include direct identifiers (e.g., names, phone numbers, device IDs) or indirect identifiers that would enable re-identification of individuals. Analyses were performed at a spatially and temporally aggregated level (four-hour intervals) and are reported only in aggregate, thereby minimizing any risk of re-identification and ensuring compliance with relevant privacy standards.

Declarations

Competing interests

The authors declare no competing interests.

Ethics statement

This study does not involve human participants, human biological material, or the collection of identifiable personal data. The analyses rely on aggregated traffic-flow indicators (e.g., vehicle counts, average travel time/speed) computed over four-hour time windows for a predefined road segment, and on publicly available air-quality measurements from an environmental monitoring station. No information is available at the level of individual persons, devices, or vehicles, and no attempt was made to identify, track, or infer the behavior of specific individuals. The traffic dataset was provided in anonymized and aggregated form by the data provider and processed in accordance with applicable privacy and data-protection protocols. On this basis, an ethics statement and informed consent procedures were not required for this work. All traffic data were handled exclusively in anonymized, aggregated form. The dataset does not include direct identifiers (e.g., names, phone numbers, device IDs) or indirect identifiers that would enable re-identification of individuals. Analyses were performed at a spatially and temporally aggregated level (four-hour intervals) and are reported only in aggregate, thereby minimizing any risk of re-identification and ensuring compliance with relevant privacy standards.