A Study on a Framework for Identifying Critical Roads in Urban Road Traffic Networks Based on the Resilience Perspective Against the Background of Sustainable Development

Abstract

Traffic network resilience refers to the ability of a traffic network to maintain a certain capacity and service level even when disturbed by external factors, as well as its capacity to recover following a disruptive event. This paper integrates traffic simulation with resilience analysis of urban road traffic networks and proposes a framework for identifying critical roads in urban road traffic networks from a resilience perspective. This framework is both theoretical and applicable to any unanticipated disruptive event. By incorporating four attribute indicators—traffic, topology, urban function, and socio-economic factors—the framework assesses the importance ranking of each road segment in an urban road traffic network both before and after an unanticipated disruptive event. A case study is conducted using a real urban road traffic network in Shanghai. From the perspective of policymakers, corresponding policy recommendations are made to enhance the resilience of urban road traffic networks against unanticipated disruptive events and to mitigate socio-economic losses.

1. Introduction

The urban road transport network plays a key role in stimulating economic growth and social progress, and it is an important means of ensuring the normal functioning of cities. The booming development of urban road transport networks has significantly advanced transportation infrastructure, yet concurrently, it has inevitably brought substantial traffic issues. The unpredictable disruptions often precipitate severe consequences, inflicting substantial losses in terms of life and property, and generating substantial negative impacts [1,2]. Traffic accidents are the main cause of road incidents, which are highly valued by government departments for the protection of public life and property, and the assessment of the impact of these unforeseen incidents, as well as the rapid restoration of the normal functioning of the urban road transport network after the incidents, have attracted a great deal of attention from scholars at home and abroad.

Behnood and Mannering [3] utilized statistical data on traffic accident severity spanning the period 2004 to 2012, discovering that the influences of road characteristics, vehicle characteristics, and driver characteristics on accident severity exhibited significant annual variations. Ren Rui et al. [4] conducted an analysis of tunnel fire accidents, determining that such incidents were associated with the seasonal weather and location of heavy truck occurrences. Song Xin et al. [5] developed an evolutionary fault tree for causal inference, explaining the logical relationships between accident causes and contributing factors by performing qualitative and quantitative calculations on the fault tree. Zhang Chao et al. [6] constructed an EEB model by integrating event trees, event evolution diagrams, and Bayesian networks, capable of identifying initial and secondary events and detailing their evolution paths. Additionally, numerous other researchers have employed CNN [7], random forests [8], fault trees [9], event trees [6], probabilistic analysis [6], and other methodologies to investigate the impacts of unforeseen disruptive events.

Holling introduced the concept of toughness to the field of ecology in 1973, initially termed as “resilio” in Latin, signifying a material’s capacity to absorb energy during plastic deformation and bending [10]. Since then, the concept of resilience has been extensively extrapolated to various domains, including the socio-economic and engineering domains [11,12,13]. The study of road traffic system resilience was initiated by Hansen and Sutter, who investigated the effects of the Loma Prieta earthquake on road closures [14]. In recent years, resilience has emerged as a focal point in transportation engineering research. The resilience of urban road transport networks, the foundational structures for urban transport activities, refers to the networks’ ability to sustain a certain level of capacity and service level when externally disturbed and to rapidly recover post-disturbance. Research on the resilience of urban road traffic networks plays the role in enhancing the management of these networks’ operations. Bruneau et al. [15] proposed a classical conceptual framework of resilience and introduced a resilience triangle based on time distribution to measure road system resilience. Sahitya et al. [16] provided an in-depth discussion on the performance of transportation infrastructure systems during disruptive events and proposed a model based on connectivity, accessibility, maturity, and development characteristics to measure resilience. Murray-Tuite et al. [17] defined resilience as the network characteristics of a transportation network to operate normally under extreme disaster conditions and proposed 10 indicators to measure transportation in terms of cooperation, redundancy, diversity, efficiency, safety, self-organization, strength, adaptability, mobility, and the ability to recover quickly. Jia et al. [18] identified key stations by combining the topology structure of the public transport network and dynamic passenger flows at bus stops. However, most current research on the resilience of transport systems focuses on abstract accident studies, i.e., random damage to roads, and most assessments of resilience are static. There are few studies of the overall dynamic evolution of urban road transport systems and the mechanisms of damage to critical road sections when subjected to perturbing events.

By conceptualizing each urban transportation hub as a node and the roads connecting these hubs as edges, the urban road traffic network can be abstracted into a complex network topology, consisting of two basic elements: nodes and edges. When a hub or road is affected by a disruptive event, this impact can be abstracted as the corresponding node or edge in the network being affected and disappearing. Consequently, the traffic that was originally carried by the affected road will be diverted to surrounding roads, and the road capacity will undergo a significant transition from linear to surface-based distribution. In particular, for some especially critical hubs or roads, damage to them may affect the overall functionality of the entire road network. Therefore, identifying these important and critical hubs or roads, studying their resilience when they are impacted by disruptive events, and finding ways to resist the effects of such events, recover rapidly from them, and maintain the smooth operation of the urban road network are of paramount importance for the proper functioning of cities.

This paper integrates traffic simulation technology into the resilience study of urban road traffic networks, proposing a framework for identifying critical roads within these networks from a resilience perspective. The framework provides a theoretical and applicable method for determining the importance ranking of each road segment within urban road traffic networks, both prior to and following an unanticipated disruptive event. A real-world urban road traffic network in Shanghai is utilized as a case study to establish the importance ranking of the network before and after a disruptive event. The damage to urban roads caused by an unanticipated disruptive event is simulated using SUMO, a micro-traffic simulation platform, to investigate the impact of the entire process, from pre-disruption to post-recovery measures, on the resilience of the urban road traffic network. From a governmental management perspective, corresponding policy recommendations are proposed to enhance the resilience of urban road traffic networks in response to unanticipated disruptive events.

The rest of the paper is organized as follows. Section 2 establishes an abstract framework for identifying key roads in urban road traffic networks based on a resilience perspective, which is divided into pre-accident identification and post-accident identification. Section 3 describes a case study using the Shanghai urban road traffic network as an example. Section 4 presents the results of simulation experiments and provides an analysis. Finally, the conclusion is provided in Section 5. The structure of Section 2 to Section 4 of this paper is illustrated in Figure 1.

2. Methodology

Resilience represents a multi-dimensional and comprehensive attribute of urban road traffic networks. Optimal resilience allows these networks to more effectively resist and rapidly recover from unforeseen disruptive events, thereby minimizing the impacts induced by such events. Based on the resilience perspective, we propose a framework for identifying critical roads within urban road traffic networks under the circumstances of unanticipated disruptive events.

The critical road identification framework for urban road traffic networks, based on a resilience perspective, is bifurcated into two components: pre-accident identification and post-accident identification. Pre-accident identification primarily ranks the criticality of road sections based on the relevant attributes of the urban road traffic network from a resilience perspective. Currently, the assessment of the severity of the impact caused by a disruptive event primarily relies on data pertaining to human casualties and property damage, and there are few statistics on the impact of the damage event on the traffic network. Therefore, in the context of missing data, we rank the criticality based on the relevant static attributes of the urban road traffic network from a resilience perspective. Post-accident identification primarily relies on the actual consequences caused by the damage to rank the criticality of road sections. After an accident, a judgment on the severity of the accident can be formed based on the actual consequences caused by the accident. Identifying critical road sections in this manner is a manifestation of the specific analysis of specific problems in accordance with the actual situation.

Before presenting the framework, we need to introduce an important ranking function, rank(). The rank() function is used to rank the performance of road segments according to their attributes. Since each attribute measure is positively or negatively correlated with the keyness ranking, the function of rank() is to identify the degree of performance of these measures: the better the performance of a particular indicator, the higher the ranking of the road under this attribute, thus eliminating the problem of positive and negative data correlation.

Before the accident, we select the relevant attribute of the urban road traffic network from a resilience perspective, and we use the relevant indicator that reflects that attribute as a measure, as shown in Equation (1).

$$R_i=rank\left(A\left(x\right)\right)$$

(1)

where $R_i$ denotes the ranking of road sections under a certain attribute, and A(x) denotes the relevant index that reflects attribute i.

To achieve this, we first select a set of relevant attributes from the resilience perspective. These attributes are used to obtain the importance ranking of each road section. Next, based on the significance of each attribute, we assign corresponding weights to the attributes. We then use a weighted combination of the ranking results to derive the final ranking. This process yields the comprehensive ranking of road sections from the resilience perspective before the disruptive event occurs. The formula for this calculation is shown in Equation (2):

$$R_{before}=rank\left(a_1{R}_1+a_2{R}_2+\cdots +a_n{R}_n\right)$$

(2)

Here, R before represents the pre-event resilience-based ranking of the road sections, R_i denotes the ranking of the i-th attribute, and a_i is the weight assigned to the i-th attribute.

After the accident, we use the severity of the actual impact brought about by the accident as a measure to rank the criticality of the road section. The main actual impact is the socio-economic loss, including various aspects such as the casualties caused by the accident, property damage, and traffic delays; the formula is shown in Equation (3).

$$R_{after}=rank\left(social-economical loss\right)$$

(3)

As a result, a complete resilience perspective-based framework for identifying critical roads in urban road traffic networks is developed, using the equation shown in Equation (4), which is a theoretical and applicable framework for determining the importance ranking of each road segment in urban road traffic networks before and after an unanticipated disruptive event.

$$\left\{\begin{array}{c}{R}_{before}=rank\left(a_1{R}_1+a_2{R}_2+\cdots +a_n{R}_n\right)\hfill \\ R_{after}=rank\left(social-economical loss\right)\hfill \end{array}\right.$$

(4)

3. Case Study

Shanghai boasts a well-established transportation system, comprising a comprehensive transportation network on an extensive scale, which includes railroads, waterways, highways, airways, railways, and other transportation modes.

In order to construct the Shanghai urban road traffic network required for this study, the entire Shanghai road network was downloaded from OpenStreetMap (OSM) and imported into ArcGIS 10.7 for processing. In order to simplify the complexity of the Shanghai urban road traffic network, ArcGIS software’s road filtering function was utilized to retain three types of roads: highways, expressways, and trunk roads. The remaining roads were eliminated to yield a sparse Shanghai urban road traffic network, with each road assigned a unique OSMID. The urban road traffic network in the Simulation of Urban Mobility (SUMO) is depicted in Figure 2, encompassing 5933 nodes and 13,630 roads, with each road’s maximum speed limit consistent with the actual road network. To more closely align with the real scenario, SUMO’s batch traffic signal addition function was used, setting up default phase traffic signals at all the main road intersections within the Shanghai urban road traffic network.

The Simulation of Urban Mobility (SUMO) platform offers a random Trips function, enabling users to generate a network-wide distribution of random traffic flows across any network. The probability of an edge in the network serving as the starting and ending edge of a trip can be determined by the road’s speed limit. In this study, three types of urban roads are selected for the Shanghai urban road traffic network, each with distinct speed limits. The parameter for selecting the road section speed limit as the edge probability is set at 2, implying that the probability of a road section serving as the starting or ending edge is proportional to the square of the road section’s speed limit. This approach yields the traffic flow throughout the Shanghai urban road traffic network. The timing of traffic generation and the magnitude of traffic flow are determined based on several pre-experiments. The principle for determining the timing of traffic generation and the magnitude of traffic flow is to approximate the real traffic flow of the Shanghai urban road traffic network. Under normal conditions, the traffic flow in the network runs smoothly without congestion. However, when a disruptive event occurs, the existing traffic flow leads to congestion due to re-routing, thereby magnifying the impact of the disruptive event on the urban road traffic network. Based on this, we set the traffic flow at 100,000 vehicles per hour, issued at equal intervals during each hour. For the vehicle following model and lane change model, we selected the default Krauss following model and the LC2013 lane change model.

This research simulates scenarios where road sections are subjected to disruptive events, resulting in a loss of their capacity and service level. Building upon the resilience-based critical road identification framework for urban road traffic networks established in previous research, we integrate the actual urban road traffic network in Shanghai and apply the critical road identification framework to the Shanghai road network, thereby determining the failure mode and recovery mode in the simulation experiment. In the pre-accident identification framework, we select three attributes of the urban road traffic network: traffic attributes, topological attributes, and urban functional attributes. These are used to assess the criticality of each road segment in the network, and the failure mode is comprehensively determined based on the criticality of the road segments within the Shanghai urban road traffic network. In the post-accident identification framework, we consider the impact of the damage caused by each road segment in the network according to the actual socio-economic loss induced by the disruptive event, and we determine the recovery mode based on the criticality of the road segments within the Shanghai urban road traffic network.

To obtain real-time traffic attributes, we utilized the API interface provided by AMAP to calculate the real-time average speed data for driving on all road sections within a specific area. Specifically, we collected the real-time average speed data for all roads across the entire city of Shanghai at 18:00 during an evening peak hour on a weekday. This data was then matched with the corresponding road sections in the SUMO road network, allowing us to determine the real-time average speed for all roads within the studied network. Based on the relationship between traffic flow, speed, and density, and leveraging the classical Underwood model, we inferred the real-time traffic flow on each road section using the real-time average speed data. The road sections were subsequently ranked according to their traffic volume.

The relationship between flow, speed, and density is shown in Equation (5), the equation for the Underwood model is shown in Equation (6), the equation of the traffic attributes in the pre-accident identification framework is shown in Equation (7), and the results of ranking the road sections according to traffic flow size are shown in

Table 1. Results of the ranking of road sections according to traffic flow (partial).

id	Speed (km/h)	Flow Rate (veh/h)	Traffic Sorting
Nanliu Highway	45	1765.493	1
Shenzhuan Highway	45	1765.493	1
Nanlu Highway	45	1765.493	1
Puxing Highway	45	1765.493	1
Huadong Road	45	1765.493	1
Boyuan Road	45	1765.493	1
Zhaozhong Highway	45	1765.493	1

.

$$q=uk$$

(5)

$$u=u_f{e}^{-{\displaystyle \frac{k}{k_m}}}$$

(6)

$$R_{traffic}=rank(traffic volume)$$

(7)

where q denotes the flow rate, u denotes the travel speed, k denotes the density, $u_f$ denotes the free flow velocity of the road section, and $k_m$ denotes the density corresponding to a large flow rate, i.e., the optimal density.

For topological attributes, we modeled the road network using Python 3.0 software, utilizing the coordinates of the road section endpoints provided by the SUMO road network file. We computed the betweenness centrality of each road section in the Shanghai urban road traffic network as its topological attribute characterization. The formula for betweenness centrality is presented in Equation (8), and the formula for the topological attributes in the pre-accident identification framework is shown in Equation (9). The road sections are ranked according to the magnitude of betweenness centrality, and the results of the road section ranking are shown in

Table 2. Results of ranking of road sections according to betweenness centrality (partial).

id	Side Betweenness Centrality	Side Betweenness Centrality Sorting
Inner Ring Elevated Road	0.094833	1
Cheting Highway	0.08727	2
Husong Highway	0.071907	3
Zhonghuan Road	0.065454	4
Beisong Highway	0.055049	5

.

$$C_b\left(i\right)={\displaystyle \frac{2\sum _{j<k}\frac{g_{jk}\left(i\right)}{g_{jk}}}{\left(n-1\right)\left(n-2\right)}}$$

(8)

$$R_{topology}=rank\left(betweenness centrality\right)$$

(9)

Here, C_b(i) represents the betweenness centrality of road section i, n denotes the total number of nodes in the network, g_jk is the total number of shortest paths between nodes j and k, and g_jk(i) indicates the number of those shortest paths that pass through road section i.

To assess urban functional attributes, we utilized the API interface provided by AMAP to extract the locations and attributes of all Points of Interest (POIs) of specific types within a defined area. Specifically, we focused on four key types of POIs across the entire city of Shanghai: higher education institutions, government agencies, shopping malls, and hospitals. We obtained their coordinate locations and attributes and mapped them onto the Shanghai urban road traffic network. Using the nearest neighbor analysis function of ArcGIS software, we matched each POI to its closest road section within the network. The number of POIs matched to each road section was then used as a measure of the urban functional attributes for that particular road section. In other words, the greater the number of POIs associated with a road section, the stronger its urban functional attributes. The formula for calculating the urban functional attributes in the pre-accident identification framework is presented in Equation (10). The road sections were ranked based on the number of matched POIs, with the ranking results shown in

Table 3. Results of the ranking of road sections according to the number of POIs (partial).

id	Number of POIs for Higher Education Institutions	Number of POIs for Government Agencies	Number of Mall POIs	Number of General Hospital POIs	Total Number of POIs	POI Number Sorting
Wenchuan Highway	10	11	2	2	25	1
Inner Ring Elevated Road	16	2	0	0	18	2
Shanghai Ring Expressway	6	2	1	5	14	3
Humin Road	7	0	4	1	12	4
Caoan Highway	11	0	0	0	11	5
Longwu Road	0	10	0	0	10	6
Zhaojiabang Road	2	2	3	2	9	7
Dalian West Road	9	0	0	0	9	8

.

$$R_{city-function}=rank\left(number of poi\right)$$

(10)

After obtaining the separate ranking of the three attributes, a weight of 1/3 is assigned to each of the traffic attributes, topological attributes, and urban function attributes. The specific formula of the pre-accident identification framework is shown in Equation (11), and the weighted comprehensive ranking results based on the keyness of the road segments are shown in

Table 4. Comprehensive ranking of road sections based on criticality (partial).

id	Traffic Sorting	Side Intermediate Number Sorting	POI Number Sorting	Total Sort	Ranking
Nanlu Highway	1	106	137	81	1
Longwu Road	333	71	12	137	2
Beiqing Highway	333	36	50	138	3
Nanliu Highway	1	28	474	166	4
Hunan Highway	333	44	137	170	5
Shenzhuan Highway	1	88	474	186	6
Jungong Road	1	500	65	187	7
Zhonghuan Road	333	10	248	195	8

.

$$R_{before}=rank\left({\displaystyle \frac{1}{3}}{R}_{traffic}+{\displaystyle \frac{1}{3}}{R}_{topology}+{\displaystyle \frac{1}{3}}{R}_{city-function}\right)$$

(11)

Using this ranking method, the top 50 roads in the Shanghai urban road traffic network in terms of criticality are selected as the target roads for simulated failure, and they are failed in turn in the simulation experiment.

Based on the actual results of the failure of the road sections in the urban road traffic network, recovery measures are prioritized for the failed road sections with high impact. It is assumed in this study that only one road can be recovered at a time, implying that failed roads will be sequentially recovered in the failure mode. The average waiting time of all the road sections in the network is aggregated to obtain the total waiting time of the whole network. Since the failure of one road segment is set in each time interval, the difference between the total network wait time in the two intervals before and after the event can be considered as the impact of the failure of this road segment on the total network wait time. To better represent the socio-economic loss to road users caused by the road section failure, we propose the concept of “value of time”. Using the average monthly salary of Shanghai residents in 2021 as a benchmark, which is RMB 9580, and the average hourly wage of Shanghai residents in 2021 is USD 8.17, considering the current exchange rate. The concept of the value of time links the roadway waiting time and socio-economic loss, providing a conduit to calculate the socio-economic loss from the SUMO experimental data. Consequently, we obtain the formula to calculate the socio-economic loss from each road section failure, as shown in Equation (12).

$$\mathrm{SEL}=\mathrm{VoT}\times \left({\mathrm{T}}_i-{\mathrm{T}}_{i-1}\right)$$

(12)

where SEL represents the Social–Economic Loss (SEL) and VoT represents the value of time (VoT), which is USD 8.17/h. $T_{i-1}$ represents the total waiting time of the whole network in the previous time interval. $T_i$ represents the total waiting time of the whole network in the latter time interval.

The resulting as shown in

Table 5. Ranking of socio-economic losses of road segments (partial).

id	Total Network Wait Time Increase Value (h)	Socio-Economic Loss (USD)
Huqingping Highway	52.31	427.34
Yingbin Expressway	47.07	384.55
Zhouhai Road	44.99	367.64
Zhaozhong Highway	44.78	365.85
Chuannanfeng Highway	42.65	348.47
Puxing Highway	41.78	341.32
Boyuan Road	41.66	340.37
Zhonghuan Road	38.51	314.61
Shenzhuan Highway	29.08	237.61

, the ranking method ranks the socio-economic loss impacts of the failures generated by the 50 critical roads selected in the failure model as the order of the recovery model, and it restores them sequentially in the recovery process.

In the simulation experiment, disruptive events sequentially occur on the road sections in the order identified in the failure mode at specific time intervals. These events cause the target road sections to lose capacity and service level. Subsequently, recovery measures are implemented sequentially in the order identified in the recovery mode at certain time intervals to restore the capacity and service level of the target road sections. The detailed simulation experiment process is as follows.

During the initial hour of the simulation experiment, traffic flows are gradually generated randomly and dispersed throughout the network, slowly reaching a balanced and stable state [19]. Based on the preliminary experiments, it takes approximately 50 min for the traffic flow to disperse throughout the Shanghai urban road traffic network and reach a stable operational state. To avoid interference with subsequent experiments, we allow the traffic flow to run freely in the network for the first hour. After one hour, a road is closed every 10 min according to the sequence established in the failure model, simulating the occurrence of a disruptive event that eliminates the roadway capacity and service level. Simultaneously, the software is set to allow all road users to re-route every 10 min based on road conditions, simulating the process of road users re-routing to the shortest alternative routes upon learning of the incident. After all 50 critical roads identified in the failure mode have sequentially failed, the simulation experiment is allowed to continue running for one hour to reach a new steady state. This stage simulates the process of officials data on the impact of the disruptive event and specifying a recovery strategy. After one hour, one road is opened every 10 min in the order identified in the recovery model to simulate the completion of the disruptive event and the restoration of capacity and service level to the roadway. After the 50 roads identified in the recovery model are sequentially restored, the simulation is allowed to continue running for one hour to reach a new steady state, at which point the simulation concludes. The flow of the entire simulation is shown in Figure 3.

4. Results

Using the data output from SUMO, the average speed of each road section in the Shanghai urban road traffic network in every ten-minute time interval is selected as a measure of the network function, and the waiting time in every ten-minute time interval is used to calculate the socio-economic loss. Since the Shanghai urban road traffic network in SUMO is a directed graph, we have to process it into an undirected graph in order to facilitate the visualization of the data. The speed of a road closed due to a vandalism event is set to zero, and the speed of the same road section in both directions is averaged to obtain the average speed of each road section interval in the network every ten minutes.

The average speed of the whole network during the ten-minute interval can be obtained by summing up the average speed of all the road sections during the ten-minute interval and averaging them. The horizontal axis represents the time and the vertical axis represents the average speed of the whole network, so we can draw a graph of the dynamic change in the average speed of the whole network over time. The total waiting time in the network can be obtained by summing up the waiting time of all the sections in each ten-minute interval, and the socio-economic loss of the network can be calculated by Equation (12). With the horizontal axis representing the time and the vertical axis representing the socio-economic loss of the whole network, a graph of the dynamic change in the socio-economic loss of the whole network with time can be drawn. By fitting these two curves with a polynomial, we can obtain the network-wide average speed and socio-economic loss distribution in time under the scenario of a bad traffic accident.

The network-wide average speed and the time distribution of the network-wide socio-economic loss for the disruptive event scenario are shown in Figure 4 and Figure 5, respectively. The blue dashed lines in the two figures indicate the processed simulation experimental data, and the red solid lines indicate the polynomial fitted curves.

The time distribution of the average speed of the whole network shown in Figure 3 can be divided into five phases: the initial smooth phase (0–t1), the disruption phase (t1–t2), the post-disruption smooth phase (t2–t3), the recovery phase (t3–t4), and the post-recovery smooth phase (t4–t5). Before the damage event (initial smooth phase), the whole network is in a normal operation state, and the average speed of the whole network is in a smooth and slightly fluctuating state. After the disruptive event (disruption phase), the average speed of the whole network starts to fluctuate and drop. When the drop reaches its lowest value (post-damage stabilization phase), a new stabilization phase is reached. However, at this time, the capacity and level of service are low and the network average speed is in a very low, slightly fluctuating state. After the roadway network gradually starts to take recovery measures (recovery phase), the network average speed gradually increases and reaches a new phase (post-recovery smooth phase) at a specific value. It is worth pointing out that since we are simulating a short recovery period, the remaining traffic congestion has an impact on the average speed of the whole network, and the average speed of the post-recovery smooth phase is slightly lower than that of the initial smooth phase.

Similarly, the time distribution of the socio-economic loss of the whole network shown in Figure 4 can be divided into five phases: initial smooth phase (0–t1), disruption phase (t1–t2), post-disruption smooth phase (t2–t3), recovery phase (t3–t4), and post-recovery smooth phase (t4–t5). Before the disruptive event, the entire network is in a normal operating state, with a slight extension of the waiting time due to the gradual increase in vehicles and a gradual increase in socio-economic losses. After the disruptive event (disruption phase), the network-wide waiting time increases rapidly, thus leading to a rapid increase in socio-economic losses. The socio-economic loss also reaches a maximum when the full network reaches the lowest value of capacity and level of service (the post-damage plateau phase). After the road sections gradually start to undergo restoration measures (recovery phase), the total waiting time decreases due to the restoration of road capacity and the socio-economic losses gradually decrease. After all the sections are restored (post-recovery stabilization phase), the socio-economic loss stays at a specific value.

To visualize the spatial distribution of traffic conditions, each road section is assigned a color based on its average speed. By selecting a representative moment from each of the five phases described above, we can plot the spatial distribution of average speed across the network. This allows us to observe how the average speed of road sections changes over time and identify the spatial patterns associated with different phases of the disruptive event, as illustrated in Figure 5.

Figure 6a represents a moment in the initial smooth phase when the traffic flow runs smoothly throughout the network. Due to the traffic signal phasing, the average speed of the road segments near intersections with traffic signals is slightly lower than the average speed of other road segments. Figure 6b represents a moment in the disruption phase, where the disruptive events occur sequentially on each road segment. Here again, we define a road segment as congested if the average speed of the road segment is below 80% of the maximum speed limit. At this moment, congestion is generated on the road where the disruptive event occurs and has a tendency to spread to the surrounding roads. Figure 6c represents a moment in the post-disruption smooth phase, where the disruptive event occurs on 50 critical roads in Shanghai’s urban road traffic network, resulting in the loss of capacity and level of service on these 50 roads and the spread of congestion to the surrounding roads. Figure 6d represents a point in the recovery phase where traffic congestion on the surrounding roads is relieved as road capacity is sequentially restored. Then, there are still impacts on the network. Figure 6e represents a point in the post-recovery smooth phase at which the whole Shanghai urban road traffic network enters a new smooth operation phase. However, the overall capacity and service level will be slightly lower than during the initial smooth phase.

5. Conclusions

In this paper, we propose a critical road identification framework for urban road traffic networks, grounded in a resilience perspective. This framework comprises both a pre-incident identification framework and a post-incident identification framework. It serves as a theoretical and applicable identification framework for any unanticipated disruptive event, enabling the determination of the importance ranking of each road segment within the urban road traffic network, both prior to and following the disruptive event. The importance ranking of the road sections derived from the pre-incident identification framework can identify critical road sections before the onset of the disruptive event, facilitating the timely deployment of relevant human and material resources to protect these important road sections in advance. Moreover, the importance ranking of the road sections obtained from the post-incident identification framework can inform the formulation of corresponding restoration orders and strategies following the disruptive event, given limited resources. Thus, this approach enables the optimal and swiftest mitigation of the negative impacts induced by the disruptive event.

Furthermore, this paper utilizes a real-world urban road traffic network in Shanghai as a case study, establishing the importance ranking of the urban road traffic network in Shanghai both prior to and following the occurrence of disruptive events. The disruption to urban roads caused by unanticipated disruptive events is simulated using the micro-traffic simulation platform SUMO. The study explores the impact of the entire process, from before the occurrence of unanticipated disruptive events to after the implementation of recovery measures, on the resilience of the urban road traffic network. The findings indicate that, in terms of temporal distribution, the average network speed under the scenario of a disruptive event occurrence transitions through five phases: the initial smooth phase, damage phase, post-damage smooth phase, recovery phase, and post-recovery smooth phase. Regarding spatial distribution, congestion due to the occurrence of disruptive events initially increases with time across the five phases, then gradually eases until it returns to normal, exhibiting an outward spread during the disruption phase. The proposed framework not only enhances the resilience of urban road traffic networks but also aligns with the broader goals of sustainable development. By prioritizing critical roads for protection and recovery, it minimizes traffic congestion and reduces carbon emissions, contributing to environmental sustainability. Additionally, the framework has significant economic value since it reduces the socio-economic losses caused by traffic disruptions, thereby supporting the efficient functioning of urban economies.