## 2 Related Works
In addition, in [46; 47], they studied the dynamic light connection provisioning problem of spectrally spatially flexible optical networks based on MCFs and compared the performance gains of the proposed algorithms in three application scenarios. Network Resource Allocation in SCNs. Since the SCN architecture is a newly proposed optical network architecture, only two papers are known to study the network resource allocation problem based on SCN architecture [48; 49]. In [48], a heuristic routing and SDM/WDM multilayer resource assignment (RSWA) algorithm to minimize the occupied resources has been proposed and the techno-economic analysis of the SCN architecture has been performed. Through simulations, ref. [48] demonstrated the effectiveness of the RSWA algorithm and clearly showed that hierarchical spatial bypassing and spectral grooming are beneficial, in terms of the number of required network resources and network-total node cost. However, ref. [48], as a first step in the techno-economic analysis of SCNs, focused only on a simple SCN model, setting the links in the SCN to operate in a single MF and not considering MFC, which may limit the flexibility of routing and grooming. Furthermore, ordering traffic demands in descending order performs significantly better than the ascending order in the RSWA heuristic. SA can be used to further improve the performance. In [49], the network resource allocation problem has been defined as a routing, spatial channel, and spectrum allocation (RSCSA) problem, and an ILP model and a heuristic algorithm has been designed to solve the RSCSA problem. This is the first study to focus on the network optimization problem in SCNs. The simulation results show that both the proposed ILP model and the heuristic algorithm can effectively find the optimal solution or a solution close to the lower bound. However, the ILP model is not very efficient for solving realistic large-scale problem instances. Furthermore, all traffic requests are also routed end-to-end using the same MF, without considering the potential network benefits of flexible MF adoption. These aforementioned studies provide us with ideas to solve the network resource allocation problem in SCNs. We defined the network resource allocation problem in static SCNs as the routing, modulation format, spatial lane, and spectrum block assignment (RMSSA) problem. In this paper, we use flexible MFs to solve the RMSSA problem. By selecting an appropriate MF, the spectrum resources occupied by individual traffic requests can be reduced, and SCNs can carry more traffic requests. Most previous studies have focused on using the same MF throughout an optical connection, which is equivalent to selecting a less efficient MF for a shorter length segment and inevitably leads to a waste of network resources. Hence, to maximize the effectiveness of MFs in improving the utilization of network resources, modulation format conversion (MFC) and conversion nodes (CNs) are introduced at the intermediate nodes of an optical route. Performing MFC, the optical route can be divided into multiple segments using different MFs, and these segments are called modulation format segments (MFSs). The current study does not consider the extra latency and cost due to the use of MFC. Therefore, we proposed a heuristic algorithm considering the effects of MF and MFC to solve the RMSSA problem. Furthermore, the effectiveness of the heuristic algorithm is verified by comparing it with two other algorithms. To the best of our knowledge, this is the first paper to consider the use of MFs, CNs, and MFC in solving the SCN resource allocation problem. The rest of the paper is organized as follows. In Section 3, the system model is constructed and the MF adoption method in SCNs is given. The RMSSA problem and its associated constraints are defined in Section 4. Three heuristic algorithms to solve the RMSSA problem are given in Section 5. In Section 6, the performances of the proposed algorithms are compared.