Transportation networks face escalating challenges to cater to increased mobility demand while addressing trafic congestion. Traditional remedies, such as adding roads, can paradoxically worsen congestion, as seen in Braess's paradox. This study emphasizes the potential benefits of strategically closing roads to alleviate congestion and carbon emissions. Milan serves as a case study, where various road closure strategies were tested to identify scenarios where strategic removal not only eased congestion but also significantly reduced CO2 emissions. The findings provide practical insights for urban planners and policymakers, ofering a roadmap to develop more eficient and eco-friendly urban transportation systems.
sions, we use SUMO [
The complexity of the urban system can result in phe- The code for full replication of this work at https://
nomena like Braess’s paradox [
• Some contiguous edges are named with diferent names (pseudonyms) but are the same road.
We cannot automatically change these names
because they are culturally or regionally dependent,
so after detection, we change them manually.
tion: Buscema et al. [
In Barcelona, Sánchez-Vaquerizo and Helbing [
Mobility demand. We model the vehicle flows through the city’s mobility demand where a pair (o,d) identifies each vehicle’s trip definition, representing the origin and destination location. First, we divide the urban environment into tiles, each of which will be a possible origin or destination location. We choose hexagonal tessellation H3 developed by Uber and available in library scikit-mobility [21]. Then, we use real mobility data, such as vehicles’ GPS traces, to estimate the flows between tiles. In practice, we build an Origin-Destination (OD) matrix where an element indicates the number of vehicle trips from an origin tile to a destination tile.
Routes. For each (, ) pair in the mobility demand, we use a routing algorithm from SUMO, called Duarouter1, that connects two edges on a road network 3. Simulation Framework following the fastest path, i.e., the path that minimizes the expected travel time. The fastest path can be perturbed Our simulation framework generates urban trafic sce- using a randomization parameter ∈ [1, +∞) where narios under various road closure strategies. The frame- the higher the , the more the path is randomized ( = 1 work consists of two phases, each serving a specific pur- is exactly the fastest path). Duarouter dynamically dispose. The first phase simulates urban trafic under normal torts edge weights (i.e., travel time) by a chosen random conditions without road closures (baseline). The second factor drawn uniformly in [1, ). A value greater than phase simulates vehicular trafic by systematically clos- 1 allows us to model imperfections in human driving ing one or more roads through diverse closure strategies. behavior, reflecting the lack of complete knowledge of
Road network. We model the road network as a di- the road network while driving.
rected graph = (, ) where the set of edges con- Trafic simulation. We generate trafic from the
vetains the road or the streets, and the set of nodes con- hicle routes using SUMO (Simulation of Urban MObility)
tains the intersections (junctions) between roads. Each [
If those two road names are the same, we assign Road closure. To simulate the efects of road closures that name to . on CO2 emissions, we define a road closure simulation • We use the ArcGIS service to get the midpoint framework that allows us to select a set of roads and coordinates (latitude, longitude) of each unnamed remove them from the road network, maintaining the edge using reverse geocoding, thus obtaining the mobility demand as similar as possible. The steps of the missing road name. framework are the following: • Since the road network may include more than one municipality, there may be some edges with 1. Select a set of roads to close. the same name (aggregated as roads) but geo- 2. Modify the edge parameters in the road network graphically distant from each other. We identify using the “disallow" SUMO attribute to prevent these roads using the boundaries of municipal- the passage of vehicles on the roads from being ities and assign to each edge its name and the closed.
corresponding municipality. 1https://sumo.dlr.de/docs/duarouter.html 3. Recompute the mobility demand. We iterate through all the (, ) pairs and see if the vehicle trip needs to be changed or not as follows: • If or belongs to an edge of the removed roads, we recompute a new trip for that vehicle. • If and are not removed from the road, we verify if the two edges are still reachable after the road closure. If so, we keep the vehicle’s trip of the baseline mobility demand. • If the two edges are no longer connected, we recompute a new trip.
running a SUMO simulation with the mobility demand derived from the GPS data.
In the absence of the actual capacities of the roads, we estimated them using the 2000 Highway Capacity Manual [29]. Then, we compute the VOC for each edge as: () = () () To obtain the VOC associated with each road, we compute the weighted average of the VOC of each edge in the road: () = ∑︀∈ () · ℎ() ∑︀ ∈ ℎ() (2) (3) (4) (5)
Inspired by previous works [23, 24], we classify roads using a combination of theoretical measures derived from graph theory, such as betweenness centrality, and datadriven metrics like Volume-Over-Capacity (VOC) and , a metric indicating the degree of road usage. Road betweenness centrality. It is a theoretical measure of centrality in a graph (road network) based on the shortest paths. For our aim, we use the edge betweenness centrality [25, 26] to obtain the road betweenness centrality using a weighted average with the length of the edge as weight: () = ∑︀∈ () · ℎ() ∑︀ ∈ ℎ() (1) where is the road on which to compute the betweenness, and it is composed of multiple edges , and ℎ() represents the length of the edge .
(VOC) is the ratio between the trafic flow on a road and the capacity of the road. It is a standard metric to evaluate a road’s service level and indicates how congested a road is [27, 28]. When < 1, the road can still contain other vehicles without undergoing particular slowdowns.
A road with ≥ 1 sufers from congestion.
First, we compute the VOC to the edge level and then aggregate them to the road level. We compute the volume edge of each road segment using a data-driven approach, () and the (). An area is a driver source for an edge if at least one vehicle, which passes through the edge , starts its trip from an edge ∈ . Similarly, an area is a driver destination for if at least one vehicle, which passes through the edge , ends its trip to an edge ∈ . An area can be both a source and a destination. For each edge, , the driver sources and driver destinations can be ranked based on how many vehicles traverse , starting or ending in the respective area.
We compute the weight of each driver source as follows: ()() = {︃1 if passes through from , 0
otherwise ( ) = ∑︁ (,)()
∈ where is the edge on which compute the driver sources, is a neighborhood, and is the set of vehicles crossing the city. Similarly, we can define the driver destinations ( ). We rank the list of driver sources (DS) and driver destinations (DD) for each edge and keep only the DS and the DD responsible for 80% of the trafic lfow on the edge. These new lists are the major driver sources (MDS) and the major driver destinations (MDD) for each edge . After identifying the MDS and the MDD, we can build the bipartite road usage networkFinally, If we aim to remove six roads, the list of removed roads we compute () and () from the bipartite would be = [1, 2, 1, 2, 1, 2], such that the list network : has the same amount of roads from each category.
The rationale behind employing a mixed strategy lies in the road categorization based on their significance or ()() = |{ | ∃− ← , ∀ ∈ , ∈ }| (6) attractiveness in the network. This approach increases the likelihood of obtaining clusters with similar types of roads, such as highways or freeways. Simply removing all roads from a single category may have a detrimental ()() = |{ | ∃→− , ∀ ∈ , ∈ }| (7) impact because vehicles previously using those roads where is the set of area-nodes of the bipartite graph are now directed to alternative routes lacking similar , is the set of links of , is an edge ∈ the characteristics, such as reduced capacity or lower speed set of edge-nodes of the bipartite graph, and is an in- limits. Therefore, removing roads from diverse categories going or an out-going link from an area-node . Actually, helps mitigate this efect. () and () are respectively the in-degree and the out-degree of each ∈ of the bipartite graph. 6. Experimental Setup Ultimately, we aggregate these measures to road level with a weighted average using the length of each edge as weight.
to a squared area of almost 380 2 from the centre of Milan and download the corresponding road network Road clustering. We use a clustering approach to di- from OpenStreetMap, obtaining 24, 063 intersections vide the roads into categories and obtain an efective and 46, 488 edges, which we aggregate into 7,654 roads. closure strategy to evaluate the impact on CO2 emis- Mobility Demand. We split the selected area into sions. We use the road betweenness centrality, the VOC, tiles using H3 hexagonal tessellation with a resolution (), and the () as features for clustering to of 8, covering the selected Milan area with 680 tiles. We obtain several road categories. We use the K-Means clus- then use GPS data describing 17,087 vehicles travelling tering2 to group the roads and a grid search to find the between April 2nd and 8th, 2007 (658k points after preoptimal number of clusters. processing) to extract the flows of vehicles between tiles.
We test = 2, . . . , 10, choosing the best using the Next, we create a realistic synthetic OD matrix that mirelbow method [30]. rors real-world mobility patterns, maintaining the typical distribution of trip distances and the power-law behavior in the number of trips between two locations. We 5. Closure Strategies compute the mobility demand for 30, 000 vehicles as it minimizes the Jensen-Shannon divergence between We design diferent road closure strategies and evaluate the travel time distribution in real data and that of the their impact on CO2 emissions. simulated vehicles [31, 32, 33].
CO2 policy. It removes roads based on their level of Routes. We generate the routes from the mobility CO2 emissions. We normalize emissions by road length, demand using Duarouter, which computes the perturbed obtaining CO2 per meter of road. fastest path using a randomization parameter = 7.5,
Category policy. It closes roads based on a classifica- which allows us to model the real behavior of drivers tion of roads. We analyze the impact of CO2 emissions who typically do not follow the fastest route [34]. when roads are closed from each category, closing roads Closure strategy. We simulate the trafic demand with the highest CO2 per meter first. using SUMO, obtaining the CO2 emissions for each edge
Mixed policy. We choose a list of roads for removal, and aggregating the results by road. We first simulate ensuring that it comprises an equal number of roads the original road network as a baseline and then select a from every category. These roads were ranked in de- closure strategy to remove a set of roads from the origscending order based on their CO2 emissions per meter inal road network. A closure strategy consists of two in each category. Initially, we eliminate the road with the parallel steps. The first is the informed strategy, where highest emissions within each category, progressively we remove the roads from the road network based on working towards those with lower emissions. As an ex- the defined strategy. The second is an uninformed policy ample, consider three road categories denoted as = in which we close random roads from the road network. [1, 2, 3, 4], = [1, 2, 3, 4], = [1, 2, 3, 4], The removed roads in the uninformed strategy preserve where each list is arranged in decreasing order of CO2/m. the same length as the informed one. For each policy, we close 1, 10, 20, . . . , 100 roads. Independently of the policy applied, the road closures are selected with respect to the baseline experiment, the original road network. Thus, each set of roads is a subset of the next set 1 ⊆ 10 ⊆ 20 ⊆ . . . ⊆ 100. We rank roads within each strategy based on their CO2/m in descending order.
Subsequently, we incrementally select the set of roads for closure, employing a precise approach to optimize the reduction of carbon emissions. While this decision is inherent in the CO2 policy by its definition, for both the category and mixed policies, we follow the strategy outlined in Section 5. This involves ranking roads based on emission levels (CO2/m) in descending order and prioritizing the closure of the most polluted roads from each road category.
Road classification. We classify the roads of Milan to identify similarities and diferences between roads that can be impactful in terms of CO2 (mg) emissions. As suggested in [24], we characterize roads with their betweenness centrality and () [24], as well as additional features such as the VOC, a useful metric to classify to quantify road congestion, and () to capture the attractiveness of each road based on the destination of the flows. We then apply a clustering algorithm using the Silhouette score’s progression to determine that the best number of clusters is four. We name the clusters as follows: • (HF): High , high relative VOC and emis- sure strategy. Now, we discuss each policy individually.
sions (in yellow); CO2 policy. It exhibits a beneficial impact on reduc• (HE): High , low relative VOC and emis- ing CO2 emissions up to a certain threshold (Figure 2a).
sions (in green); Closing up to 50 roads leads to a decrease in the overall • (LF): Low , high relative VOC and emis- emission compared to the baseline scenario. After this sions (in orange); threshold, the emissions increase exponentially with the • (LE): Low , low relative VOC and emissions closing of every additional set of ten roads. The CO2 (grey). policy also highlights that an informed strategy based on the level of CO2/m is more efective than an uninformed
First, we run a SUMO simulation on the original Milan strategy with the same emissions level as the baseline. road network, i.e., without any road closure. Through Category policy. The impact of this policy depends this simulation, we identify the roads with higher emis- on the road category. Closing HF roads (Figure 2b) leads sions levels. Figure 1 shows the roads from each cluster to similar results to the CO2 policy: there are beneficial previously identified for the and the mixed policy. efects until a certain threshold (40 closed roads). After In Figure 1a and 1b, we observe the roads characterized closing 100 HF roads, CO2 emissions decrease, even if reby high () and (). The yellow roads within maining above the baseline level. After closing 50 roads, these figures can be diferentiated from the green roads the random closure strategy outperforms the informed based on their CO2/m (mg/m) and VOC levels. Notably, strategy regarding CO2 emissions, although still worst the yellow roads exhibit higher levels of both CO2/m and concerning the baseline. Closing HE roads (Figure 2c) VOC than the green roads. In Figure 1c and 1d, we show consistently results in a negative impact, with CO2 emisthe roads classified with low . We can distinguish sions increasing up to 50% above the baseline. Even in between two groups based on their VOC values: high the case of the uninformed strategy, emissions levels rise, VOC for the orange roads and low for the dark grey roads. although to a lesser extent. Closing LF roads (Figure 2d) always leads to an increase in CO2 emissions, although 7. Results to a lesser degree than other removal strategies. The closed roads cause a maximum increase of 15% compared to the baseline. Lastly, closing LE roads does not change emissions levels compared to the baseline (Figure 2e).
Figure 2 provides an overview of total CO2 emissions (mg) across the entire road network for each applied clo
Mixed policy. Even if the impact of this policy does we are not simply redistributing the vehicles through not exhibit a clear trend (Figure 2f), it is worse compared the road network but also removing roads from it. Road to the baseline scenario. Focusing on the closure experi- removal limits the available route options for drivers, ment of 20 roads, we find no linear relationship between leading to a situation that replicates or worsens the initial the roads closed and the resulting CO2 emissions. conditions.
To gain insights into the impact of road closures on the routed paths of vehicles, we analyze how the vehicles are rerouted after a closure. Figure 4 shows an example of vehicle rerouting after a road closure. The closed roads are represented in black, while the routed paths are depicted in blue and orange. The orange path represents the routed path in the baseline scenario; the blue path is the rerouted path in the closure experiment. In this case, we consider the CO2 policy with the removal of ten roads.
The rerouted path does not difer significantly from the original path because the roads used in the closure experiment have a smaller capacity than the baseline roads. As a result, when simulating all trafic flows, this capacity discrepancy leads to earlier congestion levels.
analysis of the diferent closure strategies from multiple perspectives. In Figure 3a, we show the percentage of vehicles impacted by each closure strategy. A vehicle is considered impacted if its previous route contains at least one road closed in the closure strategy. The closure of HE roads yields a higher percentage of impacted vehicles due to two key factors. Firstly, HE roads encompass highly frequented routes, including highways, which afect a larger proportion of vehicles. Secondly, HE roads comprise a larger number of roads, some longer, thereby amplifying the impact on vehicle paths.
Figure 3b shows the percentage of the traveled road network to the total available road network. In theory, the more vehicles are spread on the road networks, the fewer the emissions as we reduce the likelihood of road congestion. However, this efect is not observed because 7.1. Discussion Road closures impact CO2 emissions. Emissions decrease for specific road categories up to a certain threshold of removed roads. However, increasing the number of removed roads, CO2 emissions increase exponentially, reaching peaks of 50% above the baseline scenario with the original road network. This happens because highly polluted roads are also typically those with higher capacity, and better equipped to handle larger trafic flows.
Not all roads count equally. Certain roads are pivotal in maintaining smooth trafic flow and preventing congestion. Those roads cannot be removed without increasing CO2 emissions. We also identify roads whose removal does not significantly afect CO2 emissions.
Removing sparse roads is inefective. Emissions only decrease for a specific subset of roads, while most closure experiments result in increased emissions. In other words, removing scattered roads throughout the road network may not be optimal. The underlying reason lies in the rerouting of vehicles onto alternative roads, which are often close to the removed roads and have lower capacity. Consequently, this necessitates considering a “zone" closure strategy to mitigate this efect and optimize emissions reduction eforts.
some roads is beneficial, but the removal becomes detrimental above a certain threshold of closed roads. The closure of other roads led to an increase in CO2 emissions, while certain roads have negligible influence on CO2 emissions. Our work can be further improved in several directions. For instance, another road closure strategy could be to close all roads in specific “eco-zones" rather than closing single roads, which may lead to trafic redirection onto adjacent roads with lower capacity.
Nazionale di Ripresa e Resilienza) nell’ambito del programma di ricerca 20224CZ5X4_PE6_PRIN 2022 “URBAI - Urban Artificial Intelligence” (CUP B53D23012770006), Finanziato dall’Unione Europea - Next Generation EU.
This research has also been partially supported by EU project H2020 SoBigData++ G.A. 871042; and NextGenerationEU—National Recovery and Resilience Plan (Piano Nazionale di Ripresa e Resilienza, PNRR), Project “SoBigData.it—Strengthening the Italian RI for Social Mining and Big Data Analytics”, prot. IR0000013, avviso n. 3264 on 28/12/2021.