Network resource allocation method considering risk avoidance in survivable space division multiplexing elastic optical network

Abstract

The invention relates to a network resource allocation method considering risk avoidance in a survivable space division multiplexing elastic optical network, belongs to the technical field of communication, and aims to solve the problems of low spectrum utilization rate, long fault recovery time and insufficient inter-core crosstalk suppression of a traditional method. According to the technical scheme, the method comprises the following steps: constructing a hybrid protection mechanism in which a dedicated path and a shared backup path are coordinated, optimizing routing, fiber core and spectrum allocation based on an integer linear programming model, and implementing a trusted service cross-core isolation strategy and a fault domain separation algorithm. The method has the technical effects that the utilization rate of network resources is improved through compact spectrum allocation and shared resource multiplexing, the fault recovery reliability is enhanced by adopting path physical isolation and a dynamic degradation mechanism, and the transmission quality degradation is inhibited in combination with crosstalk perception and modulation format adaptation, so that high-safety elastic optical network resource management is realized.

Description

Technical Field

[0001] The present invention belongs to the field of communication technologies and relates to a network resource allocation method considering risk aversion in a survivable space-division multiplexing elastic optical network. Background Art

[0002] With the rapid development of bandwidth-intensive applications such as big data, cloud computing, generative large models, the Internet of Things, and the 5th generation mobile network, the overall Internet traffic is expected to grow exponentially. This trend poses higher requirements for the capacity and flexibility of fiber optic communication networks. Traditional wavelength-division multiplexing networks have difficulty meeting the current dynamic and diverse bandwidth demands due to using a fixed 50 GHz grid for spectrum allocation. Elastic Optical Networks (EONs) have become a key technology for the next-generation optical networks with their flexible spectrum allocation method. EONs achieve efficient utilization of spectrum resources by dynamically selecting adaptive modulation formats and using fine-grained grids (such as 12.5 GHz or 6.25 GHz). However, as the network capacity demand further grows, the capacity of a single-core EON gradually approaches saturation, and the research direction has started to turn to exploring the spatial dimension of optical fibers. Space Division Multiplexing (SDM) technology provides new possibilities for large-scale data transmission by introducing multiple independent optical cores (Multi-Core Fiber, MCF) or multiple transmission modes in a single optical fiber. In particular, MCF-based SDM-EON has become the most promising implementation due to its advantages in enhancing transmission capacity and suppressing inter-core crosstalk. MCF integrates multiple independent optical cores in the fiber cladding, enabling each core to carry an independent optical signal, thereby achieving higher transmission capacity. In addition, MCF can share spectrum resources among multiple cores, relaxing the spectrum continuity constraint in single-core fiber transmission.

[0003] Although MCF-based SDM-EON technology significantly improves the network capacity and resource utilization efficiency, its inherent inter-core crosstalk problem remains an important challenge to be solved. When traffic requests on adjacent cores use the same frequency slot, it will cause inter-core crosstalk, thereby significantly reducing the transmission quality. This phenomenon not only poses a threat to the transmission quality but may also trigger more serious security risks. Inter-core crosstalk may be maliciously exploited to carry out attacks. For example, an attacker can initiate high-power interference through inter-core crosstalk, causing the interruption of high-speed data transmission, or eavesdrop on the data content of other traffic requests by using inter-core crosstalk. These security risks pose higher requirements for the stability and reliability of optical networks.

[0004] In SDM-EON, resource allocation not only involves routing and spectrum assignment, but also needs to consider core allocation issues, forming the problem of Routing, Modulation Level, Core, and Spectrum Assignment (RMLCSA). Although SDM-EON technology has significantly improved network capacity, network failure problems are still challenges that cannot be ignored. For example, faults such as fiber breaks may cause services on multiple cores to be interrupted simultaneously, seriously affecting the stability and reliability of the network. Traditional protection technologies such as Dedicated Path Protection (DPP) and Shared Backup Path Protection (SBPP) have played important roles in enhancing network survivability. DPP provides the highest level of protection, but its resource overhead is high; while SBPP effectively improves resource utilization efficiency by allowing multiple services to share backup paths.

[0005] In order to restore the communication of service requests when network links fail and meet the diverse survivability requirements of service requests, that is, using dedicated path protection or shared backup path protection schemes for the requirements of service requests in the same network, additional network resources need to be allocated for backup paths to ensure the survivability of the space-division multiplexing elastic optical network. Then, due to the limited bandwidth resources of the network, an RMLSCA strategy that supports a hybrid protection scheme of dedicated and shared paths and considers risk avoidance is particularly important, which can improve spectrum utilization efficiency, reduce network blocking rate, and thus enhance the reliability and survivability of the network. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide a network resource allocation method considering risk aversion in a survivable space-division multiplexing elastic optical network.

[0007] To achieve the above purpose, the present invention provides the following technical solutions:

[0008] A network resource allocation method considering risk aversion in a survivable space-division multiplexing elastic optical network. This method first describes the resource allocation problem of adopting different protection schemes for requests of different survivability requirement types in the space-division multiplexing elastic optical network as an integer linear programming model, and based on the integer linear programming model, the following steps are carried out:

[0009] S1. Sort all service requests from large to small according to the bandwidth rate of the service requests;

[0010] S2. In the sorted order, search for K shortest paths between the source node and the destination node for the service requests that have not been allocated spectrum resources as the working path set, and determine the minimum feasible modulation format with the least number of frequency slots used for each path in the set;

[0011] S3. Obtain each available core spectrum block on each working path. If there is no available spectrum block, block the request;

[0012] S4. Calculate the weight of each available core spectrum block according to the working path core spectrum weight calculation formulas for trusted services and untrusted services;

[0013] S5. Select the link, core, and spectrum combination with the minimum weight as the working interval for the service request;

[0014] S6. Check whether the selected working path resource allocation scheme meets the crosstalk threshold requirement. If it does not meet the requirement, perform crosstalk degradation until a combination that meets the threshold requirement is selected as the final working path resource allocation scheme, or mark the request as blocked.

[0015] S7. Search for K shortest paths between the source node and the destination node for the service request that have no common links with the working paths as the alternative protection path set, and determine the minimum feasible modulation format with the least number of frequency slots used for each path in the set;

[0016] S8. Obtain each available core spectrum block on each protection path. If there is no available spectrum block, block the request;

[0017] S9. Calculate the weight of each available core spectrum block according to the protection path core spectrum weight calculation formulas for trusted services and untrusted services;

[0018] S10. Select the link, core, and spectrum combination with the minimum weight as the protection interval for the service request;

[0019] S11. Check whether the selected protection path resource allocation scheme meets the crosstalk threshold requirement. If it does not meet the requirement, perform crosstalk degradation until a combination that meets the threshold requirement is selected as the final protection path resource allocation scheme, or mark the request as blocked.

[0020] S12. Allocate the link, core spectrum resources of the network for the request according to the determined working interval and protection interval in S6 and S11, and update the network status information; if there are still requests that have not been allocated resources, return to S2 to continue allocating resources for the next request; if all requests have been allocated resources, calculate the blocking rate, network resource utilization rate, average number of frequency slot sharing times, number of fragments, and average crosstalk amount of frequency slots.

[0021] Furthermore, in the network model constructed by the method, the undirected graph G(N, L) is defined as the network topology of the SDM-EON. N is a set of optical switching nodes, denoted as N = {n1, n2,..., n |N|}, and L is a set of optical fiber links, denoted as L = {l1, l2,..., l |L|}. Each optical fiber link consists of a set of cores C, denoted as C = {c1, c2,..., c |C|}. The spectrum of each core is divided into frequency slots of 12.5 GHz. F = {f1, f2,..., f |F|} is a set of available frequency slots. Moreover, |N|, |L|, |C|, and |F| represent the number of optical switching nodes, the number of optical fiber links, the number of cores, and the number of available frequency slots in the SDM-EON, respectively.

[0022] Furthermore, in the service request model of the method, the service request set is denoted as R. Each service request in R can be represented as r(s r , d r , λ r , σ r , γ r ). Among them, s r and d r represent the source node and the destination node of the request, respectively. λ r represents the bandwidth rate of the service request. σ r is a binary variable indicating which protection scheme the request uses. Specifically, σ r = 1 represents the DPP scheme, while σ r = 0 represents the SBPP scheme. γ r is a binary variable indicating whether the request is trustworthy. Specifically, γ r = 1 indicates that the request is trustworthy and the crosstalk-aware scheme is used, and γ r = 0 indicates that the request is untrustworthy and the crosstalk avoidance scheme is used.

[0023] Furthermore, since the optical fiber is multi-core, crosstalk between adjacent cores should be considered when allocating resources. In the crosstalk model of the method, the crosstalk between two adjacent active cores c and c adj on the same frequency slot f of the link l is calculated using formula (1), where the length of the link l is denoted as L(l), and h is regarded as the power coupling coefficient, which is a function of different parameters of the optical fiber, such as the propagation constant, the coupling coefficient, the core pitch, and the bending radius.

[0024]

[0025] If the fiber cores are evenly distributed on the same link and the distances between all fiber cores are the same, then the crosstalk magnitude of a frequency slot on link l is only related to the link distance. It represents the crosstalk magnitude when one frequency slot on link l overlaps with another, as shown below:

[0026]

[0027] Then, sum up the crosstalk of all adjacent cores of fiber core c to calculate the total crosstalk of the frequency slot on the link, as shown below:

[0028]

[0029] Where is a binary variable. When the f-th frequency slot of request r in fiber core c on link l and the frequency slot at the corresponding position of its adjacent fiber core c adj have been occupied by other service requests, the value of this variable is 1; otherwise, the value is 0.

[0030] Furthermore, to determine the end-to-end crosstalk EEXT(f) of the frequency slot on the path, sum up the total crosstalk of the frequency slot on all links of the path as follows:

[0031]

[0032] Furthermore, the ultimate optimization objective of the integer linear programming model is:

[0033]

[0034] Where and are boolean variables. If the f-th frequency slot in fiber core c on the working path or protection path of request r overlaps with the frequency slot of its adjacent core fiber, then or has a value of 1. and are boolean variables. If the working path or protection path of request r occupies the f-th frequency slot in fiber core c on link l, then or has a value of 1. φ l,c,f is a boolean variable. If the f-th frequency slot in fiber core c on link l of the request is used, then φ l,c,f has a value of 1. α and β are parameters used to adjust the weights of the optimization objective. w and b are subscripts of variables used to distinguish the working path and the protection path.

[0035] 1) To ensure that each request is assigned a working path and a protection path, and a modulation format is assigned to each path, set the following constraints:

[0036]

[0037] wherein and are Boolean variables. If the working path or protection path selected by request r is candidate path k and the modulation format is m, then or has a value of 1.

[0038] 2) To clarify the links included in the requested working path and protection path, the following constraints are set:

[0039]

[0040] wherein and are Boolean variables. If the working path or protection path selected by request r includes link l, then or has a value of 1. and are Boolean variables used to indicate whether candidate working path or candidate protection path k includes link l. If it includes, then or has a value of 1;

[0041] 3) To avoid having common links between the working path and protection path selected by the same request, it is necessary to ensure that the selected working path and protection path are within the same pair of candidate paths. The constraint is set as:

[0042]

[0043] 4) To ensure that each link in the requested working path and protection path selects a fiber core, the constraint is set as:

[0044]

[0045] wherein and are Boolean variables. If request r selects fiber core c on working or protection link l, then or has a value of 1.

[0046] 5) To ensure traffic balance at each node, that is, to maintain conservation between the total traffic entering the node and the total traffic leaving the node, the constraint is set as:

[0047]

[0048] where n r,w and n r,bInteger variables representing the number of frequency slots required for the selected working path and protection path respectively, whose values are determined by the modulation format selected for the working path and protection path. If the core c on the working or protection link l is selected for request r, then or has a value of 1.

[0049] 6) To ensure that the frequency slots occupied by the request meet the spectrum continuity requirements of the elastic optical network, the constraint is set as:

[0050]

[0051] where and represent the starting frequency slot indices of the working path and protection path of the request respectively.

[0052] 7) To ensure that the frequency slots occupied by the request do not exceed the capacity limit of the link, the constraint is set as:

[0053]

[0054] 8) To ensure that the frequency slots occupied by the request meet the spectrum non - overlapping requirements of the elastic optical network, the constraint is set as:

[0055]

[0056] Among them, formula (24) ensures that the spectra used on the working paths between requests do not overlap. Formula (25) ensures that the spectrum of the working path assigned to a certain request does not overlap with the spectrum of the protection path assigned to other requests. Formula (26) ensures that the spectrum assigned to the dedicated protection path does not overlap with the spectra on the protection paths of other requests.

[0057] 9) To determine the crosstalk threshold according to the modulation format selected by the request, the constraint is set as:

[0058]

[0059] where τ m is the crosstalk threshold corresponding to the modulation format m. Ω r,w and Ω r,b represent the crosstalk thresholds corresponding to the working path and protection path of request r respectively.

[0060] 10) To determine whether the frequency slot f overlaps with the frequency slots at the corresponding positions of adjacent cores, the constraint is set as:

[0061]

[0062] 11) To ensure that there is no crosstalk between untrusted services and trusted services, and the crosstalk between trusted services does not exceed the crosstalk threshold, the following constraints are set:

[0063]

[0064] Furthermore, in S1, sort the service requests; by default, sort them in descending order of bandwidth rate during sorting. If there are requests with the same bandwidth rate, then sort them in descending order of the sum of the number of links in the working path and the protection path;

[0065] Furthermore, in S2, adopt the K - shortest path algorithm based on the Dijkstra algorithm to search for K shortest paths between the source node and the destination node for the service request. To determine the modulation format of the path, first calculate the path length of each path, then determine the maximum feasible modulation format according to the length, then calculate the number of frequency slots actually used based on the maximum feasible modulation format, and then calculate the number of frequency slots corresponding to the modulation format one level lower than the maximum feasible modulation format. If the number of frequency slots corresponding to the sub - level modulation format is more than that of the original modulation format, select the original modulation format for the request; if the number of frequency slots is the same, select this level of modulation format.

[0066] Furthermore, in S3, the process of obtaining the available spectrum blocks for each working path is to check each edge on the working path one by one, obtain its available spectrum blocks, and filter out the effective cores according to the conditions. First, for each link in the path, find the corresponding resource information through the index, traverse all the cores on this edge, and check the availability of the specified spectrum block. If the spectrum block is not occupied, all the frequency slots are in the idle state, and under the crosstalk avoidance scheme, the spectrum blocks of its adjacent cores are also not occupied, then the spectrum block on this core is considered available.

[0067] Furthermore, in S4, the formula for calculating the weight of the spectrum block of each core in the working path of the trusted service request is:

[0068]

[0069] where j c is the number of adjacent cores of core c, and j max is the maximum number of adjacent cores of a certain core in the currently used core structure; is the change in the number of fragments using the current core spectrum block; ε(0 < ε < 1) is a parameter that adjusts the influence of ΔB c The smaller the ε value, the more ΔB cThe greater the impact; the calculation results of each core spectrum are sorted by weight and saved. If no available core and spectrum block are found on a certain edge, return failure; if valid cores and spectrum blocks are found on all edges, return success, and store the available cores and their weight values for each edge. The formula for calculating the weight of each core spectrum block on the working path of an untrusted service request is:

[0070]

[0071] The weight calculation formula for untrusted service requests takes more into account the fragmentation situation in this core and adjacent cores.

[0072] Furthermore, in S5, for each available spectrum block, the core with the minimum weight of each link in the working path is sequentially selected, and then the weights of the selected core spectrum blocks are summed. The summation result represents the weight of this spectrum block. After calculating the weights of all available spectrum blocks, select the link, core, and spectrum block combination with the minimum weight as the working interval.

[0073] Furthermore, in S6, calculate the sum of the crosstalk suffered by the frequency gaps on the path in the working interval, and check whether the total crosstalk of the frequency gaps meets the crosstalk threshold requirement corresponding to the modulation format selected for the path. If it meets the threshold requirement, use it as the final resource allocation result for the requested working path; if it does not meet the requirement, perform crosstalk degradation until a working path resource allocation scheme that meets the threshold requirement is found or the request is blocked. The crosstalk degradation operation is as follows: First, identify the corresponding frequency gap on the current path that causes the crosstalk to exceed the threshold, and find the link where this frequency gap suffers the most crosstalk. Subsequently, search for alternative core combinations on this link, and select the core with the sub-optimal weight to update the current core combination. If there are no alternative cores on this link, it means that the crosstalk cannot be further reduced through core optimization. At this time, directly end the degradation operation and block the request. After successfully updating the core combination, recalculate the total crosstalk value of all frequency gaps on the path and check whether it meets the crosstalk threshold corresponding to the modulation format. If it meets the threshold, end the degradation and use it as the final resource allocation result; if it does not meet the requirement, continue to repeat the above crosstalk degradation operation for the new core combination. The entire process will continuously try to optimize the core allocation until a resource allocation scheme that meets the requirements is found or it is confirmed that no feasible scheme that meets the threshold can be found.

[0074] Furthermore, in S7, search for K shortest paths between the source node and the destination node for the service request that do not have any common links with the selected working path. In S8, when obtaining the available spectrum blocks of the protection path, when the survivability strategy is shared backup path protection, it can also occupy the frequency gaps in the shared state.

[0075] Furthermore, the formula for calculating the weight of each core spectrum block of the protection path in S9 is:

[0076]

[0077] where κ shared is the sharing degree of the core spectrum block, and its value is the ratio of the number of frequency slots in the shared state in the spectrum block to the total number of frequency slots. The formula for calculating the weight of each core spectrum block of the untrusted service request working path is:

[0078]

[0079] Furthermore, S10 - S11 is executed in a manner analogous to S5 - S6 to determine the protection interval. In S12, the blocking ratio value is the ratio of the number of blocked service requests to the total number of service requests; the resource utilization value is the ratio of the number of frequency slots occupied by service requests in the network to the network frequency slot capacity; the average frequency slot sharing times value is the ratio of the total number of occupied times of all shared frequency slots to the number of frequency slots in the shared state in the network. The number of fragments is the total number of fragments generated in the network due to the occupied discontinuous positions by requests. The average frequency slot crosstalk is the ratio of the total crosstalk received by the spectrum in the network to the number of frequency slots occupied by service requests in the network.

[0080] The beneficial effects of the present invention are as follows: The beneficial effects of the present invention are reflected in:

[0081] (1) By constructing a hybrid mechanism of dedicated path protection and shared backup path, and combining an integer linear programming model to perform collaborative optimization on routing, core, and spectrum, the contradiction between spectrum compact allocation and backup resource sharing is effectively balanced. The spectrum block weight calculation strategy is adopted to preferentially select low - fragment cores to ensure the continuous utilization of spectrum resources and significantly reduce the generation of network fragments.

[0082] (2) Based on the fault domain separation algorithm, the physical links of the working path and the protection path are strictly isolated, and combined with the pre - configured protection switching mechanism, millisecond - level service restoration in the single - point fault scenario is realized. Trusted services use dedicated protection paths to ensure zero - interruption characteristics, and untrusted services improve resource reuse rates through shared backup pools, forming a hierarchical survival guarantee system.

[0083] (3) Through the crosstalk perception model, the interference received by the spectrum block is evaluated in real - time, and the cross - core isolation strategy is adopted to force trusted services to exclusively occupy adjacent core spectra. When the crosstalk limit is detected, a downgrading operation is triggered, and the core allocation scheme is dynamically adjusted until the crosstalk threshold of the modulation format is met, ensuring the transmission quality of high - sensitive services.

[0084] (4) Dynamically select protection strategies according to service types. For trusted services, a dedicated protection mode with crosstalk awareness is adopted, and for untrusted services, a shared protection mechanism for crosstalk avoidance is implemented. By sorting path priorities and adaptively adjusting modulation formats, the differentiated requirements of diverse services for latency, reliability, and security are met.

[0085] Other advantages, objectives, and features of the present invention will be described to some extent in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be learned from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following specification. Brief Description of the Drawings

[0086] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0087] Figure 1 It is the overall framework diagram of the hybrid protection method of dedicated and shared paths considering risk avoidance for the space-division multiplexing elastic optical network of the present invention;

[0088] Figure 2 It is the network topology diagram of the 6-node network used in the simulation of the present invention;

[0089] Figure 3 It is the NSFNet network topology diagram used in the simulation of the present invention;

[0090] Figure 4 It is the schematic diagram of the comparison of the simulation results of the method of the present invention with the existing method and the linear solution method in the number of occupied frequency slots in the 6-node network;

[0091] Figure 5 It is the schematic diagram of the comparison of the simulation results of the method of the present invention with the existing method and the linear solution method in the row time in the 6-node network;

[0092] Figure 6 It is the schematic diagram of the comparison of the simulation results of the method of the present invention with the existing method in the blocking rate of the 7-core NSFNet network;

[0093] Figure 7 It is the schematic diagram of the comparison of the simulation results of the method of the present invention with the existing method in the spectrum resource utilization rate of the 7-core NSFNet network;

[0094] Figure 8 It is the schematic diagram of the comparison of the simulation results of the method of the present invention with the existing method in the average sharing times of frequency slots in the 7-core NSFNet network;

[0095] Figure 9Schematic diagram of the comparison of the simulation results of the method of the present invention and the existing method in terms of the number of fragments in the 7-core NSFNet network;

[0096] Figure 10 Schematic diagram of the comparison of the simulation results of the method of the present invention and the existing method in terms of the average crosstalk of frequency slots in the 7-core NSFNet network. Specific implementation manners

[0097] The following uses specific specific examples to illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the drawings provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0098] Among them, the drawings are only for illustrative purposes, showing only schematic diagrams, not physical diagrams, and cannot be understood as a limitation to the present invention; in order to better illustrate the embodiments of the present invention, some components in the drawings will be omitted, enlarged or reduced, and do not represent the size of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0099] In the drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or positional relationship, it is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the drawings are only for illustrative purposes and cannot be understood as a limitation to the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0100] Please refer to Figures 1 to 10 , which is a network resource allocation method considering risk aversion in a survivable space-division multiplexing elastic optical network. This method includes the following steps:

[0101] With the development of bandwidth-intensive applications, fiber optic communication networks face challenges in capacity, flexibility, and reliability. Elastic optical networks improve resource utilization efficiency through flexible spectrum allocation. However, as demand grows, single-core networks are gradually reaching their bottlenecks. Space-division multiplexing technology based on multi-core optical fibers increases transmission capacity by introducing multiple independent optical cores, while reducing the spectrum continuity constraint. However, inter-core crosstalk has become the main problem affecting transmission quality and security.

[0102] To solve the above problems, the present invention proposes a hybrid protection method for dedicated and shared paths considering risk aversion. By constructing a mixed-integer linear programming model, path, modulation format, core, and spectrum allocation are comprehensively optimized. Critical traffic uses dedicated path protection to improve reliability, while non-critical traffic uses shared backup path protection to save resources. In addition, through risk aversion strategies and spectrum allocation optimization, fault recovery is achieved, the blocking rate is reduced, and network performance is improved. While enhancing network survivability, the present invention improves resource utilization efficiency and provides an efficient and reliable solution for future optical networks. This method is implemented based on a network model, crosstalk model, request model, and integer linear programming model, and specifically includes the following steps:

[0103] S1. Sort all service requests in descending order according to the bandwidth rate of the service requests.

[0104] S2. In the sorted order, sequentially search for K shortest paths between the source node and the destination node for the service requests that have not been allocated spectrum resources as the working path set, and determine the minimum feasible modulation format with the least number of used frequency slots for each path in the set.

[0105] S3. Obtain each available core spectrum block on each working path. If there is no available spectrum block, block the request.

[0106] S4. Calculate the weight of each available core spectrum block according to the core spectrum weight calculation formula for the working paths of trusted and untrusted services.

[0107] S5. Select the link, core, and spectrum combination with the minimum weight as the working interval of the service request.

[0108] S6. Calculate the total crosstalk received by the selected spectrum block on the working path, and check whether all frequency slots meet the crosstalk threshold requirements. If not, perform crosstalk degradation until a combination that meets the threshold requirements is selected as the final working path resource allocation scheme, or mark the request as blocked.

[0109] S7. Search for K shortest paths between the source node and the destination node for the service request that have no common links with the working path as the alternative protection path set, and determine the minimum feasible modulation format with the least number of used frequency slots for each path in the set.

[0110] S8. Obtain each available core spectrum block on each protection path. If there is no available spectrum block, block the request.

[0111] S9. Calculate the weight of each available core spectrum block according to the protection path core spectrum weight calculation formulas for trusted services and untrusted services.

[0112] S10. Select the link, core, and spectrum combination with the minimum weight as the protection interval for the service request.

[0113] S11. Calculate the total crosstalk received by the selected spectrum block on the protection path, and check whether all frequency slots meet the crosstalk threshold requirements. If not, perform crosstalk degradation until a combination that meets the threshold requirements is selected as the final protection path resource allocation scheme, or mark the request as blocked.

[0114] S12. Allocate the link, core spectrum resources of the network for the request according to the working interval and protection interval determined in S6 and S11, and update the network status information. If there are still requests without allocated resources, return to S2 to continue allocating resources for the next request. If all requests have been allocated resources, calculate the blocking rate, network resource utilization rate, average number of times of frequency slot sharing, number of fragments, and average crosstalk amount of frequency slots.

[0115] Furthermore, in the network model constructed by the method, the undirected graph G(N, L) is defined as the network topology structure of SDM-EON. Each optical fiber link is composed of a group of cores C. The spectrum of each core is divided into frequency slots of 12.5 GHz. In the service request model of the method, the service request set is denoted as R. Each service request in R can be expressed as r(s r , d r , λ r , σ r , γ r ). In the crosstalk model of the method, the crosstalk between two adjacent active cores c and c on the same frequency slot f of link l is calculated using formula (1): adj between:

[0116]

[0117] In a uniform core, calculate the crosstalk between two adjacent active cores c and c on the same frequency slot f of link l: adj between:

[0118]

[0119] Add up the crosstalk of all adjacent cores of optical fiber core c to calculate the total crosstalk of the frequency slot on the link, as follows:

[0120]

[0121] Add up the total crosstalk of all frequency slots of the links in the path to calculate the total crosstalk of the frequency slot on the path:

[0122]

[0123] Furthermore, the final optimization objective of the integer linear programming model is:

[0124]

[0125] 1) To ensure that each request is assigned a working path and a protection path, and a modulation format is assigned to each path, the following constraints are set:

[0126]

[0127] 2) To clarify the links included in the request working path and protection path, the following constraints are set:

[0128]

[0129] 3) To avoid having common links between the working path and the protection path selected for the same request, it is necessary to ensure that the selected working path and protection path are among the same candidate path pairs, and the constraint is set as:

[0130]

[0131] 4) To ensure that each link in the request working path and protection path selects one fiber core, the constraint is set as:

[0132]

[0133] 5) To ensure the traffic balance of each node, that is, to maintain conservation between the total traffic entering the node and the total traffic leaving the node, the constraint is set as:

[0134]

[0135] 6) To ensure that the frequency slots occupied by the request meet the spectrum continuity requirements of the elastic optical network, the constraint is set as:

[0136]

[0137] 7) To ensure that the frequency slots occupied by the request do not exceed the capacity limit of the link, the constraint is set as:

[0138]

[0139] 8) To ensure that the frequency slots occupied by requests meet the non - overlapping requirements of the elastic optical network spectrum, the constraints are set as follows:

[0140]

[0141] Among them, formula (24) ensures that the spectra used on the working paths between requests do not overlap. Formula (25) ensures that the spectrum of the working path assigned to a certain request does not overlap with the spectrum of the protection path assigned to other requests. Formula (26) ensures that the spectrum assigned to the dedicated protection path does not overlap with the spectra on the protection paths of other requests.

[0142] 9) To determine its crosstalk threshold according to the modulation format selected by the request, the constraints are set as follows:

[0143]

[0144] 10) To determine whether the frequency slot f overlaps with the frequency slots at the corresponding positions of adjacent cores, the constraints are set as follows:

[0145]

[0146] 11) To ensure that there is no crosstalk between untrusted services and trusted services, and the crosstalk between trusted services does not exceed the crosstalk threshold, the constraints are set as follows:

[0147]

[0148] Furthermore, in S1, it is necessary to sort the service requests to improve the efficiency and rationality of resource allocation. By default, they are sorted in descending order according to the bandwidth rate, and the service requests with larger bandwidth rates are processed first because these requests have higher demands for network resources, and processing them first can reduce the probability of resource conflicts. If there are requests with the same bandwidth rate, they are further sorted in descending order according to the total number of links involved in the working path and the protection path. The total number of links refers to the sum of all the links passed through in the working path and the protection path, and the requests with a larger total number of links are processed first.

[0149] Further, in S2, the K - shortest path algorithm based on the Dijkstra algorithm is adopted to search for K shortest paths between the source node and the destination node for the service request. This algorithm is also known as Yen's algorithm and can be divided into two stages: First, use Yen's algorithm to calculate the first shortest path; then, on this basis, calculate the other K - 1 shortest paths in turn. Specifically, when finding paths other than the first shortest path, all nodes on the first shortest path except the end node are regarded as deviation nodes, and the shortest path from each deviation node to the end node is calculated. Subsequently, the path from the start node to the deviation node in the original shortest path is concatenated with the newly calculated shortest path from the deviation node to the end node to form a candidate path, thereby obtaining a new shortest deviation path.

[0150] To determine the modulation format of the path, first calculate the path length of each path, then determine the maximum feasible modulation format according to the length, then calculate the number of frequency slots actually used according to the maximum feasible modulation format, and then calculate the number of frequency slots corresponding to the modulation format one level lower than the maximum feasible modulation format. If the number of frequency slots corresponding to the lower - level modulation format is more than that corresponding to the original modulation format, select the original modulation format for the request; if the number of frequency slots is the same, select this level of modulation format.

[0151] When determining the modulation format of the path, first calculate the path length of each path, and determine the maximum feasible modulation format supported on this path according to the path length. After determining the maximum feasible modulation format, calculate the number of frequency slots required for the service request under this modulation format according to its modulation efficiency. Subsequently, further calculate the number of frequency slots corresponding to the modulation format one level lower (one level lower than the maximum feasible modulation format). If the number of frequency slots required for the lower - level modulation format is more than that corresponding to the current maximum feasible modulation format, select the maximum feasible modulation format to save resources; if the number of frequency slots corresponding to the lower - level modulation format is the same as that of the current maximum feasible modulation format, select the lower - level modulation format to increase the crosstalk threshold of the service request.

[0152] Further, in S3, obtaining the available spectrum blocks on each working path is a key link in resource allocation. The specific process includes analyzing the link resource status on the path one by one, and screening out the qualified available optical cores and their available spectrum blocks according to the preset conditions. First, perform resource information indexing on each link in the path to extract its corresponding spectrum resource status. Subsequently, traverse all the optical cores on the link one by one and evaluate the availability of the specified spectrum block. The availability judgment of the spectrum block is based on the following constraints: First, the spectrum block is not occupied, that is, all frequency gaps are in an idle state; Second, for untrusted requests, crosstalk between frequency gaps needs to be avoided, requiring that the same spectrum block on adjacent optical cores is not occupied. When the above conditions are met, the spectrum block on this optical core is considered available and marked as an effective resource. After the analysis of each link in the path is completed, to meet the resource continuity requirements of the path, perform an intersection operation on the available spectrum blocks on each link, and only retain the spectrum blocks that are available on all links of the path, and finally determine the set of available spectrum blocks on the working path.

[0153] Further, in S4, the formula for calculating the weight of the spectrum block of each optical core in the working path of the trusted service request is:

[0154]

[0155] where j c is the number of adjacent optical cores of optical core c, and j max is the maximum number of adjacent optical cores of a certain optical core in the currently used optical core structure; is the change in the number of fragments using the current optical core spectrum block; ε (0 < ε < 1) is a parameter that adjusts the influence of the change in the number of fragments. The smaller the ε value, the greater the influence of the change in the number of fragments; in the calculation process, the weight of the optical core spectrum block comprehensively considers the number of adjacent optical cores of the optical core, the change in the number of fragments of the current spectrum block, and the influence of the weight parameter. After the calculation, sort the results of the optical core spectrum block from high to low according to the weight. If no available optical core and spectrum block are found on a certain link, return failure; if available optical cores and spectrum blocks are found on all links, return success and save the effective optical cores and their corresponding weights on each link. The formula for calculating the weight of the spectrum block of each optical core in the working path of the untrusted service request is:

[0156]

[0157] The weight calculation formula for the untrusted service request considers more the fragmentation situation of the current optical core and adjacent optical cores. By optimizing the fragmentation influence of adjacent optical cores, it ensures the maximization of resource allocation efficiency and improves the overall performance of the network.

[0158] Further, in S5, the weight calculation for each available spectrum block is completed by sequentially selecting the fiber core with the minimum weight on each link in the working path. Specifically, for each available spectrum block, the fiber core with the minimum weight is selected on each link of the working path to ensure that resource allocation is carried out under optimal conditions; then, the weights of the selected fiber core spectrum blocks are summed up, and the summation result represents the total weight of the spectrum block, which is used to measure its comprehensive applicability on the working path. This process is repeated until the weights of all available spectrum blocks are calculated. Finally, the spectrum block with the minimum weight, as well as its corresponding link and fiber core combination, is selected as the allocation scheme for the working path to ensure that the impact of resource allocation on the network is minimized while meeting the requirements of the service request.

[0159] Further, in S6, it is necessary to calculate the total crosstalk value of each frequency slot in the working interval on the path and check whether it meets the crosstalk threshold requirement of the currently selected modulation format on the path. First, the crosstalk value of each frequency slot on the path is calculated and accumulated one by one on the link to obtain the total crosstalk value; if the total crosstalk value meets the threshold requirement of the modulation format, the current allocation scheme is used as the final working path resource allocation result of the request, and the operation ends. If it does not meet the threshold requirement, a crosstalk degradation operation needs to be performed to optimize the allocation scheme. The crosstalk degradation operation first identifies the frequency slot that causes the crosstalk to exceed the threshold and the link on the path that is most affected by crosstalk; then, an alternative fiber core combination is searched for on this link, and a new fiber core is selected according to the sub-optimal weight principle to update the current fiber core combination. If there is no alternative fiber core on this link, the crosstalk cannot be further reduced, and the degradation operation ends, blocking the request. If the fiber core combination is successfully updated, the total crosstalk value of all frequency slots on the path is recalculated, and it is checked whether it meets the threshold requirement; if it meets, the degradation ends and the current scheme is used as the final allocation result; if it does not meet, the above degradation operation is repeated, continuously optimizing the fiber core allocation until a resource allocation scheme that meets the requirements is found or it is confirmed that the threshold cannot be met. The entire process adjusts the fiber core allocation, reduces the total crosstalk value on the path, and at the same time ensures the efficient utilization of network resources and signal transmission quality.

[0160] Further, in S7, K shortest paths that do not have any common links with the selected working path are searched for between the source node and the destination node for the service request. Specifically, first, the path search conditions are initialized, and all link sets of the selected working path are recorded as the constraint conditions for subsequent path screening; then, the shortest path algorithm is used to successively calculate the shortest path from the source node to the destination node, and at the same time, candidate paths that contain the links of the working path are filtered out through the constraint conditions to ensure the complete independence of the protection path and the working path. After each search, the found protection path is added to the protection path set, and the links of this path are temporarily removed to avoid repeated selection of the same path. The search process is repeated until K protection paths are found or there are no more available paths.

[0161] Furthermore, in S8, when obtaining available spectrum blocks for the protection path, if the survivability strategy is shared backup path protection, frequency slots in the shared state are allowed to be occupied during the resource allocation process. Shared backup path protection allows multiple service requests to share the same frequency slots during normal operation.

[0162] Furthermore, the formula for calculating the weight of each core spectrum block of the protection path in S9 is:

[0163]

[0164] where κ shared is the sharing degree of the core spectrum block, and its value is the ratio of the number of frequency slots in the shared state in the spectrum block to the total number of frequency slots. During the calculation process, the weight of the core spectrum block comprehensively considers the number of adjacent cores of the core, the change in the number of fragments of the current spectrum block, the weight parameter, and the influence of the spectrum sharing degree. The formula for calculating the weight of each core spectrum block of the working path of an untrusted service request is:

[0165]

[0166] Furthermore, in S10, the calculation of the spectrum block weight of the protection path is similar to that in S5. For each available spectrum block, each link in the protection path is analyzed one by one. By selecting the core with the minimum weight, it is ensured that the core combination with the least impact is preferentially used during resource allocation. Subsequently, the weights of the spectrum blocks of the selected cores are accumulated, and the sum result is the comprehensive weight of the spectrum block. By repeating the above calculation process for all available spectrum blocks on the protection path, the weight of each spectrum block is determined. Finally, the spectrum block with the minimum weight and its corresponding link and core combination are selected from all available spectrum blocks as the preliminary resource allocation scheme for the protection path to ensure the efficiency of resource allocation and the minimization of the overall network impact.

[0167] Further, in S11, the resource allocation scheme of the protection path needs to be subjected to crosstalk checking to ensure that it meets the signal transmission quality requirements, which is similar to the processing flow of S6. First, for each frequency slot of the protection path, calculate its crosstalk value on all links of the path one by one, and accumulate to obtain the total crosstalk value of the protection interval. If the total crosstalk value meets the crosstalk threshold corresponding to the modulation format, then use the current scheme as the final allocation result of the protection path; if not, perform the crosstalk degradation operation. The crosstalk degradation operation first identifies the frequency slots with excessive crosstalk and the link on the path that is most affected by them, and then searches for alternative core combinations in this link, and updates the core allocation according to the sub-optimal weight principle. If there are no alternative cores, the crosstalk cannot be further optimized, and it is necessary to mark that the protection path allocation of the service request fails. If the core allocation is successfully updated, recalculate the total crosstalk value and check whether it meets the threshold requirements. The whole process repeatedly optimizes the core allocation until a compliant allocation scheme is found or it is confirmed that no optimization is possible, so as to provide reliable resource support for the protection path allocation and meet the survivability requirements.

[0168] Further, in S12, according to the working interval and protection interval determined in S6 and S11, allocate the corresponding network links, cores, and spectrum resources for the current service request, and synchronously update the network status information to reflect the resource usage. If there are still service requests without allocated resources, return to S2 and continue to allocate resources for the next request according to the scheduling rules; if all requests have completed resource allocation, calculate the following key performance indicators according to the final network status: blocking rate (the ratio of the number of blocked service requests to the total number of service requests), network resource utilization rate (the ratio of the number of allocated frequency slots to the total capacity of network frequency slots), average sharing times of frequency slots (the ratio of the total number of occupied times of all shared frequency slots to the number of frequency slots in the shared state), number of fragments (the total number of fragments generated due to discontinuous allocation positions), and average crosstalk amount of frequency slots (the ratio of the total spectrum crosstalk in the network to the number of frequency slots occupied by service requests). Through the above operations, not only the resource allocation of all service requests is completed, but also the network performance can be comprehensively evaluated, providing a basis for optimizing the resource allocation strategy.

[0169] Embodiment 2

[0170] This embodiment conducts simulation experiments on the dedicated and shared path hybrid protection method considering risk avoidance in the space-division multiplexing elastic optical network of the present invention and the integer linear programming model mentioned in the method, and presents the experimental results.

[0171] A hybrid protection method for dedicated and shared paths considering risk avoidance in a space-division multiplexing elastic optical network of the present invention constructs an integer linear programming model to describe the problem to be solved. In this embodiment, the hybrid protection method for dedicated and shared paths considering risk avoidance in a space-division multiplexing elastic optical network considering crosstalk, fragmentation, core structure, and spectrum sharing degree of the present invention is abbreviated as RAHPA; the crosstalk sensitivity core spectrum allocation algorithm in the existing method is abbreviated as CSA_SS; the shared backup path heuristic method in the existing method is abbreviated as SBPPHA; the path allocation method adopts KSP, and the spectrum allocation scheme adopts the first-fit method, abbreviated as KSP+FF. In this embodiment, the method of the present invention is compared with the existing methods. The service blocking rate of the present invention is lower, the average number of shared frequency slots is higher, and the comprehensive performance is the best.

[0172] To solve the integer linear programming problem, a small-scale network topology N6S9 with 6 nodes and 9 links is constructed, as Figure 2 shown. At the same time, a large-scale network topology, namely NSFNet, is used for stress test simulation. In Figure 3 , NSFNet contains 14 nodes and 21 links. In all network topologies, each fiber link contains 7 optical fibers, the bandwidth of each optical fiber is 1 THz, and the bandwidth of a single frequency slot is set to 12.5 GHz. Therefore, each fiber link has 80 frequency slots. The selectable modulation formats include BPSK, QPSK, 8-QAM, and 16-QAM. Table 1 shows the specific parameter settings of the modulation format, the maximum transmission distance, and the crosstalk threshold.

[0173] Table 1

[0174]

[0175] In the N6S9 network topology, the integer linear programming problem is solved by IBM ILOG Cplex 12.80. Figure 4 shows the relationship between the number of occupied frequency slots and the number of service requests of the integer linear programming model, the proposed algorithm, and the three comparison algorithms. The proposed RAHPA algorithm is superior to the other three comparison algorithms, and its result is almost close to the integer linear programming model. When the number of service requests is 16, the objective value of the integer linear programming model is 106, while the objective values of the RAHPA and CSA_SA algorithms are 119 and 122 respectively. The convergence rate of the RAHPA algorithm and the integer linear programming model is 10.9%, which is 2.5% lower than that of the CSA_SS algorithm. However, the calculation time required by the integer linear programming model increases significantly and grows exponentially with the increase in the number of service requests, as Figure 5 shown.

[0176] Figure 6It shows the trend of the blocking probability of four algorithms changing with the increase in the number of service requests on the NSFNet network topology. As the number of service requests increases, the blocking probability of all algorithms rises. However, the blocking probability of the RAHPA algorithm is always lower than that of other algorithms. In the NSFNet topology, when the number of service requests is 700, the blocking probability of the RAHPA algorithm is 5.4%, 17.3%, and 21.5% lower than those of the CSA_SS, SBPPHA, and KSP+FF algorithms respectively. Figure 7 It shows the performance of the RAHPA algorithm in terms of spectrum resource utilization. Compared with the CSA_SS and KSP+FF algorithms, the spectrum utilization rate of the RAHPA algorithm is 0.9% and 9.3% higher, but 1.8% lower than that of the SBPPHA algorithm. The RAHPA algorithm's consumption of spectrum resources is in the middle position. In Figure 8 and Figure 9 , the average sharing times of frequency slots and the number of fragments in the network are calculated. When the number of requests is 700, the average sharing times of frequency slots of the RAHPA algorithm are 5.7%, 31.4%, and 36.1% higher than those of the CSA_SS, SBPPHA, and KSP+FF algorithms respectively, and the number of fragments of the RAHPA algorithm is 22.9%, 30.7%, and 33.1% lower than those of the CSA_SS, SBPPHA, and KSP+FF algorithms. The results show that the RAHPA algorithm has the highest average sharing times and the fewest number of fragments. This is because the proposed RAHPA algorithm considers more about the spectrum sharing degree and spectrum allocation location when allocating spectrum resources, making more future spectrum allocated to the spectrum already occupied by shared paths, and also reducing network fragments so that there are more available spectrum blocks for future requests. The RAHPA algorithm not only maximizes resource sharing but also achieves load balancing, thus providing an efficient spectrum resource allocation strategy to achieve a lower blocking probability. In Figure 10 , the communication quality is reflected by the index of the average crosstalk amount of frequency slots. When the number of requests is 700, the average crosstalk amount of frequency slots of the RAHPA algorithm is close to that of the CSA_SS algorithm, but 0.05% higher than that of the CSA_SS algorithm, and 5.4% and 0.9% lower than those of the SBPPHA and KSP+FF algorithms respectively.

[0177] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A network resource allocation method considering risk aversion in a survivable space-division multiplexing elastic optical network, characterized in that: It includes the following steps: S1: Sort all service requests from large to small according to the bandwidth rate of the service request; S(2): In the sorted order, search for K shortest paths from the source node to the destination node for each service request in turn as the working path set, and determine the minimum feasible modulation format for each path; S3: Obtain the available core spectrum blocks on each working path, and block the request if they do not exist; S4: Calculate the weight of each available core spectrum block according to the credibility of the service. For trusted services, use the crosstalk-aware weight formula, and for untrusted services, use the crosstalk-avoidance weight formula; S5: Select the link, core, and spectrum combination with the smallest weight as the working path resource allocation scheme; S6: Check whether the end-to-end crosstalk of the working path meets the threshold of the modulation format. If not, perform crosstalk degradation until it meets the requirement or block the request; S7: Search for K shortest protection paths for the service request that have no common links with the working path; S8: Obtain the available core spectrum blocks on the protection path, and block the request if they do not exist; S9: Calculate the weight of the core spectrum blocks on the protection path. For trusted services, consider the influence of sharing degree, and for untrusted services, consider adjacent core fragments; S10: Select the protection path resource allocation scheme with the smallest weight; S11: Check the crosstalk threshold of the protection path. If it is not met, perform crosstalk degradation; S12: Allocate resources and update the network state, and count the blocking rate, resource utilization rate, and crosstalk metrics.

2. The network resource allocation method considering risk aversion in a survivable space-division multiplexing elastic optical network according to claim 1, wherein: The sorting rule in the S1 is: First, sort in descending order of bandwidth rate. If the rates are the same, sort in descending order of the total number of links of the working path and the protection path.

3. The method for allocating network resources considering risk aversion in a survivable space-division multiplexing elastic optical network according to claim 1, wherein: The method for determining the minimum feasible modulation format in the S2 includes: Select the maximum modulation level according to the path length. If the number of frequency slots required for the next lower modulation format is the same, downgrade the selection.

4. The network resource allocation method considering risk aversion in a survivable space-division multiplexing elastic optical network according to claim 1, characterized in that: The crosstalk-aware weight formula for trusted services in the S4 is: where j c is the number of adjacent cores to core c, and j max is the maximum number of adjacent cores, is the crosstalk coefficient of link l, is the amount of debris change, and ε is the attenuation factor.

5. The network resource allocation method considering risk aversion in a survivable space-division multiplexing elastic optical network according to claim 1, characterized in that: The crosstalk degradation in the S6 includes: Identify the link where the over-standard frequency slot is located and replace it with the sub-optimal core combination. If it cannot be replaced, block the request.

6. The network resource allocation method considering risk aversion in the survivable space-division multiplexing elastic optical network according to claim 1, characterized in that: In the S7, the protection path and the working path satisfy the fault domain separation constraint, and the shared backup path is allowed to occupy the shared state frequency slot.

7. The network resource allocation method considering risk aversion in a survivable space-division multiplexing elastic optical network according to claim 1, characterized in that: The weight formula of the trusted service protection path in S9 introduces a sharing degree factor κ shared , and the calculation formula is as follows: where κ shared is the sharing frequency gap ratio, and is the core spectrum block weight of the working path.

8. The network resource allocation method considering risk aversion in a survivable space-division multiplexing elastic optical network according to claim 1, characterized in that: The method uses multi-core fiber (MCF) in the network model. Each link contains multiple independent cores. The spectrum is divided into 12.5 GHz frequency slots. The service request attributes include the bandwidth rate λ r , the protection scheme type σ r , and the credibility γ r .

9. The method for allocating network resources considering risk aversion in a survivable space-division multiplexing elastic optical network according to claim 4, wherein: The crosstalk threshold is dynamically adjusted according to the modulation format, including: -14 dB for BPSK, -18.5 dB for QPSK, -21 dB for 8-QAM, and -25 dB for 16-QAM.

10. The method for network resource allocation considering risk aversion in a survivable space-division multiplexing elastic optical network according to claim 1, wherein: The spectrum continuity constraint in S12 is achieved by restricting the starting frequency gaps of the working path and the protection path and the number of frequency gaps n r,w n r,b to ensure that the allocation does not exceed the link capacity.

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