Serviceability of large-Scale systems
Simulation modelling practice and theory
One of the most important research fields of network sciences is the robustness of networks. A recently answered important question was the following: Which network topologies are more resistant to random malfunctions and/or direct attacks? Nevertheless, until now, "which system topology can be maintained and how to manage maintenance more efficiently and effectively" have been open questions. However, these questions are the keys both to designing large-scale systems and to scheduling
... scheduling maintenance tasks. This paper proposes a new means to analyze the maintainability of a large system by combining two kinds of networks, i.e., the reliability diagram of the system (1) and the network of scheduled maintenance tasks (2). This paper shows how to assign maintenance task(s) to a system component to increase the reliability of the system. With the proposed method, the maintainability of large-scale systems can be analyzed. Introduction The robustness and resistance of networks are widely studied in network science (see  for an excellent review). Scholars showed that so-called small-world 1 (hereinafter SW, e.g., (electrical) power grids, see  ) and scale-free (SF, e.g., the Internet and social networks, see  ) networks are more resistant to random failures than random networks [4, 5] . SW and SF networks have common features (see  for a great synthesis). These networks can be measured by the average shortest path length, as these networks allow limiting the number of stops (intermediate nodes) between two given nodes, on average. In addition, these networks contain many hubs (bridge nodes)  . However, SW and SF networks contain only a few large degree nodes (hubs, in this study, power plants); therefore, these networks (similar to power grids) are slightly resistant to direct attacks  . The distribution degree of the SF and, usually, SW networks follows a power law, at least asymptotically. That is, the fraction P ( k ) of nodes in the network having k connections to other nodes obeys P (k ) ∼ k −γ , where γ is a parameter that is typically in the range of [2, 3] for SF networks, although it may occasionally lie outside these bounds. The structure of the power grid can be characterized usually as a planar network (meaning edges do not cross each other). This network is an SF network instead of an SW network; however, the degree of distribution can also follow a power function, and the typical parameter γ ∈ [1, 2]. A planar network is more physically constrained and thus is more assortative, with a higher probability of containing a giant component (i.e., a connected subgraph containing a majority of the nodes)  . Similar to the SF networks, these networks are also less vulnerable to random failures than random networks and slightly more resistant to a direct attack than SF networks  . 1 SW networks exhibit a small average path length between pairs of nodes. For an excellent classification of small-world networks, see Amaral et al.  .