## 4 Algorithms
The key element of the ARBR algorithm is that it accounts for two types of important resources in optical networks, namely, spectrum and transponders. In a nutshell, the ARBR is a highly adaptive routing algorithm that utilizes the key benefits of B2B regeneration. In the preprocessing phase of ARBR, using \(k\) shortest paths, a set of configurations defined by routing paths and location of regeneration points are computed for each node pair. For each transparent segment of a particular configuration, the most spectrally efficient modulation format is selected that supports transmission reach larger than the length of the considered segment. For each new request that occurs in the network, the ARBR algorithm executes the following procedure. Given the set of pre-computed configurations, a special adaptive metric is calculated for each configuration. This metric contains two elements: (i) static usage of spectrum (i.e., the number of slices essential to provision the considered configuration for a particular request) and transponders (i.e., the number of transponders essential to provision the considered configuration for a particular request); and (ii) dynamic usage of the spectrum and transponders resources (i.e., cost of the configuration that represents the current utilization of spectrum and transponders resources). Both elements (i.e., static and dynamic) are weighted with parameter \(\alpha\). Next, the configurations are processed in increasing order of the obtained configuration's metric. The ARBR tries to provision the request on the currently analyzed configuration, namely, using the first-fit approach, the algorithm searches for a sufficient range of spectrum checking various spatial modes. If the analyzed configuration is feasible, the request is provisioned in the network using this configuration. Otherwise, if none of the configurations is feasible, the request is rejected. To summarize, ARBR is able to analyze different configurations of routing paths and regeneration points to select the best option that balances between two key resources in the network, namely, spectrum resources (slices) and transponders. Moreover, the ARBR algorithm can adapt to the dynamically changing conditions in the network by selecting routing paths and regeneration points according to the current utilization of spectrum and transponders resources. For more details on ARBR, the reader is referred to Reference [11]. The first traffic-based transponder placement algorithm is MSU proposed in Reference [17] and adapted to our problem. In particular, MSU distributes \(T\) transponders over the network based on the maximum instantaneous number of transponders used in each node during the simulation of the dynamic routing simulation with the use of the ARBR method. During the simulations, it was assumed that nodes were equipped with an unlimited number of transponders and the traffic is generated following a known (predicted) traffic pattern. Finally, we present a novel SAUR algorithm. In Figure 3, we report the general workflow of this method, while Figure 4 shows the pseudocode. The idea of SAUR is to utilize knowledge on network traffic and allocation method in order to predeploy the transponders in such a way that the network performance in terms of bandwidth blocking probability is improved, or in other words, more traffic can be accepted in the network. The key idea of SAUR is quite simple. First, each network node is assigned with the same number of transponders (Step 1), i.e., \(t(v)=\lfloor T/|V|\rfloor\), which according to Reference [12] provides good results. Next, we run the ARBR dynamic routing algorithm described above to simulate the network operation assuming a randomly generated lightpath requests following a known (predicted) traffic pattern (Step 2). During simulation, various statistics on transponder usage in network nodes are collected.