# Spectrum Allocation Using Integer Linear Programming and Kerr Optical Frequency Combs
## 3 Results and Discussion
As the number of requests increases, allocating each client to dedicated or multiple carriers becomes increasingly challenging, especially as the demand for channels rises to meet growing bandwidth requirements. When the available carriers are exhausted, the algorithm must optimize the allocation, but it faces limitations in maintaining full bandwidth request allocation. This increase in BBR indicates the algorithm's reduced capacity to manage a growing number of clients effectively. At this stage, the algorithm shows a high probability of blocking, with the most critical cases marked by circles. The findings highlight that an increase in requests and required bandwidth significantly raises the likelihood of network blocking. This underscores the need for efficient carrier management to minimize rejections, as scenarios with the highest rejection rates occur when large bandwidths are requested, reducing carrier availability and increasing the risk of blocking. To improve upon the previous model, where all requests were treated with equal priority, we propose a reconfigurable approach that assigns greater weight to requests requiring more bandwidth. This model allows for the dynamic adjustment of priorities through a new cost function formulation, offering flexibility to adapt resource allocation based on the network's specific conditions and needs. By giving higher priority to critical requests, such as those with high bandwidth demands, the efficiency of resource usage is enhanced, maximizing network performance. The system's reconfigurability facilitates prioritizing different types of traffic based on their importance, such as mission-critical traffic or low-latency services, enabling more effective adaptation to the varying demands of each scenario. This optimizes the real-time allocation and distribution of bandwidth, as demonstrated in Equation (15). The new cost equation is formulated by multiplying the constraint matrix by a vector called \"\(V_{p}\)\". \[f_{o}=\sum_{k}\sum_{m}\sum_{\omega}x_{kmu\omega}\cdot pp_{\omega}+\sum_{\omega} t_{k\omega}\cdot V_{p} \tag{15}\]  
Instead of simply multiplying by a constant weight of 100 (as seen in Equation (4)), a new approach was introduced using a weight vector that combines 80% bandwidth and 20% distance, as detailed in Equation (16). This adjustment places greater emphasis on users requiring more bandwidth, ensuring that a 500 GHz request, for instance, is prioritized over a 20 GHz request, thus optimizing resource allocation efficiency. These values are based on Ref. [19], which prioritizes bandwidth as the primary objective to maximize in this process. Assigning an 80% weight to bandwidth emphasizes its critical importance in the allocation process. A lower weight would reduce its significance, potentially leading to suboptimal allocation. However, increasing this weight further could overlook other essential factors, such as transmission distance. This balance is crucial to prevent misallocating longer-range wavelengths to shorter connections, which would reduce their availability for clients requiring extended reach. The weighted approach ensures that both bandwidth and spacing within the frequency comb are adequately prioritized, aligning with the network's multi-level structure. \[V_{p}=0.8[\text{Bandwidth}]+0.2\ [distance] \tag{16}\]  
As shown in Figure 5, the proposed approach significantly improves the BBR, consistently keeping it below 1 across all scenarios. The highest BBR values are highlighted with ellipses to indicate critical points. Additionally, a red line marks the point at around 170 requests, where the allocation method begins to show a decline, leading to an increase in the BBR. This represents a significant improvement over previous models, ensuring a good Quality of Service (QoS). For requests requiring the maximum bandwidth, the BBR remains below 0.8, indicating a substantial improvement in resource use efficiency.