Modeling Resilience of Metro-Based Urban Underground Logistics System Based on Multi-Layer Interdependent Network

Abstract

The metro-based underground logistics system (M-ULS) has been identified as an effective solution to urban problems resulting from the expansion of urban freight traffic. However, there is a paucity of current research that examines the resilience of a M-ULS in the context of unexpected events during operations. Therefore, this paper presents a methodology for assessing the resilience of the M-ULS. The method considers the propagation paths of various failures in a multi-layered, interdependent network that includes topology, functionality, facilities, and information, as well as network performance indicators based on network freight flow and logistics timeliness. The effectiveness of the method is demonstrated using the case of the Nanjing Metro. The results show that the type of disruption, the duration, and the direction of train travel all have a significant impact on the resilience of the M-ULS. The method proposed in this paper provides a scientific basis for the assessment and optimization of M-ULS resilience and also offers new insights into the use of urban rail transit to promote the sustainable development of urban logistics.

1. Introduction

Sustainable and intelligent transportation systems are an essential part of urban development [1,2]. Among them, urban logistics, as a critical component of freight transport, is an indispensable part of the urban transportation system [3,4,5]. However, in the context of a thriving digital economy, urban logistics has simultaneously generated significant economic value and created a number of urban-related challenges, including traffic congestion, pollution, and safety concerns [6]. For example, in Beijing, China, freight activity is estimated to account for about 30% to 40% of traffic congestion [7,8]. These issues present novel challenges for the construction of sustainable and intelligent transportation systems and impede the advancement of sustainable urban development. Traditional traffic management strategies have been used but with limited effectiveness and, to a limited extent, have constrained urban growth. These problems pose new challenges for the construction of sustainable and intelligent transportation systems and hinder the progress in sustainable urban development [9].

As a novel freight transportation mode, the underground logistics system (ULS) is perfectly aligned with the concept of sustainable urban development [10,11,12,13]. The ULS is represented by a transportation infrastructure network consisting of tunnels, pipelines, and underground nodes at different levels located deep in the urban underground space [14,15,16,17]. A number of countries, including Switzerland, Germany, France, and the Netherlands, have initiated planning and pilot projects for ULSs [18,19,20]. However, the high technical requirements and substantial investments needed for new ULS construction have so far prevented their widespread adoption and application in most cities. In light of this, researchers have proposed integrating ULSs into existing infrastructure, such as metro systems and utility tunnels, to reduce costs and increase feasibility [21].

The M-ULS is widely recognized as the most promising technology form of the ULS for widespread implementation [22,23,24,25,26]. This assertion is mainly based on the following reasons. First, the technologies used in underground construction have matured significantly through years of practice, providing a solid foundation for the construction and implementation of the M-ULS [27,28,29,30,31,32,33]. Second, the M-ULS has significant advantages in a number of domains, including transportation, the environment, society, and logistics [34,35,36]. Third, the expansion and upgrading of existing metro networks can significantly reduce the costs associated with underground projects compared to the construction of entirely new ULSs, making it highly economically feasible [37]. Significant progress has been made in M-ULS research [38]. For example, Hu et al. [24] undertook a comprehensive investigation of the intricacies inherent in actual operational contexts as part of their network planning research.

There is currently no industry consensus on the specific form of M-ULS technology. However, two dominant application modes can be identified: the mixed passenger and freight mode and the segregated passenger and freight collocated mode [39,40]. While the mixed mode has limitations in organizational flexibility and relatively low freight capacity, the segregated collocated mode, with its superior organizational flexibility and robust freight capacity, is more in line with actual demand and development trends. To demonstrate the operational mode of the segregated M-ULS in a concrete context, we can consider the example of inbound freight. This is shown in Figure 1. The system consists of a three-level network. The first-level network includes the point of origin, namely metro stations, logistics parks, and the metro network itself. Freight from out-of-town logistics parks is transported to the original metro stations via connecting corridors or direct ground transportation. After the completion of secondary packaging, coding, and other necessary procedures, the packages are converted into standardized metro transport containers and loaded onto the metro for transportation through the metro network to designated terminal metro stations. The second-tier network consists of terminal metro stations, intracity cluster distribution centers, and the pipeline network connecting them. Upon arrival at the terminal metro stations, the cargo is unpacked, sorted, and loaded into capsule vehicles, which are then transported to the intracity cluster distribution centers via the pipeline network at high speeds. The third-level network consists of the intracity cluster distribution centers, the customer terminals, and the ground delivery routes connecting them. At the intracity cluster distribution centers, freight undergoes final unpacking to form packages ready for direct delivery to customers. These packages are then delivered to customers via last-mile delivery services.

Despite the considerable technological advancement of the M-ULS, its operational processes remain intricate and fraught with difficulties. The successful implementation and performance of the M-ULS are contingent upon the assurance of its operational process stability and reliability [41,42,43]. The M-ULS, as an innovative mode of metro freight transportation, is considerably more complex than the widely used metro passenger transportation mode. In light of the considerable differences between freight and passenger flows with regard to transport demand, transport modes, and transport organization, it is of the utmost importance that the planning and implementation of M-ULSs adhere closely to the constraints of the existing metro network [44,45]. Inevitably, the metro system may encounter a variety of unexpected events during operation, such as equipment failure and natural disasters [46,47]. Such occurrences may result in a disruption in the normal operation of the subway system, which in turn affects the smooth operation of the M-ULS. Therefore, the operational stability and reliability of the M-ULS in response to unexpected events become crucial criteria for its successful implementation and anticipated performance.

The application of resilience theory and methods provides new insights into M-ULS operational stability and reliability research [48,49]. In the context of urban infrastructure, such as electricity, energy, water supply, and transportation, resilience is defined as the capacity of these systems to withstand and maintain a certain level of functionality after extreme and uncertain events, as well as their ability to swiftly recover and effectively respond to future shocks [50]. To date, research on the resilience of urban infrastructure has yielded significant findings [51,52,53,54]. For example, Liu et al. [55] proposed a resilience assessment framework for urban water networks, adopting a life cycle perspective. Sun et al. [56] focused on the Beijing metro system, examining the redistribution of passenger flows under a variety of static passenger flow scenarios and node failures. The study indicated that in the event of substantial external disruptions, the failure of stations may occur at an earlier point in time than previously anticipated.

The evaluation indicators for resilience can be primarily classified into two categories: network topology-based indicators and system performance-based indicators [57,58,59]. Among topology-based indicators, in accordance with complex network theory, researchers have devised a series of network topology resilience indicators, including the average shortest path length and node centrality. Performance-based indicators and network performance curves have been extensively utilized in the assessment of urban infrastructure resilience. For example, Lu et al. [60] integrated network topology with passenger flow distribution to investigate the impact of different operational incidents on metro network operations. They conducted an empirical analysis with the Shanghai metro network as a case study. Ouyang et al. [61] employed mathematical models to quantify the resilience of critical infrastructure in the face of deliberate attacks and natural disasters. The electric power grid was employed as a case study for the assessment of resilience in the context of earthquake disasters.

In summary, the M-ULS has achieved remarkable results in network planning and feasibility analysis. However, research on the operational resilience of the M-ULS is comparatively scarce. In light of the existing research results on infrastructure resilience, this paper defines M-ULS resilience as the capacity to withstand and maintain a certain level of functionality after extreme and uncertain events, as well as its ability to swiftly recover and effectively respond to future shocks. The aim of this paper is to propose a resilience assessment methodology tailored to the M-ULS.

The main contributions and innovations of this paper can be summarized as follows. First, we construct a multi-layer interdependent network model for an M-ULS that integrates topology, functionality, facilities, and information and conduct an in-depth analysis of the propagation paths of different types of operational incidents within this multi-layer network structure. Second, we develop quantitative evaluation indicators for M-ULS network performance based on two dimensions: real-time freight flow and logistics timeliness. We then propose a methodology for assessing the resilience of the M-ULS. Finally, the effectiveness of this methodology is validated through a case study of the Nanjing Metro. The core innovation of this paper is the proposal of a methodology for assessing the resilience of the M-ULS, which provides a scientific basis for the assessment and optimization of M-ULS resilience and also offers new insights into the use of urban rail transit to promote the sustainable development of urban logistics.

The following sections of this paper are organized as follows: Section 2 will detail the M-ULS resilience assessment methodology; Section 3 will focus on the case of the Nanjing Metro, showing the process and simulation experiment; Section 4 will show the results and discussion; and finally, Section 5 will summarize the whole paper and suggest possible future research directions.

2. Methodology

In order to gain a comprehensive understanding of the resilience of the M-ULS, it is first necessary to identify the critical factors that influence the stability and reliability of the M-ULS. An extensive literature review and expert interviews have revealed that the operation of the M-ULS can be affected by a variety of factors originating from both internal and external sources within the system. These factors have the potential to disrupt the normal functioning of the M-ULS to varying degrees. The specific relevant factors are listed in

Table A1. The specific relevant factors affecting the operation of the M-ULS.

No.	Factors	Description
F1	Loading and unloading	The loading and unloading system, such as forklifts and AGVs, may fail to operate normally due to various reasons, including battery system failure, navigation system malfunction, drive system issues, and improper operation.
F2	Warehousing	The warehousing system may encounter hardware equipment failure, such as the inability to utilize the stacker in a typical manner [45].
F3	Sorting	The sorting system may encounter hardware failures, such as the typical damage to the gripping device.
F4	Coding and identification	The coding and identification system may encounter malfunctions, such as the RFID being unable to function as intended.
F5	Conveyor Equipment	The horizontal freight conveyor equipment may experience failures, such as the conveyor belt suddenly ceasing operation.
F6	Monitoring	The monitoring system may malfunction, for example, if the camera fails to operate correctly.
F7	Train	The failure of the train doors and the platform screen doors is a potential risk [60].
F8	Track	The track system may encounter failure, such as track deterioration.
F9	Electricity	The cable lines may experience failure due to aging.
F10	Communication and Signal	The communication and signal system may encounter hardware failures, such as the server malfunctioning.
F11	Communication and Signal	It is possible that the communication and signal system may experience software failures, such as data loss.
F12	Elevator	The vertical freight conveyor equipment, particularly the vertical elevators, may malfunction due to power outages, improper operation, and other factors, leading to an inability to perform its intended functions.
F13	Train	The train’s traction and braking system may fail as a result of mechanical issues, improper operation, environmental factors, and other causes.
F14	Warehousing	The warehousing system may encounter software failures, such as those reported by the warehouse information management platform.
F15	Sorting	The sorting system may encounter software failures, such as those reported by the sorting information management platform.
F16	Train	Derailment, collision, and other factors may result in train failure.
F17	Train	Overloading may result in failure of the train.
F18	Train	The train may experience failure due to human factors, such as the inability to start due to foreign objects falling onto the tracks.
F19	Warehousing	It is possible that the warehousing system may cease to function due to a power outage.
F20	Coding and identification	It is possible that the coding and identification system may cease to function due to power outages.
F21	Sorting	A power outage may result in the failure of the sorting system.
F22	Communication and signal	The communication and signal systems may cease to operate due to power outages.
F23	Loading and unloading	The loading and unloading system may cease to function due to power outages.
F24	Information management	The logistics information management system may encounter hardware failure, such as server crashes.
F25	Information Management	The logistics information management system may encounter software failure, such as errors in the logistics tracking function.
F26	Ground subsidence	The tunnels and underground spaces that support the physical facilities of the M-ULS may face the risk of ground subsidence.
F27	Groundwater inrush	The tunnels and underground spaces that support the physical facilities of the M-ULS may be susceptible to the phenomenon of groundwater inrush.
F28	Structural cracks and damage	The tunnels and underground spaces that support the M-ULS may be susceptible to structural cracks and damage due to the aging of materials, changes in load, and other factors.
F29	Temperature and humidity	The tunnels and underground spaces that support the M-ULS may experience fluctuations in temperature and humidity, which may affect the optimal functioning of equipment that requires precise temperature and humidity control.
F30	Fire	The tunnels and underground spaces that support the physical facilities of the M-ULS may experience a fire due to equipment failures, such as those of electrical equipment.
F31	Management	The auxiliary electromechanical equipment may stop working due to management oversight or other reasons.
F32	Fire	The tunnels and underground spaces that support the physical facilities of the M-ULS may experience a fire due to human factors, such as a failure to adequately inspect flammable and explosive materials.
F33	Earthquake	An earthquake may result in the partial or complete paralysis of a specific station or a certain line of the M-ULS.
F34	Flooding	Flooding has the potential to cause the paralysis of a specific station or a certain line of the M-ULS.
F35	Blizzard	A blizzard may result in the paralysis of a specific station or a certain line of the M-ULS, with a common direct impact being widespread power outages.
F36	Terrorism and War	While the probability of terrorist attacks and wars is relatively low, it is not possible to discount the possibility that they may result in the paralysis of a specific station or line of the M-ULS.
F37	Shopping Festival	It is possible that the M-ULS may experience a state of paralysis during the shopping festival due to an overload of operations.
F38	Surrounding Construction	The temporary closure of a specific station or a certain line of the M-ULS may be attributed to surrounding construction or other factors.
F39	Operational Adjustment	Temporary operational adjustments may result in the closure of a specific station or a certain line of the M-ULS.
F40	Others	This category encompasses other extreme and uncertain incidents.

in Appendix A. The literature review further highlights that despite the complex interplay of multiple factors affecting M-ULS operations, operational incidents under day-to-day conditions, due to their high frequency, emerge as the primary and fundamental key factors influencing M-ULS operations. Accordingly, the following sections of this paper will focus on daily operational incidents and investigate the resilience of the M-ULS under such circumstances.

2.1. Representing M-ULS Multi-Layer Interdependent Network

After a comprehensive review of Table A1, we have constructed a multi-layered, interdependent M-ULS network that includes topology, functionality, facilities, and information, as shown in Figure 2. The M-ULS incorporates a variety of critical subsystems, including the logistics, power, train and track, information (including communications and signaling), section tunnels, and stations. These subsystems are composed of a number of physical entities that work together to ensure the smooth operation of the M-ULS. In particular, the M-ULS network can be topologically abstracted into a series of nodes and the lines connecting them. Each node is associated with a currently operating station. Given the different functional orientations of different stations, the resource allocation at each station is necessarily different. In addition, the operation of the M-ULS is inextricably linked to the support of information systems. The deep integration of information and physical systems ensures the normal operation of the M-ULS.

The topology layer: The M-ULS is represented as a network graph, denoted as $\mathrm{N}=(\mathrm{I},\mathrm{J})$, which consists of a set of nodes $\mathrm{I}$ and a set of edges $\mathrm{J}$. Specifically, the sets are expressed as follows:

$$\mathrm{I}=\{{\mathrm{i}}_1,{\mathrm{i}}_2,\dots ,{\mathrm{i}}_{\mathrm{n}}\}$$

(1)

$$\mathrm{J}=\{({\mathrm{i}}_{\mathrm{p}},{\mathrm{i}}_{\mathrm{k}})|{\mathrm{i}}_{\mathrm{p}},{\mathrm{i}}_{\mathrm{k}}\in \mathrm{I},\mathrm{p}\ne \mathrm{k}\}$$

(2)

In the above expression, $({\mathrm{i}}_{\mathrm{p}},{\mathrm{i}}_{\mathrm{k}})$ represents the edge between nodes ${\mathrm{i}}_{\mathrm{p}}$ and ${\mathrm{i}}_{\mathrm{k}}$, where ${\mathrm{i}}_{\mathrm{p}}$ and ${\mathrm{i}}_{\mathrm{k}}$ are different nodes within the M-ULS network, and $\mathrm{n}$ denotes the total number of nodes in the network.

Functionality layer: In the M-ULS, stations are classified into three categories based on their functional characteristics: original stations, transfer stations, and terminal stations.

It is worth noting that some transfer stations can also function as terminal stations. The primary function of original stations is to receive freight from logistics parks, and they are equipped with the capacity to accommodate high logistics flows. Transfer stations, which occupy a key position in the logistics process, are responsible for handling freight awaiting transfer and have the capacity to handle moderate logistics flows. Terminal stations, on the other hand, are primarily responsible for the final distribution of freight and require relatively less freight handling capacity. These three types of stations are represented by the sets ${\mathrm{F}}_{\mathrm{o}\mathrm{r}}$, ${\mathrm{F}}_{\mathrm{t}\mathrm{r}}$, and ${\mathrm{F}}_{\mathrm{t}\mathrm{e}}$, which denote origin, transfer, and terminal stations, respectively. Specifically, the sets are expressed as follows:

$${\mathrm{F}}_{\mathrm{o}\mathrm{r}}=\{{\mathrm{f}}_{\mathrm{o}\mathrm{r}}^1,{\mathrm{f}}_{\mathrm{o}\mathrm{r}}^2,\dots ,{\mathrm{f}}_{\mathrm{o}\mathrm{r}}^{{\mathrm{n}}_1}\}$$

(3)

$${\mathrm{F}}_{\mathrm{t}\mathrm{r}}=\{{\mathrm{f}}_{\mathrm{t}\mathrm{r}}^1,{\mathrm{f}}_{\mathrm{t}\mathrm{r}}^2,\dots ,{\mathrm{f}}_{\mathrm{t}\mathrm{r}}^{{\mathrm{n}}_2}\}$$

(4)

$${\mathrm{F}}_{\mathrm{t}\mathrm{e}}=\{{\mathrm{f}}_{\mathrm{t}\mathrm{e}}^1,{\mathrm{f}}_{\mathrm{t}\mathrm{e}}^2,\dots ,{\mathrm{f}}_{\mathrm{t}\mathrm{e}}^{{\mathrm{n}}_3}\}$$

(5)

In the above expression, ${\mathrm{n}}_1$, ${\mathrm{n}}_2$, and ${\mathrm{n}}_3$ represent the number of original stations, transfer stations, and terminal sites, respectively.

Facilities Layer: In the M-ULS, station configuration standards are defined by their functional attributes. Notably, origin stations must be equipped with specialized transfer equipment to quickly convert cargo into unit containers that meet M-ULS transportation standards. In contrast, transfer stations have more stringent specifications and requirements for transfer equipment related to sorting, loading, and unloading. It is critical to recognize that terminal and transfer stations are often located in urban environments where underground space is at a premium. Consequently, the constraints of underground space must be carefully considered during the facility configuration process for these stations. Conversely, the facility configuration requirements for terminal stations are relatively straightforward. The aforementioned three types of station facility configurations are represented by the sets ${\mathrm{C}}_{\mathrm{o}\mathrm{r}}$, ${\mathrm{C}}_{\mathrm{t}\mathrm{r}}$, and ${\mathrm{C}}_{\mathrm{t}\mathrm{e}}$, which denote origin station facilities, transfer station facilities, and terminal station facilities, respectively. Specifically, the sets are expressed as follows:

$${\mathrm{C}}_{\mathrm{o}\mathrm{r}}=\{{\mathrm{c}}_{\mathrm{o}\mathrm{r}}^1,{\mathrm{c}}_{\mathrm{o}\mathrm{r}}^2,\dots ,{\mathrm{c}}_{\mathrm{o}\mathrm{r}}^{{\mathrm{n}}_1}\}$$

(6)

$${\mathrm{C}}_{\mathrm{t}\mathrm{r}}=\{{\mathrm{c}}_{\mathrm{t}\mathrm{r}}^1,{\mathrm{c}}_{\mathrm{t}\mathrm{r}}^2,\dots ,{\mathrm{c}}_{\mathrm{t}\mathrm{r}}^{{\mathrm{n}}_2}\}$$

(7)

$${\mathrm{C}}_{\mathrm{t}\mathrm{e}}=\{{\mathrm{c}}_{\mathrm{t}\mathrm{e}}^1,{\mathrm{c}}_{\mathrm{t}\mathrm{e}}^2,\dots ,{\mathrm{c}}_{\mathrm{t}\mathrm{e}}^{{\mathrm{n}}_3}\}$$

(8)

In the above expressions, ${\mathrm{n}}_1$, ${\mathrm{n}}_2$, and ${\mathrm{n}}_3$ represent the number of origin stations, transfer stations, and terminal stations, respectively.

Information layer: The M-ULS information system is based on the well-established metro information control and management paradigm, which consists of a CCC, station workstations, and a wireless communications network. Typically, a single CCC is responsible for overseeing the information operations of one or more lines. Real-time operational status data from stations and trains is transmitted instantaneously to the CCC via an advanced wireless communications network. The CCC uses sophisticated algorithms and big data analysis techniques to process and analyze the data in real-time, enabling precise operations such as train scheduling, logistics information tracking, and safety monitoring. When the CCC manages a line, all stations associated with the CCC include all stations along the line. The above stations are represented by $\mathrm{C}\mathrm{C}{\mathrm{C}}_{\mathrm{s}\mathrm{t}}$, which is expressed as follows:

$$\mathrm{C}\mathrm{C}{\mathrm{C}}_{\mathrm{s}\mathrm{t}}=\{\mathrm{c}\mathrm{c}{\mathrm{c}}_{\mathrm{s}\mathrm{t}}^1,\mathrm{c}\mathrm{c}{\mathrm{c}}_{\mathrm{s}\mathrm{t}}^2,\dots ,\mathrm{c}\mathrm{c}{\mathrm{c}}_{\mathrm{s}\mathrm{t}}^{{\mathrm{n}}_4}\}$$

(9)

In the above expression, ${\mathrm{n}}_4$ represents the number of stations associated with the CCC.

2.2. M-ULS Operational Incident Propagation Modeling

As described in Section 2.1, the operation of the M-ULS depends on the coordinated actions of numerous subsystems. The occurrence of an unexpected incident in any of these subsystems has the potential to negatively impact the functioning of the M-ULS. Essentially, however, these incidents directly or indirectly affect the transportation system involved in logistics operations, thereby affecting the normal operation of the M-ULS. For example, engineering problems, such as sudden water ingress in tunnel sections, essentially disrupt the connectivity between nodes indirectly. Therefore, this section is dedicated to the analysis of the impact of operational incidents on the M-ULS from the perspective of the transportation system, including the three subsystems of logistics, trains, and information. In this analysis, the influence of tunnel sections and station construction issues on the system is excluded, and it is assumed that the track subsystem remains in normal operation throughout.

As shown in Figure 3a, for any given node, the operational processes can be divided into three distinct phases: unloading, logistics processing, and loading. If the logistics equipment at a particular node fails, the subsequent loading and logistics processing stages at that node are directly affected. However, in terms of failure propagation paths, the failure of logistics equipment at one node does not directly affect the normal operation of handling processes at other nodes. If we assume that the logistics facilities at the node fail at time $\mathrm{t}$ and that the duration of the failure is $\Delta \mathrm{t}$, we can express the effectiveness of the node during $\Delta \mathrm{t}$ as follows:

$${\mathrm{E}}_{\log }^{\mathrm{i}}={\mathrm{E}}_{\log -\mathrm{i}}^1+{\mathrm{E}}_{\log -\mathrm{i}}^2+{\mathrm{E}}_{\log -\mathrm{i}}^3$$

(10)

In the equation, ${\mathrm{E}}_{\log -\mathrm{i}}^1$ represents the effectiveness of the unloading stage at node $\mathrm{i}$. It takes the value 1 if the unloading stage is not affected by the failure, and 0 if it is. ${\mathrm{E}}_{\log -\mathrm{i}}^2$ represents the effectiveness of the logistics processing stage at node $\mathrm{i}$. It is equal to 1 if the failure does not affect this stage and 0 if it does. ${\mathrm{E}}_{\log -\mathrm{i}}^3$ represents the effectiveness of the loading stage at node $\mathrm{i}$. It is equal to 1 if the loading stage is not affected by the failure, and 0 if it is.

As shown in Figure 3b, in the event of a failure occurring during the operation of a metro train, where a train designated ${\mathrm{m}}_{\mathrm{a}\to \mathrm{b}}$, traveling from origin station a to destination station b, is unable to proceed to the next station due to the aforementioned failure, the train will remain stationary at the node for the duration of the failure. It is important to note that due to the temporary suspension of the train at the node, subsequent trains on the same line will be temporarily suspended from departing until normal service is resumed. This is to prevent potential safety hazards, such as rear-end collisions. Assuming that this failure occurs at a time $\mathrm{t}$ and persists for a duration of $\Delta \mathrm{t}$, the effectiveness of the train during this period can be quantified by the travel time impact index ${\mathrm{T}}_{{\mathrm{m}}_{\mathrm{a}\to \mathrm{b}}}$, which is formulated as follows:

$${\mathrm{T}}_{{\mathrm{m}}_{\mathrm{a}\to \mathrm{b}}}={\mathrm{T}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}+{\mathrm{T}}_{\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}$$

(11)

In the equation, ${\mathrm{T}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}$ is the normal dwell time of ${\mathrm{m}}_{\mathrm{a}\to \mathrm{b}}$ at node $\mathrm{i}$ and ${\mathrm{T}}_{\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}$ is the additional delay caused by the failure.

The effectiveness of subsequent trains, denoted by ${\mathrm{m}}_{\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{s}}$, can be expressed by the travel time impact index $\mathrm{T}({\mathrm{m}}_{\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{s}})$, which is formulated as follows:

$$\mathrm{T}({\mathrm{m}}_{\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{s}})=\left\{\begin{array}{c}{\mathrm{T}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}-\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{s}}+{\mathrm{T}}_{\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}},\begin{array}{cc}\mathrm{i}\mathrm{f}& \mathrm{a}\mathrm{f}\mathrm{f}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}\end{array}\\ {\mathrm{T}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}-\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{s}},\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}\right.$$

(12)

In the equation, ${\mathrm{T}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}-\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{s}}$ is the normal departure time of the train and ${\mathrm{T}}_{\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}$ is the additional delay caused by the failure.

As shown in Figure 3c, in the event of a failure in the CCC, all nodes directly under its control will be affected, while lines not directly associated with that CCC will continue to operate normally. In the event of a failure in the information system of a particular node, the node will still maintain a certain level of operational performance through the implementation of manual intervention. As a result, the affected nodes will not lose all functionality, but their overall effectiveness will be reduced. Assuming that this failure occurs at a time $\mathrm{t}$ and persists for a duration of $\Delta \mathrm{t}$, the effectiveness of the affected node during the specified time interval can be expressed as follows:

$${\mathrm{E}}_{\mathrm{int}}^{\mathrm{i}}={\mathrm{E}}_{\mathrm{int}-\mathrm{i}}^1+{\mathrm{E}}_{\mathrm{int}-\mathrm{i}}^2+{\mathrm{E}}_{\mathrm{int}-\mathrm{i}}^3$$

(13)

In the equation, ${\mathrm{E}}_{\mathrm{int}-\mathrm{i}}^1$ and ${\mathrm{E}}_{\mathrm{int}-\mathrm{i}}^3$ represent the effectiveness of the unloading and loading processes, respectively. However, the effectiveness of the logistics processing segment is not constant and thus affects transfer nodes and non-transfer nodes in different ways. In particular, if the node is a transfer node, then

$${\mathrm{E}}_{\mathrm{int}-\mathrm{i}}^2={\displaystyle \frac{\alpha }{\alpha +\beta }}.{\epsilon }_1.{\mathrm{E}}_{\mathrm{int}-\mathrm{i}-\mathrm{n}\mathrm{o}\mathrm{r}}^2$$

(14)

If the node is a non-transfer node, then

$${\mathrm{E}}_{\mathrm{int}-\mathrm{i}}^2={\displaystyle \frac{\alpha }{\alpha +{\beta }^{\prime }}}.{\epsilon }_2.{\mathrm{E}}_{\mathrm{int}-\mathrm{i}-\mathrm{n}\mathrm{o}\mathrm{r}}^2$$

(15)

where ${\displaystyle \frac{\alpha }{\alpha +\beta }}$ represents the weighting coefficient of the logistics processing segment at the transfer node. ${\displaystyle \frac{\alpha }{\alpha +{\beta }^{\prime }}}$ represents the weighting coefficient of the logistics processing segment at the non-transfer node. ${\epsilon }_1$ and ${\epsilon }_2$ are adjustment parameters. ${\mathrm{E}}_{\mathrm{int}-\mathrm{i}-\mathrm{n}\mathrm{o}\mathrm{r}}^2$ represents the effectiveness of the logistics processing stage at the node under normal operation.

2.3. M-ULS Network Performance Measurement

There are two fundamental dimensions to evaluating M-ULS network performance: the operational status of the system itself and the effectiveness of logistics delivery. From the perspective of the system as a whole, the primary concern is the network’s transportation capacity. At the logistics level, however, the focus shifts to on-time delivery as the key performance indicator. To quantify the performance of the M-ULS network, this paper selects freight flow and logistics timeliness as indicators of network performance. The network performance of the M-ULS is represented by $\mathsf{\omega }(\mathrm{t})$, which can be expressed as follows:

$$\mathsf{\omega }(\mathrm{t})={\displaystyle \frac{{\mathrm{T}}_1\max {\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\tau }_{\mathrm{i}}(\mathrm{t})}}{{\mathrm{T}}_2{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\phi }_{\mathrm{i}}(\mathrm{t})}}}$$

(16)

In the equation, ${\tau }_{\mathrm{i}}(\mathrm{t})$ represents the freight flow value of the node at any time under normal operation. The sum ${\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\tau }_{\mathrm{i}}(\mathrm{t})}$ denotes the total freight flow value of all nodes in the network at that specific time. Should the network freight flow value reach its maximum at time $\mathrm{t}={\mathrm{t}}_1$, then ${\mathrm{t}}_1$ is recorded as the time when the maximum freight flow occurs in the network under normal operation, and the corresponding freight flow at that moment is denoted as $\max {\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\tau }_{\mathrm{i}}}(\mathrm{t})$.

Similarly, ${\phi }_{\mathrm{i}}(\mathrm{t})$ represents the freight flow value of the node at any time under failure conditions. The sum ${\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\phi }_{\mathrm{i}}}(\mathrm{t})$ denotes the total freight flow value of all nodes in the network at that specific time. Note that if ${\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\phi }_{\mathrm{i}}}(\mathrm{t})$ is lower than $\max {\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\tau }_{\mathrm{i}}}(\mathrm{t})$, it indicates that the network freight flow is within the normal range. Consequently, in such cases, the ratio ${\displaystyle \frac{\max {\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\tau }_{\mathrm{i}}(\mathrm{t})}}{{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\phi }_{\mathrm{i}}(\mathrm{t})}}}$ is set to 1.

Furthermore, ${\mathrm{T}}_1$ represents the average delivery time for each demand point under normal operation while ${\mathrm{T}}_2$ represents the average delivery time for each demand point under failure conditions.

2.4. M-ULS Network Resilience Measurement

The resilience of the M-ULS is calculated based on the measurements of network performance indicators. The resilience of the M-ULS is represented by $\mathrm{R}$, which can be expressed as follows:

$$\mathrm{R}={\displaystyle {\int }_{{\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}}^{{\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}+\Delta \mathrm{t}+{\mathrm{t}}_{\mathrm{recovery}}}[1-\mathsf{\omega }(\mathrm{t})]\mathrm{d}\mathrm{t}}$$

(17)

where ${\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}$ is the start time of the failure, $\Delta \mathrm{t}$ is the duration of the failure, and ${\mathrm{t}}_{\mathrm{recovery}}$ is the time from the end of the failure until the system is fully recovered. The R-value is calculated from the approximate area bounded by the resilience curve and the horizontal line with a value of 1 on the ordinate. A lower value indicates less loss of network performance for the M-ULS under failure conditions, reflecting a greater resilience of the M-ULS. Conversely, a higher value indicates a lower resilience of the M-ULS.

3. Case Study

3.1. Data and Simulation Scenarios

In this paper, a specific area within the central urban district of Nanjing is selected as a case study, the exact scope of which is shown in Figure 4. The region’s logistics and distribution services mainly rely on the use of out-of-town logistics parks. The simulation experiment scenario covers a total of 79 stations on the Nanjing Metro Lines 1, 2, 3, and 4, including six major transfer hubs. The selected stations are Nanjing Station, Gulou Station, Xinjiekou Station, Jimingsi Station, Nanjingnan Station, and Daxinggong Station. According to the existing layout pattern of the Nanjing Metro, the CCC of Line 1 and Line 2 are both located at Zhujianglu Station, the CCC of Line 3 is located at Nanjing South Station, and the CCC of Line 4 is located at Lingshan Station. In addition, the simulation experiment scenario includes three out-of-town logistics parks: Yongning Logistics Park, Dingjiazhuang Logistics Park, and JD.com Nanjing Logistics Park. Considering the actual road network conditions in Nanjing, the logistics service area has been meticulously divided into 312 intracity cluster regional demand points, with the aim of receiving inbound freight from the above three logistics parks [24]. In terms of collecting and processing freight demand data, comprehensive industry surveys were conducted on the operations of the three aforementioned logistics parks. Then, scientific data processing techniques were applied to generate a 3 × 312 OD demand matrix.

The parameters of the simulation experiment scenario are described in

Table 1. The parameters of the simulation experiment scenario.

Parameters	Definition	Values	Unit
${\mathrm{V}}_{\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{o}}$	Metro speed	40	km/h
${\mathrm{T}}_{\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{o}-\mathrm{h}\mathrm{e}\mathrm{a}}$	Metro headway	3	min
${\mathrm{T}}_{\mathrm{l}\mathrm{p}-\mathrm{v}\mathrm{a}\mathrm{l}}$	The interval of the logistics park	3	min
${\mathrm{V}}_{\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d}}$	Ground transportation speed	40	km/h
${\mathrm{T}}_{\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{p}}$	Station stopping time	30	s
${\mathrm{V}}_{\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{g}\mathrm{i}\mathrm{n}}$	The logistics processing speed at the original metro station under normal operation	450	packages/min
${\mathrm{V}}_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}}$	The logistics processing speed at the transfer station under normal operation	350	packages/min
${\mathrm{V}}_{\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{i}}$	Logistics processing speed at non-transfer stations	315	packages/min
${\mathrm{M}}_{\mathrm{f}}$	Train formation	6	carriages
${\mathrm{M}}_{\mathrm{c}}$	Full load capacity per carriage	3000	packages
${\epsilon }_1$	Transfer station adjustment parameter	0.9
${\epsilon }_2$	Non-transfer station adjustment parameter	0.9
${\displaystyle \frac{\alpha }{\alpha +\beta }}$	Transfer station weighting coefficient	0.91
${\displaystyle \frac{\alpha }{\alpha +{\beta }^{\prime }}}$	Non-transfer station weighting coefficient	0.92

. A number of points need to be clarified. First, since the primary focus of this paper is on the metro network, it is assumed that freight departing from terminal metro stations will continue to be delivered to various intracity cluster distribution centers via ground transportation. Second, in order to fully meet the demand for freight transportation within the metro system while taking into account the actual operational capabilities of the Nanjing metro system, we have incorporated the actual operating schedules of the Nanjing metro system to determine the appropriate departure intervals and operating times for the metro system within the M-ULS. Although this setting has minor deviations from the actual operating schedules of the Nanjing Metro, they are within the feasible range of the metro’s operational capabilities and thus do not affect the reliability of the simulation results. Finally, given the complexity of the simulation, during the simulation process, we simplified the loading and unloading procedures during the metro dwell times and treated them as constant and normal operating modes.

A series of simulation experiments were conducted to examine the operational performance of six transfer stations under a variety of potential failure scenarios. The experiments were designed to begin at 8:00 am and continue for a period of five hours, during which a hypothetical failure would occur. The specific scenarios are described below.

In the first scenario, the six transfer stations each experience a logistical facilities failure independently at 8:00 am. Upon the occurrence of the failure, logistical processing at the affected station is immediately halted and resumed only after the logistical facilities are repaired. During the disruption, freight destined for the affected station will continue to arrive normally but will be held at the station until the disruption is resolved and subsequent logistics processing can begin.

In Scenario 2, at 8:00 am, the disruption occurs on Line 1 after the train has stopped at Nanjing Station, Xinjiekou Station, and Nanjingnan Station. The train is unable to restart. As a result, subsequent trains on the line will be suspended for a period of time that is equal to the duration of the disruption and will resume service after the disruption is resolved.

In Scenario 3, the disruption occurs in the CCC located at Nanjingnan Station, Zhujiang Road Station, and Lingshan Station. During the disruption, the processing speed of all relevant nodes is affected and fluctuates. When the CCC resumes normal operation, the processing speed of each node returns to its original state.

3.2. Simulation Platform

Any-Logic is an agent-based modeling platform that provides a comprehensive suite of capabilities, including three-dimensional dynamic simulation, optimization analysis, and data visualization, seamlessly integrated into a single, unified platform. The software has robust capabilities for simulating and optimizing discrete event problems, which has led to its adoption in a number of fields, including logistics and transportation. In this paper, the Any-Logic 8.7.1 simulation platform was used for programming purposes. The entire simulation process was performed on a Windows 10 system equipped with an Intel^® Core™ i5-8250U CPU running at 1.60 GHz and 64 GB of RAM. To ensure the reliability of the simulation, pre-test simulations were performed prior to the official run. The official simulation began after 10 consecutive pre-tests, with outputs generated at 30-min intervals.

4. Results and Discussion

Given the complex nature of the simulation experiments, the computational process for measuring the resilience of the M-ULS is divided into two distinct phases. In the first phase, a 30-min interval is used to output real-time network flow data for each time node and delivery time at each demand point across different simulation scenarios until all OD demand delivery tasks are completed. In the second phase, the network performance of the M-ULS is derived using Equation (16). The resilience value of the M-ULS is solved using Equation (17).

4.1. The Impact of Different Operational Incidents on the Network Performance of the M-ULS

As shown in

Table 2. The results of the M-ULS network performance analysis.

Scenario	Case	${\mathbf{T}}_1$ (min)	${\mathbf{t}}_1$	$\mathbf{max}{\displaystyle {\sum }_{\mathbf{i}=1}^{\mathbf{n}}{\tau }_{\mathbf{i}}}(\mathbf{t})$	${\mathbf{T}}_2$ (min)	${\mathbf{t}}_2$	$\mathbf{max}{\displaystyle {\sum }_{\mathbf{i}=1}^{\mathbf{n}}{\phi }_{\mathbf{i}}}(\mathbf{t})$	Top Three Stations
Non-failure	Normal	396.48	9:30 am	49,875.94				Daxinggong, Xinjiekou, Nanjing
Scenario 1	Nanjingnan				719.82	1:00 pm	259,933.12	Maigaoqiao, Nanjing, Nanjingnan
	Xinjiekou				691.65	1:00 pm	251,585.20	Maigaoqiao, Nanjing, Xinjiekou
	Gulou				670.90	1:00 pm	235,084.76	Maigaoqiao, Nanjing, Yuhua
	Daxinggong				582.26	1:00 pm	179,639.10	Xinjiekou, Daxinggong, Yuhua
	Jimingsi				509.81	1:00 pm	195,655.96	Linchang, Nanjing, Jimingsi
	Nanjing				494.56	1:00 pm	145,770.13	Nanjing, Yuhua, Wuding
Scenario 2	Xinjiekou-up				626.58	1:00 pm	235,084.76	Maigaoqiao, Nanjing, Yuhua
	Nanjingnan-up				626.58	1:00 pm	235,084.76	Maigaoqiao, Nanjing, Yuhua
	Nanjing -up				625.63	1:00 pm	235,084.76	Maigaoqiao, Nanjing, Yuhua
	Nanjing-down				438.12	9:30 am	61,610.14	Daxinggong, Nanjing, Xinjiekou
	Xinjiekou-down				435.42	9:30 am	59,746.58	Daxinggong, Nanjing, Xinjiekou
	Nanjingnan-down				432.70	9:30 am	58,632.39	Daxinggong, Xinjiekou, Nanjing
Scenario 3	CCC (line4)				397.00	9:30 am	50,286.12	Daxinggong, Nanjing, Xinjiekou
	CCC (line1 and line2)				393.93	9:30 am	35,097.07	Shanghailu, Daxinggong, Nanjing
	CCC (line3)				393.39	9:30 am	28,713.51	Shanghailu, Nanjing, Xianmen

Note: $\max {\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\phi }_{\mathrm{i}}}(\mathrm{t})$ represents the maximum network freight flow under different failure conditions and ${\mathrm{t}}_2$ represents the time when the maximum network freight flow occurs.

, in terms of network freight flow, under normal operating conditions, the peak flow occurs at 9:30 am, with a value of 49,875.94. The top three stations with high flow are Daxinggong Station, Xinjiekou Station, and Nanjing Station. In the event of a failure in the logistics facility at Nanjingnan Station, the peak flow is observed at 1:00 pm, reaching 259,933.12. The top three stations with high flow are Maigaoqiao Station, Nanjing Station, and Nanjingnan Station. In the event of a train facility failure, it can be assumed that an uptown train will experience a failure while approaching Nanjingnan Station. This will result in a peak flow at 1:00 pm, with a value of 235,084.76. The top three stations with significant flows are Maigaoqiao Station, Nanjing Station, and Yuhua Station.

In general, across the 12 simulation scenarios that include both logistics facility failures and train facility failures, the freight flow within the network undergoes a remarkable process of sharp increases, followed by decreases, until all OD demands are satisfied. At this point, the flow in the network finally decreases to zero. In contrast, the intranetwork flow shows less pronounced fluctuations in the CCC simulation scenarios. To better illustrate this phenomenon, we have created a diagram of the variation process of the network freight flow, using Nanjingnan Station and CCC Line 4 as illustrative examples, as shown in Figure 5.

Table 3. The variation in the M-ULS network performance under different failure scenarios.

Scenario	Case	Lowest Moment	Lowest Performance	Recovery Time
Scenario 1	Nanjingnan	1:00 pm	0.11	3:00 pm
	Xinjiekou	1:00 pm	0.11	3:00 pm
	Gulou	1:00 pm	0.13	3:00 pm
	Daxinggong	1:00 pm	0.19	2:30 pm
	Jimingsi	1:00 pm	0.20	3:00 pm
	Nanjing	1:00 pm	0.27	2:30 pm
Scenario 2	Xinjiekou-up	1:00 pm	0.13	3:00 pm
	Nanjingnan-up	1:00 pm	0.13	3:00 pm
	Nanjing-up	1:00 pm	0.13	3:00 pm
	Nanjing-down	9:30 am	0.73	10:30 am
	Xinjiekou-down	9:30 am	0.76	10:30 am
	Nanjingnan-down	9:30 am	0.78	10:30 am
Scenario 3	CCC (line4)	9:30 am	0.99	10:00 am

Note: The results of the failure scenarios for CCC (line1 and line2) and CCC (line3) are not significant and are therefore not included in the table.

illustrates the variation in the M-ULS network performance under different failure scenarios. In the case of a logistics failure, the lowest network performance is observed at 1:00 pm, with the minimum network performance ranging from 0.11 to 0.27. The system recovery period is scheduled to begin at either 2:30 pm or 3:00 pm. In contrast, the timing of the lowest network performance under train failure varies significantly. The lowest performance for the downstream train network occurs at 9:30 a.m., while the lowest performance for the upstream train network occurs at 1:00 p.m. In these scenarios, the minimum network performance ranges from 0.13 to 0.78, with the system recovery period scheduled to begin at either 10:30 am or 3:00 pm. In the case of a CCC failure, the lowest network performance is observed at 9:30 a.m., with a minimum value of 0.99. As shown in the calculations, the M-ULS network performance does not recover immediately after a failure is repaired but requires a period of time to return to normal. This is shown in Figure 6. This figure shows that the network performance of the M-ULS has a tendency to initially decrease, followed by an increase, and gradually return to its normal level.

4.2. M-ULS Network Resilience Under Different Operational Incident

Based on the results of the network performance calculations, a further evaluation was performed to analyze the resilience of the M-ULS. The results of this evaluation are shown in

Table 4. The resilience of the M-ULS network under different failure scenarios.

Scenario	Case	Performance Loss	Resilience Rank	Importance Rank
Scenario 1	Nanjingnan	69.36%	6	1
	Xinjiekou	68.21%	5	2
	Gulou	66.00%	4	3
	Daxinggong	58.69%	3	4
	Jimingsi	52.79%	2	5
	Nanjing	43.31%	1	6
Scenario 2	Xinjiekou-up	64.00%	4	1
	Nanjingnan-up	64.00%	4	1
	Nanjing-up	64.00%	4	1
	Nanjing-down	11.40%	3	2
	Xinjiekou-down	10.20%	2	3
	Nanjingnan-down	9.20%	1	4
Scenario 3	CCC (line4)	0.50%	2	1
	CCC (line1 and line2)	0.00%	1	2
	CCC (line3)	0.00%	1	2

and Figure 7. The analysis of six simulation scenarios related to the failure of logistics facilities showed that the failure of logistics facilities at Nanjingnan Station had the most significant negative impact on the network performance of the M-ULS, resulting in a 69.36% decrease. Given the inverse relationship between the degree of network performance degradation and network resilience, it can be concluded that the M-ULS had the lowest resilience when the logistics facilities at Nanjingnan Station failed. Subsequently, the failures at Xinjiekou Station and Gulou Station reduced the network performance by 68.21% and 66.00%, respectively, making these stations the fifth and fourth least resilient in the ranking. In contrast, the failure of logistics facilities at Nanjing Station had the least impact on the M-ULS network performance, with a reduction of 43.31%. As a result, it was identified as the most resilient among the stations analyzed. The assessment results indicate that the failure of logistics facilities has a significant impact on the resilience of the M-ULS. It is noteworthy that Nanjingnan Station was identified as a critical node whose failure has the greatest impact on the resilience of the M-ULS. Although Nanjing Station experienced the least significant loss in network performance, the 43.31% reduction is still a significant proportion that cannot be overlooked and warrants further attention. Therefore, in the planning and operation of the M-ULS network, it is imperative to prioritize the improvement of the resource allocation and operational maintenance standards of logistics facilities at nodes, with special emphasis on those that are of critical importance, such as Nanjingnan Station. This comprehensive approach will strengthen the resilience of the M-ULS, ensuring optimal operational stability and recovery capabilities in the event of potential disruptions.

The results of three simulation scenarios related to CCC failure show that the maximum loss of the M-ULS network performance is 0.50%, which occurs specifically within the CCC Line 4. This phenomenon suggests that failures in the CCC do not significantly affect the resilience of the M-ULS. This result can be attributed to the fact that such failures do not result in a complete loss of the logistics processing capabilities at the nodes. Rather, they lead to changes in the processing speed of logistics operations at these nodes. Nevertheless, the nodes retain the ability to maintain a minimum level of logistics processing, which effectively mitigates the accumulation of freight within the network and preserves the overall resilience of the M-ULS.

The results of six simulation scenarios related to train facility failure show that the M-ULS network performance losses are the most significant when the train encounters a failure while traveling uptown to Xinjiekou Station, Nanjingnan Station, and Nanjing Station, each of which is 64.00%. This level of loss is comparable to the maximum network performance loss observed in logistics facility failure scenarios, indicating that both train and logistics facility failures pose a significant threat to the M-ULS network performance. Given the inverse relationship between the degree of network performance loss and the resilience of the M-ULS, it can be inferred that the resilience of the M-ULS is at its lowest level when train facility failures occur at Xinjiekou Station, Nanjingnan Station, and Nanjing Station, with a simultaneous uptown travel direction. Conversely, when the train encounters failures while traveling in a downtown direction to Nanjing Station, Xinjiekou Station, or Nanjingnan Station, the losses to the M-ULS network performance are significantly reduced, with values of 11.40%, 10.20%, and 9.20%, respectively. Accordingly, these failures are ranked third, second, and first in terms of network resilience. These results indicate that failures occurring at stations during train ascent, as well as failures of logistics facilities within stations, have a much more pronounced impact on the resilience of the M-ULS compared to failures during train descent. This phenomenon is mainly due to the location of stations within the M-ULS topological structure and the uneven distribution of OD demand. To illustrate this, Nanjingnan Station serves as an intersection hub for Lines 1 and 3, with a significant volume of freight originating from the JD.com Nanjing Logistics Park, relying on the station for transfer from Line 3 to Line 1 for transportation. Therefore, failures that occur when the train ascends to Nanjingnan Station directly affect the transfer performance of freight, thereby significantly reducing the network performance and the resilience of the M-ULS. In conclusion, in order to improve the overall resilience of the M-ULS, special attention should be paid to strengthening the maintenance of train facilities and the prevention of failures of ascending trains at critical intersection stations, such as Nanjingnan Station.

The comprehensive analysis of the failure scenarios shows that, compared to train facility failures and information system CCC failures, logistics facility failures have a more pronounced impact on the resilience of the M-ULS. In light of the above findings, the subsequent focus of this paper shifts to Nanjingnan Station, where a sensitivity analysis of the duration of logistics facility failures is conducted, and the results are shown in

Table 5. The resilience of the M-ULS network under different durations.

Duration	Performance Loss	Resilience Rank	Importance Rank
1 h	13.80%	1	5
3 h	41.11%	2	4
5 h	69.36%	3	3
7 h	84.56%	4	2
9 h	90.22%	5	1

and Figure 8 and Figure 9. The sensitivity analysis shows that as the duration of the failure increases, there is a corresponding intensification in the loss of the M-ULS network performance. As a result, the resilience of the M-ULS gradually decreases as the duration increases. This finding highlights the critical importance of effectively reducing the duration of failures to improve the resilience of the M-ULS. Therefore, in practical operation, utmost attention should be paid to the maintenance and troubleshooting of logistics facilities in order to respond promptly and shorten the failure duration, thereby ensuring the operational resilience of the M-ULS system.

5. Conclusions

To address the issue of the M-ULS performance in the context of unexpected events during operation, this paper proposes a methodology for assessing the resilience of the M-ULS. The objective of the proposed methodology is to provide a scientific basis for planning and operational decisions related to the M-ULS resilience assessment and optimization. In addition, it aims to provide new ideas and insights for the sustainable development of urban logistics relying on urban rail transport. The main conclusions of this paper are as follows:

(1)

The utilization of spare metro capacity for freight transportation offers significant benefits. The Nanjing Metro case study provides compelling evidence that when the metro system has spare capacity, the M-ULS has the potential to serve as a highly efficient freight transport system. In normal M-ULS operation, the average delivery time per demand point is 396.48 min, with all goods successfully delivered between 5:30 am and 11:00 pm. This not only demonstrates the exemplary logistics punctuality of the M-ULS but also highlights its distinctive advantage of efficiently reclaiming ground space.

(2)

The impact of different failure types on the resilience of the M-ULS varies. Compared to train facility failure and CCC failure, the logistics facility failure has a more pronounced impact on the resilience of the M-ULS. The results of this paper indicate that the impact of logistics facility failure on the M-ULS network performance ranges from 43.31% to 69.36%, while the impact of train facility failure ranges from 9.2% to 64.0%. In contrast, a certain level of CCC failures, while directly reducing the speed of logistics processing at the nodes, does not have a significant impact on the final resilience of the M-ULS due to the different arrival and departure times of the freight at the nodes.

(3)

For the same type of disruption, the impact on the M-ULS resilience varies depending on the direction of train travel. The results of this paper show that within the same station, the maximum loss in the M-ULS network performance due to upstream train failure is as high as 64.0%, while the loss caused by downstream train failure is relatively low, reaching only 11.40%. This discrepancy is mainly due to the variation in freight carried by trains on different routes, which subsequently affects the M-ULS network performance in the event of a failure. Ultimately, this results in a difference in resilience.

(4)

The duration of the disruption is a significant factor affecting the resilience of the M-ULS network. As the duration of the disruption increases, its impact on the M-ULS resilience becomes more pronounced. The sensitivity analysis shows that as the duration of the disruption increases from one hour to nine hours, the magnitude of the M-ULS network performance loss increases significantly from 13.80% to 90.22%. This, in turn, results in a significant decrease in the resilience level.

Due to the complexity of the M-ULS, which involves multiple factors such as the metro system, logistics network, tunnels, and underground space technology, we decided to assess and optimize its resilience in stages. Therefore, the main objective of this paper is to propose a more general M-ULS resilience assessment method, which will serve as the basis for subsequent resilience assessment and optimization work. However, considering the complexity of the model, the assessment method in this paper mainly focuses on the case of single-point failure. In subsequent research, we will further analyze the impact of multi-node and multi-line failures in-depth and explore how to optimize the resilience of the M-ULS under different recovery strategies.