Spectrum Allocation Using Integer Linear Programming and Kerr Optical Frequency Combs

Abstract

The rapid increase in Internet usage has led to a growing demand for bandwidth. Optical microring resonators (MRRs) are emerging as a promising solution to meet this need. MRRs generate optical frequency combs (OFCs) that provide multiple wavelengths with high phase coherence, enabling communication via wavelength division multiplexing (WDM). Spectrum allocation methods, such as the Routing, Modulation Level, and Spectrum Assignment (RMLSA) approach, play a crucial role in executing this strategy efficiently. While current algorithms have improved allocation efficiency, further development is necessary to optimize network performance. This paper presents an integer linear programming (ILP)-based method for network resource allocation, aiming to maximize the number request and the bandwidth assigned to each. The proposed approach offers a flexible cost function that prioritizes system constraints such as transmission distance and bandwidth requirements, resulting in significant improvements to the bandwidth blocking rate (BBR). By integrating multilevel modulation and using wavelengths generated by MRRs, this method efficiently handles up to 1075 requests, achieving a BBR of zero. This dynamic and adaptable allocation strategy ensures optimal resource utilization, enhancing overall network performance.

1. Introduction

The implementation of technologies such as the Internet of Things (IoT), artificial intelligence, and high-performance computing has exponentially increased bandwidth demand, which is critical in optical networks, particularly in passive optical networks (PON). In this context, networks using wavelength division multiplexing (WDM-PON) provide a viable solution to enhance transmission capacity. WDM-PON networks offer significant advantages in meeting quality of service (QoS) standards [1], enabling the simultaneous transmission of multiple optical signals over different wavelengths on a single optical fiber. However, their implementation faces economic challenges due to the requirement of installing a laser for each wavelength and achieving phase synchronization. Optical frequency combs (OFCs) present a promising solution, as they are light sources with equally spaced, phase-coherent frequency lines.

In recent years, numerous cutting-edge methods for generating optical frequency combs (OFCs) have made substantial progress, improving their efficiency and expanding their applicability across various fields. One prominent approach is gain modulation in semiconductor lasers, noted for its simplicity and low cost [2]. This technique leverages the dependence of a semiconductor laser’s optical gain on the charge carrier density in its active region. By injecting a variable electric current, the carrier density is altered, which in turn modifies the optical gain, resulting in intensity modulation of the emitted light [3]. Another relevant technique is the use of microcavities, which exploit the interactions between light and mechanical vibrations to produce frequency combs with adjustable bandwidths [4,5,6].

Electro-optic modulation using Mach–Zehnder devices generates optical frequency combs (OFCs) by inducing periodic phase shifts in a continuous-wave laser. This process leads to the formation of evenly spaced spectral lines resulting from interference effects between two optical paths. However, a key limitation of this approach is its significant sensitivity to temperature variations and electrical instabilities, which can introduce unwanted distortions in the generated comb and consequently limit the system’s stability and overall performance [7]. On the other hand, optical microresonators have demonstrated improved power conversion efficiency, making them suitable for large-scale optical systems and supporting transmission speeds of up to 1.84 Pbit/s [5,6,7,8,9]. Additionally, while some advanced approaches combine both techniques to leverage their respective advantages, these hybrid solutions often come at a higher cost. This approach introduces greater complexity and operational costs due to the need for external signals and additional control variables, which can increase energy consumption and phase noise. In contrast, Kerr-based microresonator OFCs offer distinct advantages, such as lower manufacturing costs and operational simplicity. These combs generate a broad and stable spectrum without external modulating sources, which reduces system complexity and noise levels. This is crucial for telecommunications applications that require precision and stability. Furthermore, Kerr-based OFCs have strong potential to dominate OFC generation methods due to their efficiency, robustness, and scalability. Their compatibility with silicon photonics allows for miniaturization and cost-effective manufacturing, making them an attractive option for applications aiming to maximize integration without significantly altering existing network infrastructures [9,10].

A critical challenge in spectrum allocation lies in the availability and efficient management of carriers. In this context, optical frequency combs (OFCs) based on Kerr solitons, generated through microring resonators (MRRs) made from nonlinear materials like silicon nitride, have emerged as a promising solution. This technique enables the generation of equally spaced frequency lines, stabilized by auxiliary pumping and phase locking, ensuring the spectral coherence required for high-capacity optical communication networks [1]. These systems have demonstrated transmission speeds of up to 44.2 Tb/s on a single chip, highlighting their potential for large bandwidth applications [2,11].

Despite recent advancements, spectrum allocation in wavelength division multiplexing (WDM) systems continues to face significant challenges. The most common spectrum allocation methods include heuristic approaches, such as First Fit and Best Fit, which aim to minimize spectrum occupation by assigning carriers efficiently. Additionally, optimization techniques like Mixed-Integer Linear Programming (MILP) and genetic algorithms are employed to enhance spectral efficiency, reduce processing times, and improve overall network performance [12,13]. These algorithms often struggle to adapt to the point-to-multipoint structure and variable distances characteristic of PONs, which increases the computational burden [13].

One of the most common and promising methods to address the challenges of spectrum allocation in optical networks is the Routing, Modulation Level, and Spectrum Assignment (RMLSA) algorithm. This algorithm dynamically optimizes routing, modulation levels, and spectrum allocation based on transmission parameters such as distance and bandwidth requirements [14,15,16,17,18]. RMLSA is particularly effective in access networks like PONs, where the ability to adjust wavelengths and modulation levels dynamically according to the distance between the central node and the users is critical. However, despite its effectiveness, the high computational cost associated with RMLSA presents a significant challenge, especially in large-scale implementations. This has led to the exploration of more efficient solutions, such as the use of hardware acceleration techniques, including GPUs and FPGAs, to reduce processing delays. Furthermore, the implementation of OFCs in optical networks faces limitations due to the uneven distribution of carrier power, which affects the optical signal-to-noise ratio (OSNR) and complicates data transmission. Ensuring optimal transmission often requires additional optical processing, which increases both technical and economic costs. Heuristic techniques used in RMLSA also require further refinement, particularly in the context of optical MRRs. For instance, many existing methods fail to account for the sech² profile of frequency combs, reducing their efficiency in spectrum allocation. An alternative approach proposed by [19] introduces a photonic design that integrates MRRs, considering constraints such as comb shape, request distance, and multi-level modulation. Although this approach improves spectrum allocation, the proposed heuristic algorithm does not fully optimize spectrum usage or the number of requests served, highlighting the need for more advanced optimization techniques to achieve more robust and efficient allocation.

This article proposes a methodology that employs a constrained optimization approach to enhance bandwidth allocation in frequency comb systems generated by MRRs. The objective is to maximize assigned bandwidth and increase the number of requests served, thereby reducing the bandwidth blocking rate (BBR).

2. Materials and Methods

This work proposes a spectrum allocation method based on constrained optimization using Integer Linear Programming (ILP), referred to as RMLSA-ILP-OFC, to maximize the amount of allocated spectrum. This approach utilizes the optical network proposed in [19], which employs optical microresonators of 113 µm and 450 µm to achieve optical frequency combs (OFCs) with free spectral ranges (FSRs) of 12.5 GHz, 50 GHz, 100 GHz, and 200 GHz, in compliance with the International Telecommunication Union (ITU) recommendations. Although this methodology is proposed, it can be easily reconfigured to use other types of optical sources, such as electro-optic modulators, semiconductor lasers, or gain-modulated microcavities. This flexibility is due to the approach’s consideration of key physical characteristics like transmission distance, Optical Signal-to-Noise Ratio (OSNR), and frequency spacing. These features make it compatible with various Wavelength Division Multiplexing (WDM) sources, allowing the network to adapt seamlessly to the needs of operators and existing infrastructure, ensuring a scalable and future-proof design.

We use a programmable pulse shaper to physically assign one or more wavelengths, following the instructions of the ILP algorithm. This algorithm adjusts the modulation level in QAM multilevel modulators to optimize performance based on link characteristics, such as transmission distance. The ILP approach ensures efficient wavelength allocation tailored to the specific requirements of the network request. This algorithm plays a central role in dynamic spectrum management, allowing the adaptation of carriers based on transmission distance and bandwidth demands, ensuring efficient use of the available spectrum, and enabling the creation of a flexible network that adapts to changes in bandwidth and transmission distance.

Figure 1 shows the topology of the proposed network. It is important to highlight that the pulse shaper can assign an individual wavelength or a range of them in the case of a super-channel, enabling the creation of a flexible grid, a fundamental aspect of our methodology.

To generate the OFCs with the proposed spacings, we use two structures based on MRRs and the configuration from [19]. The first structure uses four MRRs with an FSR of 50 GHz, where thermal control adjusts the position of the OFCs to obtain a new FSR of 12.5 GHz. The optical combs generated by the rings are combined using an interleaver, forming a final optical comb with the desired specifications. On the other hand, the second structure uses two MRRs with a free spectral range (FSR) of 200 GHz and follows the same approach to achieve a final line spacing of 100 GHz. Figure 2 shows the schematic of these MRRs.

To obtain the optical signal from the microresonators, we utilize the Lugiato–Lefever Equation (LLE) as proposed in [19], because it allows us to simulate the optical generation of frequency combs based on intrinsic characteristics, such as the Kerr coefficient and the loss coefficient of the MRR.

The Lugiato–Lefever equation (LLE) is defined as follows:

$$t_R{\displaystyle \frac{\partial E\left(t,\tau \right)}{\partial t}}=\left[-\alpha -i{\delta }_0+iL{\sum }_{k\ge 2}{\displaystyle \frac{{\beta }_k}{k!}}{\left(i{\displaystyle \frac{\partial }{\partial \tau }}\right)}^k+i\gamma L{\left|E\right|}^2\right]E+\sqrt{\theta }{E}_{in}$$

(1)

where ${\delta }_0$ represents the laser detuning and $E_{\mathrm{in}}$ is the pump field. To solve this equation numerically, we employ the split-step Fourier method. It is important to emphasize that the pump power and detuning are normalized (see Equations (2) and (3) below).

$$∆={\delta }_0/\alpha$$

(2)

$$S=E_{in}\sqrt{\gamma L\theta /{\alpha }^3}$$

(3)

To carry out the spectrum allocation process, we propose an ILP algorithm. This approach prioritizes customer allocation using the cost equation outlined in (4).

$$\max f_o={\sum }_k{\sum }_m{\sum }_{\omega }{x}_{km\omega } · {pp}_{\omega }+{\sum }_{\omega }{t}_{k\omega } · 100$$

(4)

where $k$ represents the required requests, $m$ represents the available channels for allocation, and $\omega$ denotes the modulation for transmission and reception (QAM, 8-QAM, and 16-QAM). $p{p}_{\omega }$ is a prioritization variable determining the weight of each request depending on the modulation. The binary variable $x_{km\omega }$ controls the allocation of channels to a specific client, while the binary control variable $t_{k\omega }$ identifies active users in the allocation process. To prioritize the maximum number of requests effectively, a weight of 100 is assigned to $t_{k\omega }$. This approach ensures that the system prioritizes user requests over bandwidth in the allocation process. The number 100 was chosen because it is sufficiently large to assign significant weight to each user in the cost function. A smaller number might not effectively prioritize users, potentially reducing the number of clients allocated, while a larger number would have a similar effect on the cost function. Essentially, when a client is not allocated, they receive a penalty of 100 to reinforce the prioritization in allocation. The model includes nine constraints regulating the system’s operations.

These constraints aim to assign one channel for each request (Equation (5)), ensure only one modulation for a channel (Equation (6)), ensure only one modulation for a request (Equation (7)), guarantee the required bandwidth for modulation (Equation (8)), and ensure the channel meets the required distance $d_k$ for the request and $P_{\omega m}$. It ensures that the allocation of a channel and a modulation does not exceed the maximum capacity of distance for each modulation (Equation (9)), ensures the required lines $n_k$ for a request are obtained (Equation (10)), checks for consecutively assigned channels (Equation (11)), limits one modulation per user (Equation (12)), and ensures continuity in the assignment for a request requiring multiple channels (Equation (13)). Here, $y_p$ and $y_n$ represent the rising and falling edges, respectively. If the channel is contiguous, it should have only two edges. Please refer to

Table 1. Restrictions cost function.

Restrictions Cost Function
${\sum }_k{x}_{km\omega }\le 1$	(5)
${\sum }_{\omega }{x}_{km\omega }\le 1$	(6)
${\sum }_k{\sum }_w{x}_{km\omega } \le 1$	(7)
${\sum }_m{x}_{km\omega }=n_{\omega k}\ast t_{k\omega }$	(8)
$d_k{x}_{km\omega } \le P_{\omega m}$	(9)
${\sum }_m{\sum }_{\omega }{x}_{km\omega }\le {\sum }_k{n}_{k\omega }-1$	(10)
$x_{km\omega }-x_{k\left(m-1\right)\omega }=y_{p}km\omega -y_{n}km\omega$	(11)
${\sum }_{\omega }{t}_{k\omega }\le 1$	(12)
${\sum }_m{y}_{p}km\omega +y_{n}km\omega \le 2$	(13)

for the constraint equations.

3. Results and Discussion

To validate the proposed method, we established a reduced allocation scenario that allows us to test the assignment. This scenario can be visually verified; we anticipate that the algorithm will identify this solution. The number of lines or carriers is calculated based on the bandwidth required by each request.

Table 2. Case study of assignment requests.

Request	Distance (km)	BW (Gbit/s)	Lines
			16-QAM	32-QAM	64-QAM
U1	7	215	3	3	3
U2	5	38	1	1	1
U3	4	8	1	1	1
U4	5	234	3	3	3
U5	9	177	3	3	3
U6	8	176	3	3	3
U7	7	36	1	1	1
U8	3	174	3	3	3
U9	2	12	1	1	1
U10	8	26	1	1	1

details the characteristics of each client involved in the allocation scenario, including their distance in kilometers and bandwidth in Gbit/s. Additionally, the lines used are specified by modulation, with options for 16-QAM, 32-QAM, and 64-QAM, along with the number of carriers required according to the proposed multilevel QAM modulation format. A bit error rate (BER) of 0.7 × 10⁻⁹ was set to impose a more stringent requirement. By using a lower BER threshold, we aimed to rigorously evaluate the performance, ensuring that the methodology is robust. This format provides flexibility in modulation levels, allowing various bandwidth options to be tailored to transmission distances.

Figure 3 illustrates the allocation results. It can be observed that the proposed method assigns each client a modulation format that ensures the transmission distance while requiring the fewest possible carriers. The circles represent the distance limit, and no request exceeds this limit. Additionally, it is noteworthy that four client requests use super-channels to accommodate the modulation, and their allocation is contiguous to ensure the required bandwidth separation. Each user is assigned a different color in the figure to facilitate visualization. These observations support the conclusion that the method correctly allocates the requests and adapts to different types of demands.

We propose conducting tests in real network scenarios tailored to typical passive optical network (PON) situations, as validating the performance of the spectrum allocation algorithm in a practical environment is essential for assessing the network’s operational capabilities. Creating a simulated database is a useful tool for modeling various bandwidth demands, such as the distance of end users to the central office, the number of subscribers, and the required transmission speeds. Testing in real environments allows for observing the system’s behavior under different load conditions, the interaction between network modules, and the algorithm’s ability to efficiently adapt to users’ dynamic demands. This approach also facilitates the fine-tuning and refinement of the algorithm, improving its robustness and reliability, ensuring effective spectrum optimization, and meeting quality-of-service requirements under real operational conditions.

To complement this approach, we utilized the database proposed in [19], which includes network scenarios where key parameters such as the number of requests, their distance from the central office, and the required network speed vary randomly. In these scenarios, the number of requests ranges from [1, 200], the distance (in kilometers) ranges from [1, 80], and the transmission speed (in Gbit/s) ranges from [1, 250], with a uniform distribution. This type of distribution ensures that each value within the defined ranges has the same probability of occurring, providing an equitable representation of various network conditions.

By varying these parameters with discrete uniform distributions, we effectively model a wide range of demands and operational scenarios for PON networks, simulating both current and future conditions in terms of bandwidth requirements. The selection of these ranges is based on the typical operational characteristics of PON networks and projections of future bandwidth demand growth.

We propose the BBR as a key metric to validate the performance of our resource allocation method in optical networks. The BBR quantifies the likelihood that the network rejects requests when the required bandwidth exceeds the available resources, enabling us to evaluate the network’s capacity to meet demand without overloading its capabilities. To calculate the BBR, we analyze the ratio between the total rejected bandwidth and the total requested bandwidth, which helps identify bottlenecks and optimize network performance. By considering both the number of rejections, the number of requests, and the requested bandwidth, this metric provides a comprehensive view of resource management efficiency, which is crucial to ensure the network can adapt to growing traffic demands without compromising service quality. Equation (14) details the mathematical model used to calculate the BBR.

$$BBR={\sum }_{i=1}^N{\displaystyle \frac{BW{R}_i}{BW{S}_i}}$$

(14)

In Equation (14), BWR represents the total rejected bandwidth, and BWS represents the total requested bandwidth. These metrics allow us to verify the network’s performance. Figure 4 presents a three-dimensional graphical representation where the Y-axis corresponds to the bandwidth, the X-axis represents the number of requests, and the Z-axis illustrates the BBR index. This visualization enhances our understanding of the system’s performance by showing how the BBR varies depending on bandwidth and the number of requests.

The proposed method was evaluated across 1400 request scenarios to analyze network performance and calculate the Blocking to Bandwidth Ratio (BBR). The results demonstrated the method’s effectiveness, as most requests exhibited low blocking probabilities. Figure 4 illustrates the BBR performance in relation to bandwidth and the number of clients, showing that the method performs adequately up to 110 clients, achieving up to 15 THz of simultaneous bandwidth utilization.

Figure 4 also highlights scenarios where the BBR exceeds a value of 1, reaching up to 1.8. These scenarios are marked with ellipses indicating the highest rejection values, depicted in yellow and green. A dashed line marks the point, around 110 requests, where the allocation method begins to deteriorate, leading to a noticeable rise in the BBR. From this point onward, bandwidth rejections increase significantly, with maximum values occurring as the number of clients continues to grow. The rise in BBR between 110 and 200 clients is attributed to limitations in the number of available carriers. 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 “$V_P$”.

$$f_o={\sum }_k{\sum }_m{\sum }_{\omega }{x}_{km\omega } · {pp}_{\omega }+{\sum }_{\omega }{t}_{k\omega } · V_P$$

(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.

$$V_P=0.8\left[\mathrm{B}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}\right]+0.2 \left[distance\right]$$

(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. 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.

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. Comparative computation times.

Request Number	Method FF	Method RWA	RMLSA-OFC	Proposed Method
	t (s)	t (s)	t (s)	t (s)
1	1.042 s	1.054 s	1.06 s	12.123 s
5	1.101 s	1.215 s	1.281 s	42.236 s
10	1.153 s	1.187 s	1.333 s	80.743 s
50	1.823 s	1.985 s	2.005 s	314.806 s
100	2.131 s	2.412 s	2.311 s	651.475 s
500	6.073 s	6.150 s	6.254 s	3589.276 s
1000	9.241 s	9.298 s	9.420 s	7371.629 s
1400	12.024 s	12.098 s	12.208 s	6621.625 s

, 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. While the execution times for the proposed method are longer, this is attributable to the exploration of multiple dimensions, including client requirements, modulation formats, and available OFC channels, resulting in a more complex three-dimensional problem. It is worth noting that heuristic methods like FF, RWA, and RMLSA-OFC achieve faster performance; however, our approach excels at effectively managing a significantly larger number of client requests. For instance, with 1000 requests, the FF method processes in 9.24 s, whereas the proposed method requires approximately 122.86 min. This additional computational effort, however, results in superior network optimization, enabling more efficient resource allocation and significantly reducing blocking probability, thereby enhancing Quality of Service (QoS).

To mitigate the longer execution times, future work could explore hardware acceleration techniques such as GPUs or FPGAs, which can substantially improve processing speeds given the three-dimensional array structure of the algorithm. Additionally, these tests were conducted on a system with 8 GB of RAM and a four-core 64-bit CPU with SSE2 support, which inevitably impacts execution times. Upgrading the hardware infrastructure could further enhance performance without compromising the achieved improvements.

Although the proposed method is computationally intensive, its ability to effectively manage a higher number of clients per request makes the effort worthwhile, as it leads to significant improvements in service quality.

4. Conclusions

This paper presents an innovative methodology for resource allocation in optical communication networks, highlighting its ability to prioritize multiple objectives, such as maximizing both the number of requests served and the bandwidth assigned to each. The approach not only considers typical system constraints, such as channel capacity and transmission distances but also adapts to the characteristics of the optical MRR and the sech² spectral profile of the MRR. This adaptation is crucial as it allows the integration of spectrum allocation algorithms with the generation of optical frequency combs (OFCs) using MRR, ensuring efficient and optimal allocation of available spectral resources. In this way, the methodology enhances overall network performance, adapting to the specific needs of each operational scenario.

The proposed method demonstrates great adaptability by being applicable to any type of optical frequency comb, regardless of the technology used. This is due to the approach’s ability to consider key characteristics such as power, optical signal-to-noise ratio (OSNR), and other relevant factors, irrespective of the comb’s structure—whether it is a DKS or a constant-line comb. We did not just create an allocation method for a specific comb; we developed a versatile approach that can be applied to various technologies. This adaptability is enabled by cost function constraints that ensure precise and efficient allocation.

The flexibility of the cost function is one of our most important achievements, as it allows us to prioritize either bandwidth or distance based on the scenario’s needs, enhancing the network’s adaptability and efficiency. The use of multilevel modulation formats and wavelengths generated by optical microresonators further strengthens the system’s ability to effectively adjust to different bandwidth demands.

Although the method has a high computational cost, some techniques can speed up the algorithm and reduce this cost, which would significantly increase performance and efficiency in PON networks. The proposed methodology integrates dynamic spectrum allocation with an RMSLA-WDM approach, based on ILP, contributing to the improvement of the BBR index and optimizing the use of available network resources.

This work highlights the relevance of ILP techniques in the optimization of advanced optical communication systems and lays the groundwork for future research aimed at improving their real-time feasibility.