A Safety Level Evaluation Model based on Network Analysis: Enhancing Accessibility & Evacuation Safety in Ho Chi Minh City’s Alleyways

ABSTRACT In this study, an evaluation model is developed to analyze the safety level of a street network in terms of accessibility for emergency services and evacuation risk for residents, especially for cities experiencing rapid urbanization and densification. The evaluation model is created based on the network geometry and street width using the Network Voronoi algorithm, and four evaluation variables are developed, namely the accessibility risk, unreachability risk, edge responsibility, and flow capacity. Next, the model is applied to an alleyway neighborhood in Ho Chi Minh City, characterized by a labyrinthine mesh and tree-shaped network, and narrow street widths. Finally, improvement interventions, such as adding new links and widening alleys, are implemented in three case studies, and the results are compared in terms of cost, social impact, and safety improvement. The results show that the most efficient improvement strategy is to target the weakest point in the network, except for the flow capacity, which, however, can detect intersections at risk on evacuation routes, which cannot be derived from the network topology. The developed evaluation model is not only useful to analyze the current risk level in the network but is also a powerful tool to evaluate future infrastructure improvement projects. GRAPHICAL ABSTRACT


Background and purpose
The juxtaposition of conservation and modernization in the urban tissue and its impact on local communities has presented a great challenge for local governments and city planners. Especially in cities that have experienced rapid urbanization and densification. Labyrinthine mesh and tree-shaped street networks, characterized by dead-end streets and narrow street widths, are representing a great risk for urban safety, more specifically the access for emergency services and the evacuation safety of residents in case of a natural or human-made disaster. In the context of CONTACT Tran Thi To Uyen M.N touyen.tran4@gmail.com Cw-701, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan urban expansion and spatial development in Vietnam's cities, the World Bank (2011) states that upgrading existing neighborhoods is one of the most efficient ways to improve housing for the urban poor and the lower middle class without leading to gentrification. However, improvement projects of the alley expansion movement in Ho Chi Minh City, which started in the Phú Nhuận District in 1999, have not been based on a quantitative analysis. In this context, the purpose of this research is to develop an evaluation model to analyze and enhance the accessibility and evacuation safety of street networks in cities that have experienced rapid urbanization and densification, characterized by labyrinthine mesh and tree-shaped street networks, using a quantitative analysis to achieve a result of higher resolution. This model supports the decision-making process of city planners and local governments in policymaking and city governance, especially for alleyway upgrading projects. This model considers the social impact on local communities, the economic impact depending on the size of the affected area, and the improvement of urban safety in terms of accessibility and evacuation, to compare the projected results. The developed model is expected to assess the current safety level of a street network and detect vulnerable locations in order to decide where to execute improvement interventions.
A large number of researches have been conducted on urban safety; however, no current research focuses on the specific spatial constraints of labyrinthine mesh and tree-shaped street networks combined with narrow street widths, using network analysis. Furthermore, while numerous studies have investigated urban safety in developed countries, this research is based solely on the network topology and street width, and therefore can easily be applied in developing countries, where data availability is scarce. The robustness of the mathematical model and capacity of the model to analyze the safety level of street networks with limited data represent a powerful tool for the sustainable development and safety enhancement of fast developing cities across regions and cultures.
To verify the effectiveness of this method, the developed model will be applied to a real urban area in Ho Chi Minh City's alleyway neighborhoods, which represent the core element of the city's urban identity, and according to Gibert and Pham (2016), the urban network of alleyways still houses about 85% of the city dwellers. Shaped like a labyrinthine network between the linear axes of the existing urban grid and formed during the French colonial period, the alleyways emerged during the uncertain times of the 1950s and 1960s as part of a migration to the city and a spontaneous densification and urbanization process.
Similar urban fabrics can be found in various cities with different climates, cultures, and regional features, such as the historic center of Damascus in Syria and the old medina in the historic city of Fez in Morocco; the latter was described by Johansson (2006) as an irregular street network characterized by narrow streets and cut deep canyons where car accessibility is impossible except for a few distributor roads. This structure can also be found in many historical East Asian cities, one example is the neighborhood of Kyojima in the eastern inner city of Tokyo. Rapidly urbanized without any planning after the Great Kanto earthquake in 1923, the constant threat of natural disasters and the lack of functional efficiency compatible with the motor age still remain (Kitahara 2001). Showcasing the same labyrinthine mesh and tree-shaped street networks and narrow street widths, the developed model can be applied in these urban areas.
This research focuses on an area located in Ho Chi Minh City's Ward 2 of District 5 (see Figure 1.1). The neighborhood, displayed in Figure 1.2, is located between four main roads. The inner shape of the analytical area represents a typical urban fabric, which emerged in the 1950s and 1960s, when many refugees from rural areas migrated to the city during the war leading to housing shortages and the densification of the alleyway system. This movement and spontaneous urban development led to the formation of Ho Chi Minh City's alleyway system, which has lasted until today.

Research process and outline of the paper
The goal of this research is to create an original model using network analysis by developing new evaluation variables to estimate the safety level in the network. The outline of this paper is illustrated in Figure 1.3.
In section 3.1 the structure of the network data is described, and the data processing method, which adds new set parameters and calculations, are explained to prepare the model for the analysis.
Section 3.2. introduces specific characteristics of different nodes, such as the position and distribution of house nodes and the location of accessible points, and measures the street network considering its topological structure, using the network Voronoi algorithm.
This research is based on the concept that the safety level of a location in the network depends on two factors: the accessibility for emergency vehicles and the risks that can be encountered on the evacuation route, representing situations with two opposite directions of movement, entering or leaving the network in a case of emergency.
In section 4, these two strategies are further classified into sub-categories and four new evaluation variables are developed, namely the accessibility risk in section 4.1, the unreachability risk in section 4.2, the edge responsibility in section 4.3 and the flow capacity in section 4.4. The evaluation variables are derived from a bottom-up approach, observing the evacuation process and emergency response in dense urban areas with narrow street widths and mesh and tree-shaped street networks, and describes potential emergency scenarios and appropriate emergency response.
In section 5, the behavior of the developed safety evaluation variables is observed on typical network topologies. In section 6, the developed model is applied to Ho Chi Minh City, first, evaluating the safety level of the current situation in section 6.1, then safety improvement strategies, which modify the network structure by adding new edges or widening edges, are applied in three case studies in section 6.2. Finally, the results of the improvement interventions are evaluated in section 6.3. and concluded in section 7.

Literature review
Access to emergency services including police, fire, rescue, and medical care is essential to the overall health, safety, and general welfare of any population, and the roadway infrastructure system can greatly affect accessibility to these services (Novak D. and Sullivan J. 2014). Hence, urban safety has always been an essential focus for urban planners and governments. This section explains the relation of this study to existing network analysis models, previous researches dealing with accessibility and emergency evacuation, as well as urban safety on different scales and the socio-economic context of urban communities, in this order. Tan, Hu, and Lin (2015) state that emergency response activity relies on transportation networks, highlighting the primary role of urban street networks for emergency response. This calls for a deeper look into network theory models, where a large number of researches deal with network topologies, robustness, and modification strategies to increase their resilience. Different strategies have been developed to optimize network robustness, such as edge rewiring through degree-preserving modifications under a constrained budget (Chan and Akoglu 2016), first principled manipulation algorithms by edge/node removal or addition, based on the measure of natural connectivity (Chan, Akoglu, and Tong 2014), and an algebraic connectivity optimization via link addition compared in a topological metric-based, Fiedler vector-based and random link addition models (Wang H. and Van Mieghem P.t 2008). However, in the case of street networks, specific characteristics related to the network, such as the spatial constraints of the urban context and the metric distance, have to be considered to modify the network structure. In this regard, this study integrates, in addition to the street network topology, specific parameters of the urban structure to the model, such as the location of houses, the length of street segments and street widths.
Furthermore, while a certain strategy might work for a given type of graph, it may not work for other network topologies. Therefore, it is necessary to assess the behavior of the specific network topology of dense and traditional urban networks, which combines labyrinthine mesh and tree-shaped networks. In this regard, Buhl et al. (2006) studied topological patterns in street networks of self-organized settlements and analyzed their efficiency and robustness using the Minimal Spanning Tree (MST) and Greedy Triangulation (GT). They found shared structural properties with tunneling networks, as both types of networks exhibit a similar relationship between cost and efficiency. Buhl et al. (2004) compared the development of such networks with ant galleries and explained their structure by the strong spatial constraints under which they grow and the emergent organization of network patterns studied on social insects: a concept that aligns with the formation of Ho Chi Minh City's alleyways. Focusing on the efficiency and robustness in ant networks of galleries, they state that the efficiency of self-organized graphs is reached by increasing the meshedness, that is by merging trees. However, this needs further investigation to be applied in an urban context, especially combined with narrow street widths. Based on this study, the developed model analyzes the increase of meschedness in the alleyway network and indicates appropriate positions to add new links in the street network.
Spatial accessibility to emergency services is an important indicator for evaluating the effectiveness of public health services (Xia et al. 2019) and its enhancement is a key strategy to help improve emergency response, minimize property loss, and reduce injuries and deaths (KC, Corcoran, and Chhetri 2020). There have been numerous studies investigating accessibility of emergency services based on network theory, considering potential modifications in the network structure. The risk of disruptions in the network can have a great impact on the accessibility of emergency services. Ertugay, Argyroudis, and Düzgün (2016) consider road closure probabilities in the case of an earthquake in their accessibility analysis, due to ground failure, damage to bridges and overpasses, and collapses of buildings adjacent to road edges. Tan, Hu, and Lin (2015) developed an agent-based simulation of building evacuation, considering evacuee's spatial knowledge of the stationary environment during a normal situation and the event knowledge of the predictable spatial change for fire-fighting purposes, which breaks the spatial connectivity between adjacent spaces and consequently, some escape routes are blocked. A link-focused measure based on the network theory of closeness and connectivity has been developed by Novak and Sullivan (2014), quantifying a link's relative importance in its system-wide contribution to emergency service accessibility. Chen, Wu and Hsu (2019) modify the network structure by widening narrow alleys in the old town of Taipei, combining the facility location problem and shortest path problem and focusing on minimizing the response time of firefighting operations.
However, these studies analyzing accessibility through network structure modifications are not suitable to analyze the network topology of this study, consisting of mesh and tree-shaped networks and characterized by narrow street widths. Furthermore, whereas previous studies assume that every location in the street network is usually accessible and only faces a disconnection in case of a disaster, this study includes the evaluation of street networks where certain locations are not accessible to emergency vehicles at any time due to narrow street widths.
A number of authors have analyzed emergency service accessibility based on the floating catchment method (FCA), which methodologically enables the integration of multiple sources of information into a single one. KC, Corcoran, and Chhetri (2020) employ the enhanced two-step floating catchment method (E2SFCA) to investigate the optimality of fire station locations in relation to changing spatial distribution of the population. Xia et al. (2019) propose a model of spatio-temporal accessibility to emergency medical services (ST-E2SFCA), considering temporal variation in population distribution in the greater Tokyo area through a large volume of GPS data of millions of users and compare the accessibility over space and time.
Both studies on emergency service accessibility consider temporal variation in population distribution on a different scale, long-term population growth and real-time population location, as well as the location of emergency facilities. However, a large set of data is necessary to apply these models on an urban area, which is difficult to procure in fast-developing cities, where data availability is scarce, often not collected or difficult to obtain. Therefore, this study introduces an easily operated evaluation model, based solely on network data, such as the street network and street width, which can easily be applied in almost in every urban area without relying on large sets of data.
In terms of evacuation safety, Brachman and Dragicevic (2014) developed an emergency evacuation model based on network science accounting for biological variables (fear, survival instinct) and social variables (emergency management, disaster response) in addition to the physical variables (transportation network, location of evacuees). Because of its ability to examine various emergency scenarios, the study requires a great number of datasets, such as GIS data, to determine the number and spatial location of evacuees, registered vehicle data to evaluate the traffic flow and the location of hazards, such as oil refineries. Similarly, Chen et al. (2020) investigate the evacuation vulnerability in urban areas in a fine-grained spatiotemporal scale, overlapping mobile phone location datasets with the road network of Shanghai. While these studies provide valuable concepts to assess the complexity of emergency evacuation through ample data availability, they do not propose a solution to enhance the current evacuation safety of the urban structure. In this regard, this study evaluated the current evacuation safety level and evaluates the efficiency of network modifications, such as edge widening or adding new links, essential for the development of dense urban areas.
In this context, Zuo et al. (2021) propose a method of improving emergency evacuation effectiveness under the restriction of limited available land resources in high-density areas, which is combined with urban renewal planning, aiming at optimizing the layout of shelters and evacuation passageway. While the safety of the evacuation process is improved in a "micro update" manner, they do not consider the addition of new links in the street network, which is a highly efficient improvement method for mesh and treeshaped networks, dealt with in this study. Oki and Osaragi (2014) focus on wide-area evacuation difficulty in case of a major earthquake in a densely built-up wooden residential area in Tokyo combining a multi-agent simulation model with a property damage model describing building collapse. However, in the context of rapid urbanized areas, building information is difficult to obtain and building materials vary between regions and cultures. Therefore, this study proposes a model that can be applied in less data covered areas, where urban renewal and safety improvement is highly needed. Zhang et al. (2021) research about pedestrian evacuation modeling and simulation in multi-exit scenarios using a social force model, while Chan (2019) stresses the importance of a mandatory building inspection scheme and sustainable building maintenance for safer and healthier cities, highlighting the present situation of building deterioration in Hong Kong. In order to ensure the health and safety of people, a safe evacuation process has to be ensured in different emergency scenarios, reaching from the architectural building scale to large urban areas. This study focuses on evacuation safety on a neighborhood level, combining pedestrian evacuation of residents and the network characteristics and topology, stressing the importance of the conservation of traditional neighborhoods, especially in fast-developing cities, where community ties are deeply embedded in the daily life and social structures of residents. In the case of Ho Chi Minh City, Gibert and Pham (2016) emphasize the importance of the multifunctionality and adaptability of the alleyway neighborhoods from a socio-economic point of view and their ability to welcome a multiplicity of activities and adapt to all social structures.
Although many studies have evaluated urban safety, there seems to be no method that can be adapted in traditional and dense urban areas, especially focusing on mesh and tree-shaped network topologies, commonly found in self-organized urban structures. Furthermore, research about Vietnamese cities and their urban structures from a computational approach is scarce, which could be due to the difficulty of obtaining sufficient information. Therefore, this study introduces an easily operated evaluation model, based solely on network data; this is a necessity as Ho Chi Minh City is experiencing rapid development and modernization.

Analysis target and data processing
The model is based on the geometrical structure of the street network in order to calculate the safety level of a position in the network, more precisely, the accessibility of emergency services and the evacuation danger.

Weighted alleyway neighborhood network
An alleyway neighborhood located in Ward 2 of District 5 in Ho Chi Minh City is taken as a case study area. The site has a total area of 0.127 km 2 and contains a population density of 37,486 pers./km 2 . (Ho Chi Minh City Statistics Office 2019) The input data representing land plots was created based on the digital format map provided by the "Ho Chi Minh City Urban Planning Information" (Ho Chi Minh City Department of Planning and Architecture). The CAD drawing contains land plot borders enabling the measurement of street width attributed to the drawn edges along with their length. A new edge is drawn when there is a change in direction or at an intersection as no curves are drawn in the network and all edges represent straight lines. The entrances of each house, hereinafter referred to as house nodes, are connected to the street network by an edge traced from the middle of the land plot border perpendicular to the street and has a set length of 0. A node is positioned at each end of an edge. The edge attributes are classified into nine categories. The edges of the main street representing the border of the alleyway neighborhood, house edges, and the remaining edges are classified depending on the street width with a set safety threshold of 3.5 m, as shown in Figure 3.1.
This dataset was extracted and applied in a Python program. The proposed model was built using NetworkX, an open-source Python package, by structuring the extracted data creating an adjacent list with the neighboring nodes of each node and an attribute list containing information of the edge length and street width category.

Accessible and inaccessible networks
According to previous research by Lin and Chen (2009), the necessary space for fire operations can be estimated by adding the width of the fire engine, which is a maximum of 2.6 m, the firefighter operation space of 0.4 m, and the space for the switch door, which is 0.5 m. Therefore, the sum of 3.5 m should be the minimum space for firefighting and is set as the safety threshold to analyze the accessibility of emergency vehicles in the network. First, all edges with a width below 3.5 m are classified as narrow edges, and all edges with a width above 3.5 m are classified as wide edges, including those with the main street attribute. The safety level of a house is equal to its adjacent edge. In the next step, all the narrow edges are removed from the network graph. Setting the intersection nodes between the alleyway network and the main street, hereinafter defined as evacuation points, as source nodes and all nodes in the network as target nodes, all nodes that can be reached belong to the accessible network, as referred hereinafter, and all others belong to the inaccessible network. In Figure 3.2, the blue links in the network represent the alleys where emergency vehicles can reach, and the red links represent the narrow alleys that are impassable for emergency vehicles or wide edges that are not connected to the accessible network, and therefore belong to the inaccessible network. The evacuation points are the target locations where residents should go in case of an evacuation. The nodes where the accessible network switches to the inaccessible network are defined as accessible points, as they represent the furthest point an emergency vehicle can enter inside the network. These nodes are key for calculating and analyzing the accessibility and evacuation risk inside the network in the next steps (See Figure 3.3).
The accessible points are the generators used to calculate the accessibility network voronoi diagram, assigning each node on the inaccessible network to the closest accessible point. The evacuation points are the generators used to calculate the evacuation network voronoi diagram, assigning each node in the network to the closest evacuation point as shown in Figure 3.4.

Safety level evaluation model
This section introduces four evaluation variables of the safety evaluation model, namely the (1) accessibility risk, (2) unreachability risk, (3) edge responsibility, and (4) flow capacity, as shown in Figure 4.1.
The four evaluation variables have been developed to react to specific risks criteria and emergency situations, analyzed based on the available network data.
(1) The accessibility risk focuses on the response of emergency services like an ambulance or firetruck to a location in the network, in the case of a person needing medical care or a building fire. Dead-end streets and narrow street widths increase the risk by impeding adequate emergency response due to accessibility difficulties of emergency vehicles delaying the response time of emergency services.
(2) The unreachability risk and (3) edge responsibility consider the risk residents face on the evacuation route, if a fire or accident were to cause a disruption in the network. The unwell connected network and deadend streets cannot offer two-way evacuation route possibilities for residents, representing a great danger in case of an emergency.
(4) The flow capacity focuses on the evacuation process of residents if a building fire or the spread of smoke forces them to evacuate to a safe area. The narrow and labyrinthine network of the alleyways creates a dangerous environment during the evacuation process for residents.
While the accessibility risk and unreachability risk give us the safety information of a specific location in the network (node), identifying houses at risk, the edge responsibility and flow capacity focus on the passing of a location in the network (edge), analyzing the robustness of the network.
Fire policy and mitigation strategies in developing countries are constrained by inadequate information, which is mainly due to a lack of capacity and resources for data collection, analysis, and modeling (Masoumi, van L.Genderen, and Maleki 2019). In densely built urban areas, building fires represent a high risk as it can easily spread to adjacent buildings. In addition, the access to rescue services in case of a medical emergency can greatly affect health, injuries or deaths.
The extraction of the evaluation variables has been developed from a bottom-up approach. Due to the limited data availability, possible indicators have been derived from the network topology and street width in relation to probable emergency scenarios. As indicated in Figure 4.2, two outcomes are defined as the consequence of a disaster. First, the accessibility of emergency vehicles, such as a firetruck or ambulance, which is fundamental to respond to the disaster. In this case, the location of accessible points is essential to evaluate the difficulties emergency responders might face in the network, leading to the development of the first evaluation variable, i.e., the accessibility risk. Second, the evacuation of residents is essential to ensure their safety after a disaster occurs, thus the  importance of the location of evacuation points in the network. In this context, residents can be exposed to two possible dangers. On one side, the risk of a potential disruption in the network as a consequence of the disaster, disconnecting houses from an evacuation point and leading to the inability of residents to evacuate to a safe area. On this account, two evaluation variables are developed: the unreachability risk, evaluating the potential disconnection of a house from an evacuation point, and the edge responsibility, evaluating the criticality of an edge, if that edge is removed in the network. On the other side, the risk caused by people flows in the network, which can lead to congestion and delay in the evacuation process, is measured by the fourth evaluation variable, the flow capacity. While the studied network characteristics enhance these risks, the developed evaluation variables are able to detect the most vulnerable locations and support the improvement of the safety level of the street network.

Accessibility risk
To get a grasp of the current safety level in the network in terms of accessibility, all the house nodes were measured depending on the distance to the nearest accessible point, which represents the nearest location accessible by a vehicle from that respective node. While the ideal accessibility model includes the optimization of the location of emergency facilities and the time to reach each house on a city-wide scale, this index focuses on the scale of a local neighborhood to provide emergency response services on a community level. This first step is crucial to achieve a safe city-wide access in the future.
Accessibility risk of node i is given by The accessibility risk d i is expected to be proportional to the required emergency response time from node i to the nearest accessible point; the higher the d i value, the higher the risk. In Figure 5.2 the distance to the nearest accessible point is represented by a colorbar that depends on the value of d i as shown in the legend of the figure. The dark blue color represents nodes when d i is equal to 0, which means houses are located on the accessible network. The color gradation from blue to red represents the increase in distance from a node to an accessible point, and therefore a higher risk as emergency responders need more time and have more difficulties to reach that node in an emergency situation.

Unreachability risk
Each house in the area represents a possible location of a fire or accident that can cause a disconnection in the network. To simulate all possible scenarios, any one of the edges is removed one after another in front of every house, breaking the connection in the network in that location. By calculating the paths from all house nodes to any evacuation point, the unreachability risk u j represents how many times a house node j is not connected to any evacuation point through all possible scenarios. Unreachability risk of house node j ¼ 1; 2; . . . ; n ð Þ is given by where δ jl ¼ 0 if house node j is connected to any evacuation node when edge l ¼ 1; 2; . . . ; m ð Þ; adjacent to any house; is removed: n : Total number of house nodes m : Total number of edges adjacent to any house If u j is equal to 0, house node j has at least a two-way evacuation route to any evacuation point, represented in dark blue in Figure 5.2(b). If u j is equal to or greater than 1, house node j is located on a tree-shaped network, inside the mesh network of alleyways. The gradation of colors from blue-green to red shows the increase in risk of unreachability as shown in the graph legend.

Edge responsibility
The edge responsibility r k of edge k is defined by the number house nodes that are disconnected from any evacuation point in all scenarios simulating a disconnection in the network by removing edge k.
The edge responsibility represents the importance of an edge to provide an evacuation route between a house and a safe area.
Edge responsibility of edge k is given by where h kj ¼ 0 if house node j is connected to any evacuation node when edge k is removed ! : 1 otherwise ð Þ: n : Total number of house nodes Figure 5.2(c) illustrates edges with an edge responsibility r k equal to or greater than 1, which are located on tree-shaped parts of the network ending in a culde-sac. This leads to a higher risk if the network were to be interrupted in case of an emergency, i.e., there is no two-way evacuation possibility. The color gradation from green to red shows the increasing number of houses disconnected from any evacuation point if that edge is removed. The highest risk is represented in dark red and is located at the root of the tree network. In a tree topology, even a single point of failure can disrupt the connection from a node to a safe area. The hierarchy of the tree branches and the total number of houses on the tree network reflect the responsibility an edge holds in case of disruption of that edge in the network.

Flow capacity
The flow capacity is calculated by simulating an evacuation process from each house in the network to an evacuation point and is evaluated based on two parameters, namely edge capacity and bottleneck risk. For this evaluation variable, the input data of the edges in the network was modified by dividing the edge length into equal segments of 1.0 m. This index measures the density of evacuees at the peak time of edges and detects the locations of bottleneck risks, delaying the evacuation process.

Edge capacity
The edge capacity represents the average pedestrian space on an edge at peak time during the evacuation process and is measured by dividing the edge area by the maximum number of residents on that edge during the evacuation process. Evacuees reach the nearest evacuation point using the shortest path.
Edge capacity of edge k is given by A k : Area of edge k P kt : number of evacuees on edge k in time t We have three assumptions for the calculation of P kt : evacuees are distributed equally among all house nodes (1) , they have the same walking speed and the same evacuation starting time. Based on these assumptions, we can calculate P kt by the distance between any house node and edge k. Max t{P kt } represents the maximum number of evacuees on edge k during the whole evacuation process. If max t{P kt } is equal to 0, c k is not defined. The edge capacity c k represents the danger of congestion; which is especially high if two evacuation routes merge without an increase of street width, i.e., increase of available area per evacuee. In Figure 5.2(d), c k is illustrated by a gradation from dark blue to light blue. The darker the blue, the less space per evacuee is available, which represents a higher risk; the lighter blue means the available space per evacuee on that edge is larger, which is safer.

Bottleneck risk
The bottleneck risk of a node is caused by the decrease in area per person between its adjacent edges in the direction of the evacuation path, which creates a bottleneck effect, and can cause delays in the evacuation process.
Bottleneck risk of edge k is given by If b k is negative, edge k has no bottleneck risk; if b k is equal to or superior to 0, the end node of edge k in the direction of the evacuation route has a bottleneck risk. As seen in Figure 5.2(d), the bottleneck risk is represented by a gradation of red and proportionate size of the dot. The darker and bigger the red dot, the higher the bottleneck risk. The highest risk of flow capacity arises when the area per person of the edge capacity is low, as shown in dark blue, and the difference in density of the bottleneck risk is high, as shown in dark red.

Model behavior and application on typical street network topologies
The evaluation model is first applied on a typical street network topologies to observe the behavior of the developed model and to investigate how the model recognizes locations at risk in different network topologies. Three abstracted paradigms of street networks were constructed to demonstrate how the developed evaluation model analyzes distinctive patterns. The street network paradigms represent an abstract form of the main categories of typical street patterns found in cities across regions and cultures.
For each paradigm, first the virtual street network is drawn inside a square measuring 300 × 300 m. Then, the perimeter of the network is classified as main street, which belongs to the accessible network. In the next step, the accessible points are first located on the perimeter, hereinafter referred to as case (1). Then, the accessible points are located inside the network, expanding the accessible network inside the network, referred to as case (2). Finally, the other street width categories are distributed randomly inside the network in both cases.
As seen in Figure 5.1, the first street network paradigm is a regular grid network and represents a rectilinear network with a pattern of streets running at right angles. The second street paradigm is a degree-3 network, also referred to as T-type network. This topology has a high proportion of degree 3 nodes. The third street paradigm is a tree and dendritic network. .2 (a) shows the accessibility risk for all topologies. In the case ofgrid (1), the distance to an accessible point is increasing continuously towards the center of the network due to the equal distance distribution between nodes on the grid network. Regarding grid (2), the distance to an accessible point reacts to the location of the accessible points inside the network, but d i remains less than 75 m. The accessibility risk shows a similar result in the degree-3 network, where the center area of the network is the most vulnerable in case (1) and reacts to the expansion of the accessible network in case (2). Regarding tree and dendritic networks, the accessibility risk increases with the total length and total number of houses of the tree network and is the highest at the "leaves" of the tree network. This behavior can be observed in both cases, but the risk decreases in case (2). Naturally, the accessibility risk is lower in case (2) of all topologies due to the extension of the accessible network.
In terms of unreachability risk and edge responsibility, the evaluation model reports that all u j and r k are equal to 0 in the entire network for the grid and degree-3 topologies due to their high connectivity. In the case of tree and dendritic networks, the unreachability risk is the highest at the "leaves" of the tree networks and increases with the size of the tree network ( Figure 5.2 (b), while the edge responsibility is the highest at network roots, connecting a tree network to the accessible network as seen in Figure 5.2(c). As seen in Figure 5.2 (d), the application of the flow capacity evaluation on all network topologies shows that the result does not depend on the network topology, but rather on the distribution and location of segments with different street widths in the network.

Model application to Ho Chi Minh City
This section introduces the application of the model in a real urban area, an alleyway neighborhood in Ho Chi Minh City. In section 6.1, the current safety level of the street network is analyzed, then improvement strategies are applied in three case studies in section 6.2. First, the methodology, which combines edge widening and adding new edges in the network, is explained in section 6.2.1, then the strategies to choose the location of edges for improvement are detailed in section 6.2.2. Finally, the improvement intervention results are described in section 6.2.3, and compared and discussed in section 6.3, as illustrated in Figure 6.1.
Ho Chi Minh City was chosen as the analytical area for this study; it exhibits a very unique urban trajectory after experiencing colonization, decades of war, socialism, and de-urbanization, followed by the national reunification of 1976 and Đổi Mới reforms (Thrift and Forbes 1986). Before the two cities were merged and renamed Ho Chi Minh City after the reunification of the country, the French laid the structure for Saigon's urban grid, while Cholon's economic and social structure shaped its urban form. By 1955, a migration movement to the city created serious housing problems and overcrowding and led to the spontaneous urban development, starting the formation of Ho Chi Minh City's typical alleyway system, which has lasted until today. After the war, the migration movement continued and led to further densification of the alleyway system. Therefore, the primary grid structure is predominant in the center and becomes less dense towards the outskirts of the city. Narrow and sinuous alleyways composed of tree and mesh networks fill up the spaces of various scales between the grid structure.

Analysis of the current situation
The four evaluation variables have been applied to the network of the analytical area in Ward 2, District 5 of Ho Chi Minh City. The analyses of the network give a clear understanding of the current level of safety and helps to identify the most vulnerable areas in the network for each criterion.
The analysis of the Accessibility risk shows that currently 74.12% of the houses in the network are not accessible by an emergency vehicle, among which 38.33% are located further than 50 m from an accessible point (Figure 6.2). As can be observed in Figure 6.3, houses located on a tree-shaped network are affected by the unreachability risk as they are not provided with a two-way evacuation route. Currently, 34.87% of the houses are at risk of being unable to reach an evacuation point if an accident were to interrupt passage through the network. The Unreachability risk increases proportionately with the size of the tree network and the number of houses located between a house and an evacuation point.
In terms of edge responsibility, the risk occurs in treeshaped networks providing the only access between houses and an evacuation point. The risk level rises with an increase in the length and hierarchy layers of the tree-shaped network as well as with the number of houses located on that network. Consequently, the edge responsibility varies in accordance with the hierarchy of the branches in the tree network and the number of attached houses and increases towards the root of the tree network. Here, 21.59% of the current network has a tree shape, creating subnetworks with branches of various sizes as seen in Figure 6.4.
As for the flow capacity, illustrated in Figure 6.5, the edge capacity is represented in blue and the bottleneck risk of nodes is represented in red. The bottleneck risk of nodes with a higher difference in density appears predominantly at intersections, while the edge capacity is influenced by the width of the street and the number of times an edge appears on an evacuation route and is scattered in the network.

Methodology
Three case studies were conducted using the simulation model focusing on improving the safety level in the network by combing two strategies. The first strategy involves adding a new edge in the network. This method changes the network geometry and has a high impact on the shortest path routes and two-way evacuation routes by linking dead-end streets and creating new loops inside the network. The addition of a new edge in the network can be highly efficient while having a small impact on the local community. The second strategy involves widening existing alleyways. This method has a direct effect on the accessibility of emergency vehicles by expanding the accessible network further and also increases the area of edges on the evacuation route.
In the case studies, both methods were combined, aiming to improve the safety as much as possible by keeping the area subject to change, thereby keeping the costs and impact on the local community as low as possible. The total length of added edges in the network and the total area to expand for edge widening was equal in all the case studies. The total area for edge widening was set at 250 m 2 , and the total added edge length was set at 64 m with a width of 3.5 m. For each case study, the area of improvement was gradually expanded and was referred to as high concentration intervention area in case study 1, medium concentration intervention area in case study 2, and low concentration intervention area in case study 3, as seen in Fig.5.5. Subsequently, the concentration of interventions of improvement decreased from case study 1 to 3.

Strategy for safety level improvement
The choice of edges to add or widen was decided based on different strategies. Three strategies were applied for widening edges.
(a) The first strategy to select edges to widen involves connecting edges on the inaccessible network with a street width greater than 3.5 m  to the accessible network (see Fig. 2.1). This approach is represented in red in Figure 6.6. (b) The second approach involves extending the accessible network further into the network (see Fig. 2.2). This approach is represented in orange in Figure 6.6. In case study 1, segment (c) The third strategy involves connecting two accessible networks to one another (see Figure 3.2). This approach is represented in yellow in Fig.6   The locations for adding new edges and creating new links in the network targets tree networks with the highest risks first (See Figure 6.2 to 6.5). After targeting the most unsafe areas in the network, the focus of adding new edges shifts to medium and small size networks. The biggest tree networks are connected to the mesh network with the new edge [5]

Improvement intervention results
The safety enhancement of the improvement interventions varies for each case and is described as follows: Compared to the current situation, the accessibility risk improves considerably inside the intervention area in case study 1 as the accessible network is expanded by both, widening edges and adding new edges condensed in a small area as seen in Figure 6.7.
While widening edges have no influence, adding new edges has similar impacts on the unreachability risk and edge responsibility. No high-risk areas remain in any of the case studies, and the total length of tree networks decreases continuously compared to the current network from case study 1 to 3 as seen in Figure  6.8 and Figure 6.9.
Widening edges can improve the edge capacity, and new links can alter the evacuation route, but not all interventions have an impact on the flow capacity. Adding a new edge only has an impact on the flow capacity if this new connection in the network modifies the shortest path between any house node and an evacuation point. For instance, the new link [2] in case study 1, seen as having an edge capacity value in blue in Figure 6.10, not only decreases the length of the evacuation route of seven houses but also modifies the bottleneck risk in that area: in this case, at the intersection of segment (3). Widening edges can improve the edge capacity of that edge and improve or remove the bottleneck risk around that edge. The new edge [6] in case study 2 reduces the bottleneck risk in proximity of that edge but increases the bottleneck risk in other locations nearby. This is affected by the change in evacuation routes of 11 houses passing through the new link, which shortens the distance between these houses and the nearest evacuation point. In case study 3, the widening of edges in segment (1) removes a bottleneck with a high-risk value, but smaller bottleneck risk locations appear on the intersection of segment (2) (see Figure 6.10).

Discussion
After applying the proposed model on three case studies, an accumulative database of graphs and charts was created to compare the results of the case studies with the current situation. As seen in Figure 6.11, compared to the current situation, the houses in the network that are inaccessible for an emergency vehicle decreased by 15. 87%, 19.58% and, 13.89% in the first, second, and third case studies, respectively. In case study 3, the houses located further than 80 m from an accessible point declined sharply from 15.98% in the current situation to 1.68% (Figure 6.12). While the number of accessible houses increased in all case studies, from the    perspective of accessibility for emergency vehicles, the best improvement was observed in case study 2, with an augmentation of 52.65% of the accessible houses compared to the current situation.
The risk of unreachability decreased continuously from case study 1 to 3, with a reduction in risk of 35.43%, 44.37%, and 52.32% in the first, second and third case studies, respectively, compared to the current situation (see Figure 6.13). Case study 3 has only 16.82% of the houses with no two-way evacuation, compared to 34.87% in the current situation, and as seen in Figure 6.14, exhibits the most improvement for each value of u j .
The addition of new links in the network enabled the connection of tree subnetworks to the mesh network, thereby providing a two-way evacuation possibility in these areas. All case studies reduced the edge responsibility in all risk levels. As seen in Figure 6.15, case study 3 showed the strongest improvement by reducing the total length of tree subnetworks by 51.47% compared to the current situation, leaving only 11.56% of the total network length tree-shaped. Figure 6.16 shows that case study 3 has the lowest edge responsibility risk for each value of r k .
Regarding flow capacity, no case study showed a clear improvement in both parameters, edge capacity, and bottleneck risk. In terms of case study 2, the number of edges with c k less than 0.15 m 2 increased by 48.6% compared to the current network; however, it also showed the highest improvement with an increase of 24.29% in the safest category with c k greater than 0.6 m 2 (Figure 6.17). The total number of bottleneck risks decreased by 7.19% in case study 1, 10.07% in case study 2, and 9.35% in case study 3 compared to the current network as seen in Figure 6.18. Figure 6.19 shows the social impact of the case studies on the local residents. While alley widening impacts households by reducing the area of their land plot, adding new edges might force residents to relocate. While        the number of households forced to relocate were similar in all case studies, the number of households affected by alley widening was the highest in case study 2 and the lowest in case study 3. Case study 3 applied on a low concentration area had the lowest social impact, while showing the best improvement for the accessibility risk, especially in the high-risk categories and had the lowest unreachability risk and edge responsibility among all case studies conducted in this paper. If the weakest point in the network is targeted for alley improvement and is chosen as an investment project, it provides the most efficient result of network-wide safety improvement for the accessibility risk, unreachability risk, and edge responsibility, but this type of scenario is not valid for the concept of flow capacity, where modifications in the network only have a local result. However, the flow capacity can detect which intersections in the network are actual intersections on the evacuation routes and therefore have a bottleneck risk, which cannot be derived from the network topology. In Figure 6.5, the bottleneck risk appears to be especially high at intersections, but this is not the case for intersections located at the border of the Voronoi network cells where residents evacuate in opposite directions.

Conclusion
An original methodology for evaluating accessibility and evacuation safety using network analysis was created and applied in Ho Chi Minh City's alleyways.
The evaluation of the current street network and the modifications in the case studies disclosed various results and features of the evaluation variables and improvement methods. Showing the highest risk at "leaves" of inaccessible tree-shaped networks, the methods applied to improve the accessibility risk involve a combination of reducing the maximum distance to an accessible point and extending the accessible network. The Unreachability risk worsens gradually with an increase in the number of houses located between a house and an evacuation point on a tree-shaped network. In terms of edge responsibility, the risk is the highest at the roots of tree networks, and there is a parallel increase with the total length of the tree network and the number of houses located on that tree network. Regarding flow capacity, the edge capacity depends on the distribution of street widths across the network, and the occurrence of bottleneck risks is higher at intersections.
As confirmed in the result of the case studies, the effectiveness of the improvement interventions varies depending on the evaluation variables and the method applied: edge widening or adding an edge. Regarding adding new edges in the network, the accessibility risk can only be improved if the added edge is connected to the accessible network, but if the added edge modifies the evacuation route of residents, it can improve or deteriorate the flow capacity, depending on whether the evacuees using the shortest path from a house to the nearest evacuation point are led through more or less crowded edges, as it might increase the duration of the evacuation process. In terms of unreachability risk and edge responsibility, adding a new edge transforms a tree network into a mesh network and provides a two-way evacuation, which increases the safety the most.
As for widening edges in the network, with the applied strategy, the accessibility risk improves when the accessible network is extended, but it has no effect on the unreachability risk and edge responsibility. While improvement interventions have an impact on safety improvement over a wider area in the network for other evaluation variables, in terms of flow capacity, widening edges only has a local effect in the network.
The prospective intervention projects were compared in terms of safety improvement, economic impact (defined by the area to modify), and social impact (defined by the number of households forced to relocate and households having to give away a part of their land plot). This evaluation model is not only useful to analyze the current risk level in the network but is also a powerful tool for urban planners and governments to manage and estimate the efficiency of future infrastructure improvement projects.
From an academic point of view, this research is based on existing network analysis models, such as the Network Voronoi algorithm, which already proved their efficiency in previous researches but evolves by introducing a novel method adapted to a specific network topology and considering the urban context and narrow street widths. In practice, the structure and safety of self-organized settlements seems complex, and dangerous locations cannot be pointed out intuitively or are often overlooked in traditional urban planning approaches. In this regard, the developed model is able to identify vulnerable locations based on network data solely and evaluate future improvements, which is very helpful for urban management and sustainable development, especially in fast developing cities.
This research, however, is subject to several limitations that could be addressed in future research. As mentioned in section 3.1, in terms of accessibility, one limitation of this study is the boundary of the area, meaning that activities or the location of emergency facilities outside the analytical area, are not considered in the model. Moreover, this analysis is based on building fires and medical emergencies and does not include other natural or human-made disasters that can occur in dense urban areas. Another limitation is, that this research is based on network analysis, more specifically the network Voronoi algorithm, which is based on the assumption of the shortest path rule. Moreover, this assumption is based on a number of other assumptions, for example, that all residents are familiar with the whole network structure and positions of locations. Furthermore, it simplifies the complexity of human decisions made in case of an emergency, which can be unrealistic in certain situations. Finally, the safety threshold for the access of emergency vehicles, set at 3.5 m, is only based on the street width and does not consider the geometry of the space such as corners and turning space for emergency vehicles.
The next step would be to expand the model to a city-wide scale and include the locations of emergency facilities to evaluate the accessibility and response time of rescuers more precisely. Furthermore, in terms of edge responsibility, the extent of overlapping parts of two-way evacuation routes should be verified. Finally, the current model analyzes the four evaluation variables independently, which should be combined in future research to grasp the full potential of improvement interventions.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Funding
This work was supported by JSPS KAKENHI Grant Number JP 20H02327.