Related Work

This section discusses the related work on resilience metrics and analysis and national roaming/infrastructure sharing.

Resilience metrics and analysis: The resilience of networks have been investigated in different contexts, such as in traffic networks [32], power grids [41], ecological networks [40] and supply chain networks [62]. The resilience of the network has several aspects: whether the network is operational, and whether the service it offers is acceptable. To represent this distinction, metrics are categorized into two as topological and functional metrics [54]. Topological metrics, represent the status of the underlying network’s connectivity and network paths, e.g., relative size of the largest connected component, average two terminal reliability, average path length, motifs [25] and spectral metrics [19]. While these topological metrics provide useful insights about the existing/surviving infrastructure, they fall short of assessing the satisfaction of the served users and applications. As a remedy, functional metrics including objective (e.g., link stress and node load [54]) and subjective metrics (e.g., mean-opinion-score or other qualityof-experience metrics [48]) aim at assessing to what extent the network can satisfy its users’ expectations. Note that functional metrics need to reflect the application’s requirements, e.g., a reliability requiring application will be assessed by packet loss ratio. Some studies focus on static metrics, e.g., performance after the disruptive event, while others measure the system performance over a period of time [44], [58]. Similar to [43], our study focuses on static resilience using functional metrics, where we investigate the loss in quality of service immediately after a disruptive event.

网络韧性度量与分析： 网络韧性已在多个领域中被广泛研究，如交通网络 [32]、电力系统 [41]、生态网络 [40] 和供应链网络 [62] 等。网络韧性涵盖多个层面，包括网络是否仍然可用，以及其所提供的服务是否仍能满足用户需求。为体现这一区分，现有指标通常被分为两类：结构性指标（topological metrics）与功能性指标（functional metrics） [54]。前者侧重于基础网络结构的连接性和路径可达性，如最大连通子图的相对大小、平均两端可靠性、平均路径长度、网络结构模式（motifs）[25] 以及谱指标（spectral metrics）[19]。尽管这些结构性指标能反映网络在破坏后仍保有的基础连通性，但却难以准确评估用户及应用的实际服务体验。

为了弥补这一不足，功能性指标被提出并分为客观指标（如链路压力、节点负载 [54]）和主观指标（如平均主观评分或其他用户体验相关指标 [48]）。功能性指标需与具体应用场景结合，例如面向高可靠性的应用需使用丢包率进行评估。一些研究关注静态指标，即仅考虑破坏发生后的单点性能表现；而另一些研究则考察系统在一段时间内的动态表现 [44]、[58]。类似于 [43]，本研究采用静态功能性指标分析在扰动事件发生后，用户服务质量的下降情况。

When it comes to analyzing the resilience of a network, the closest studies to ours are [34], [61]. Yan et al. [61] propose the metric Tower Outage Impact Predictor (TOIP) to quantify the impact of a failure of a cell tower on the number of served cellular users. Due to the dense deployment of cell towers, a user might not perceive the failure of a cell-tower as it will be served immediately by another BS in the proximity. Using the data from an operational MNO, the authors propose a prediction scheme to estimate the number of users who would be affected by service outages of one or more BSs in the network. Our work differs from [61] in that we combine cellular network coverage and capacity models with the real-world data on the cellular network infrastructure to quantify the impact of failures on the user’s connectivity and satisfaction performance. Moreover, our focus is also on the potential resilience improvement due to infrastructure sharing among MNOs in the same country. Contrary to [34], our work investigates both coverage as service quality as metrics, and combines models with several data sources to assess resilience.

在网络韧性分析方面，与本研究最接近的是 [34] 与 [61]。Yan 等人 [61] 提出了“基站故障影响预测器”（TOIP）指标，用于量化某个基站发生故障时对用户服务的影响。由于蜂窝网络中基站部署密集，用户在某一基站宕机时，往往会被附近其他基站迅速接管，因而对服务中断不敏感。该研究基于实际运营商数据，提出了一种预测模型以估算受影响用户数。与之相比，我们的研究不仅结合了蜂窝网络覆盖与容量建模，还结合实际的网络基础设施数据，从连接与服务满意度角度量化网络故障对用户的影响。此外，我们进一步关注通过MNO间共享基础设施来提升网络韧性的潜力，这是 [61] 所未涵盖的。与 [34] 不同的是，我们同时分析了覆盖率与服务质量两个维度，并融合多源数据以综合评估网络韧性。

Authors of [13] consider two kinds of failures that might affect small cells in the Netherlands: power outages and cyberattacks. They investigate a case of power outage in 2015 in Noord-Holland, where after two hours 80% of the BS sites were down. In this case, providers immediately shut down the LTE network to have sufficient power supply for the essential network. Study in [13] proposes to also first deactivate small cells for keeping the emergency services functioning longer.

文献 [13] 分析了荷兰小基站受两类故障影响的情形：电力中断与网络攻击。以2015年荷兰北荷兰省一次停电为例，两小时内80%的基站宕机，运营商因此紧急关闭LTE网络，以保障核心通信服务的电力供应。该研究建议在此类情形下优先关闭小基站，以延长关键服务的可用性。

The resilience of 5G networks is of particular importance, since higher frequencies (e.g., mmWave bands) are more prone to errors [28] and links operating at these high bands might be affected by rain drastically, as the rain drops are nonnegligible in their size in relation to the wavelength of the mmWave signals [23], [37]. An eight-year measurement study [51] shows that rain might result in internet outages in some regions, and especially wireless links are more prone to these outages. Our study differs from these studies in that we combine models and publicly-available data to offer insights on the coverage and capacity performance of MNOs under two failure categories and the potential of national roaming toward mitigating the impact of these failures.

随着5G网络的发展，其韧性问题尤为重要，因为高频段（如毫米波）更易受到干扰 [28]，并且毫米波链路对降雨极为敏感，雨滴尺寸与信号波长相当时将显著影响通信质量 [23]、[37]。一项为期八年的测量研究 [51] 表明，降雨会在部分地区导致互联网中断，尤其是无线链路更容易受其影响。与这些研究不同的是，我们结合了建模与公开数据，系统分析了两类故障下MNO的覆盖与容量性能，并评估国家漫游对缓解故障影响的潜力。

National Roaming/infrastructure sharing: As resilience can be improved by increasing redundancy and overprovisioning [27], some studies investigated how infrastructure sharing can help from an economic or operations perspective [30], [63], increase rate coverage probability [39], [56], decrease energy consumption [31], or distribute the load evenly over the network [26]. Next to improved resilience, infrastructure sharing plays a key role in the future of telecommunications to keep the services affordable in developing countries [49], [50] and to increase coverage [21].Therefore, nationwide infrastructure sharing might be difficult to achieve due to possible decrease in operator revenue [22]. To mitigate this, one might consider to only share the infrastructure among certain operators, certain radio types [57] or on certain areas (Rural Access Network, [50]). Please refer to [11] for an overview of different modes of infrastructure sharing, e.g., at the core network or radio access network. Note that virtualization techniques already implemented by Mobile Virtual Network Operators [42] can be considered for implementation of the specific national roaming scenario studied in this paper, i.e., a single MVNO having access to all resources of all national MNOs.

国家漫游与基础设施共享： 提高网络韧性的一种方式是增加冗余与超配 [27]，因此部分研究从经济性与运营角度探讨基础设施共享的可行性 [30]、[63]，如提高速率覆盖概率 [39]、[56]，降低能耗 [31]，或实现负载均衡 [26]。除提升韧性外，基础设施共享在发展中国家更具重要性，有助于降低通信服务成本 [49]、[50] 并扩大覆盖范围 [21]。然而，全面的全国性共享面临运营商收入下降的挑战 [22]。为此，可以考虑仅在特定运营商之间、特定频段 [57] 或特定区域（如农村接入网络 [50]）实施共享。有关核心网或无线接入网层面的多种共享方式，可参考综述文献 [11]。此外，虚拟网络运营商（MVNO）所采用的网络虚拟化技术 [42] 亦可作为本文中所研究的特定国家漫游场景的实现手段：即由单一MVNO统一访问全国所有MNO资源。

Different from the studies that focus on infrastructure sharing [46], [52], we focus on the special case of national roaming where every user can use every existing BS of any MNO, similar to the approaches in [27] and [49]. We investigate the entire network and focus on improving resilience instead of purely on maintaining higher capacity. Moreover, since our goal is to quantify the full potential of national roaming, rather than considering national roaming only as a backup implemented in exceptional cases such as post-disasters or for a single MNO, we explore it as a default mode of operation where all MNOs can use each other’s network for serving the customers in the most efficient way. Therefore, this can be considered as the best case scenario where all MNOs are in business agreement and operating with a shared core network. Note that the economic implications, e.g., settling the roaming costs, are beyond the scope of our paper. Please refer to [38] for a thorough discussion on the economic aspects of infrastructure sharing.

不同于关注基础设施共享的一般性研究 [46]、[52]，本研究聚焦于国家漫游的特定形式，即所有用户都可以接入任一MNO的任一基站，与 [27] 与 [49] 中所提倡的做法类似。我们的目标是增强网络韧性，而非单纯提升系统容量。此外，我们假设国家漫游为默认运行模式，而非仅在灾后或个别MNO中作为备用机制启用。换言之，我们考虑的是所有MNO达成业务协议、共同使用共享核心网的最理想场景。需要说明的是，本文不涉及国家漫游的经济层面，如漫游费用的结算问题；对此，可参考文献 [38] 中关于基础设施共享经济性的深入讨论。