# Spectrum Allocation Using Integer Linear Programming and Kerr Optical Frequency Combs
## 3 Results and Discussion
These results confirm that the strategy of assigning higher weights to request with greater bandwidth demands contributes to more efficient allocation, optimizing overall network performance. Furthermore, the model's ability to efficiently manage a high percentage of requests reaffirms the suitability of the proposed approach, demonstrating its effectiveness in handling various network scenarios with precision and flexibility. To compare the proposed method with widely used state-of-the-art allocation methods, three approaches were considered: the RMLSA-OFC method [19], the First Fit (FF) algorithm, and the Random Wavelength Assignment (RWA) algorithm [20; 21]. The method in [19] employs a heuristic algorithm for allocation using optical frequency combs (OFCs). In contrast, the FF method sequentially assigns resources by selecting the first available carrier that meets the bandwidth requirement, while the RWA method allocates wavelengths in a random manner, ensuring that each selected wavelength satisfies the transmission requirements. Figure 6 demonstrates that the method proposed in [19] can effectively allocate up to 110 requests with a low BBR, reaching a maximum value of 1.5. This indicates a lower performance compared to our method (see Figure 5). The ellipses in Figure 6 highlight regions with the highest BBR values, marking critical performance areas. A dashed line indicates the threshold at approximately 110 requests, beyond which the allocation method's performance declines as the number of requests increases. This visual representation emphasizes the system's limitations under higher demand. In contrast, our approach maintains effective allocation up to 170 requests, showing a clear difference of 60 clients. When comparing the results of our RMLSA-ILP-OFC approach to those of the FF method (see Figure 7), a marked increase in the Blocking-to-Bandwidth Ratio (BBR) is observed, with rejections exceeding 1 in several instances (marked in yellow and light blue). The BBR values, ranging from 1.5 to 3.0 (highlighted with red ellipses), indicate critical points that significantly affect Quality of Service (QoS). Additionally, the allocation method begins to fail at approximately 105 requests (red dotted line), leading to a sharp rise in BBR. These findings underscore the limitations of the FF method, which struggles to manage bandwidth efficiently under high-demand scenarios, highlighting the need for more robust solutions. Our approach demonstrates its superiority by maintaining resource allocations effectively up to 170 requests. Figure 5: Number of rejections vs. bandwidth and number of requests with weight vector (\(V_{p}\)). The highest BBR values are highlighted with red ellipses, indicating critical points in the analysis. Additionally, a dotted red line marks the point where the allocation method begins to show a decline. The analysis of established methods from the literature, such as the RWA approach (see Figure 8), also reveals a significant increase in the BBR. The highest values, ranging from 1.8 to 3.0 (marked in yellow and green), are highlighted with red ellipses, indicating critical points that are detrimental to maintaining a good Quality of Service (QoS). Additionally, a red line marks the threshold at around 85 requests, where the allocation method begins to deteriorate, leading to a noticeable increase in BBR. These findings underscore the need for more efficient strategies capable of managing bandwidth effectively under high-demand conditions, which is a key strength of the proposed approach. An additional key assessment involves analyzing the computation time required by each of the proposed methods. To conduct this analysis, varying numbers of requests were processed using the evaluated methods, and their execution times were recorded to examine the computational cost of each approach. As shown in Table 3, the First Fit (FF) method demonstrates lower computational costs compared to the proposed approach, primarily due to the high dimensionality considered in our cost function.