Computing power service deployment method oriented to distributed intelligent computing center network

Abstract

The invention discloses a computing power service deployment method oriented to a distributed intelligent computing center network, and belongs to the technical field of computing power service deployment. The invention provides an algorithm deployment method and a model deployment method, and the algorithm deployment comprises the steps: obtaining a plurality of computing power businesses of a distributed intelligent computing center network, and the computing power businesses comprise starting node and destination node to-be-selected lists; determining a destination node according to the idle computing power resource quantity of the nodes in the destination node candidate list and the routing condition of the starting node; and deploying computing power business through spectrum transaction, computing power transaction or joint transaction based on the starting node and the destination node. According to the invention, the problem of resource allocation and transaction among multiple operators in the computing power service deployment process is solved, so that the overall performance of the network is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of computing power business deployment, and specifically relates to a computing power business deployment method for a distributed intelligent computing center network. Background Art

[0002] Because the resources in the distributed intelligent computing center network are private and dynamically fluctuating, it is impossible for any intelligent computing center operator to share resources for free. Different intelligent computing center nodes vary in the scale of computing power, the amount of available computing resources, and the network resources of the links between intelligent computing center nodes. When attempting to deploy computing services between intelligent computing center nodes, the success of scheduling is affected by both the amount of computing resources and the network resources. Even if there are sufficient distributed computing resources, if the current operator has insufficient optical network resources and other operators' optical networks operate independently, direct service deployment is still not feasible, hindering end-to-end data transmission.

[0003] Current spectrum trading is independent of the computing power trading system and can directly benefit general communications services. However, because computing power services require both computing power and spectrum resources, sufficient computing power at the destination node is essential for service deployment, otherwise deployment will fail. Therefore, efficiently coupling the computing power and network resource allocation and trading processes of different operators, and improving the efficiency of distributed intelligent computing center networks by enhancing computing network collaboration, has become a key issue. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a computing power service deployment method for a distributed intelligent computing center network to solve the resource allocation and transaction problems among multiple operators during the computing power service deployment process, so as to improve the overall network performance.

[0005] The present invention provides the following technical solutions:

[0006] In a first aspect, a computing power service deployment method for a distributed intelligent computing center network is provided, comprising:

[0007] Obtaining several computing services of the distributed intelligent computing center network, including a list of start nodes and destination nodes to be selected;

[0008] Determine the destination node based on the idle computing resources of the nodes in the destination node candidate list and the routing status with the starting node;

[0009] Based on the starting node and the destination node, computing power services are deployed through spectrum trading, computing power trading or joint trading.

[0010] As a preferred technical solution of the present invention, the computing power business is represented as ;

[0011] in, Indicates the computing power required by the computing business. Indicates the traffic required by the computing business. Indicates the starting node of the computing power business. Indicates the computing power business on the starting node Through virtual link The destination node for deployment.

[0012] As a preferred technical solution of the present invention, determining the destination node based on the idle computing resources of the nodes in the destination node candidate list and the routing status with the starting node includes:

[0013] Traversing all nodes in the target node candidate list, and using the idle computing power resources of each node as the starting state score of each node;

[0014] Determine whether the starting node and the nodes in the destination node candidate list belong to the same operator. If they are different, deduct the starting status score of the node;

[0015] Determine the number of routing hops from the starting node to the nodes in the destination node candidate list according to the Dijstra algorithm, and update the final state score according to the number of routing hops;

[0016] The node with the highest final state score is taken as the destination node.

[0017] As a preferred technical solution of the present invention, the deployment of computing power services based on the starting node and the destination node through spectrum trading, computing power trading, or joint trading includes:

[0018] Before deploying computing power services through spectrum trading, computing power trading, or joint trading, calculate the number of frequency slots required for the computing power service, expressed as:

[0019] ;

[0020] in, represents the number of frequency slots, Indicates the traffic required by the computing business. represents the frequency slot bandwidth, Indicates the modulation format efficiency of the path;

[0021] The spectrum trading includes:

[0022] Traverse the spectrum resources corresponding to the path in the virtual optical network controlled by the operator to which the starting node belongs. If there is a frequency gap that meets the service requirements, determine whether the starting node and the destination node belong to the same operator. If they do, deploy computing power services;

[0023] The computing power transaction includes:

[0024] Traverse the spectrum resources corresponding to the path in the virtual optical network controlled by the operator to which the starting node belongs. If there is a frequency gap that meets the service requirements, determine whether the starting node and the destination node belong to the same operator. If they are the same, deploy computing power services. If they are different, determine the cumulative credit threshold of the starting node. Is it not less than the minimum threshold? If the conditions are met, the starting node pays the supply node a computing power credit equal to the transaction resource volume. After the starting node and the supply node update the accumulated credit value, the computing power business is deployed.

[0025] The joint transaction includes:

[0026] Traverse the spectrum resources corresponding to the path in the virtual optical network controlled by the operator to which the starting node belongs. If there is a frequency gap that meets the business requirements, determine whether the starting node and the destination node belong to the same operator. If they are the same, deploy computing power services. If they are different, conduct computing power transactions to deploy computing power services. If there is no frequency gap that meets the business requirements, determine the accumulated spectrum credit value of the virtual optical network to which the destination node belongs. Is it not less than the threshold of the cumulative spectrum credit value? ,in Virtual optical network At the moment If the credit threshold is met, the system traverses the virtual optical networks managed by other operators to find a virtual link with the same physical path as the current virtual link, and determines whether its idle frequency slot can meet the service requirements. If so, the system updates the accumulated spectrum credit value of both virtual optical networks and deploys computing power services.

[0027] In a second aspect, a computing power service deployment method for a distributed intelligent computing center network is provided, including:

[0028] Obtaining several computing services of the distributed intelligent computing center network, wherein the computing services include a list of start nodes and destination nodes to be selected;

[0029] The computing power service is input into a pre-built service deployment model including an objective function and constraints, and the service deployment model is solved to obtain a computing power service deployment plan; wherein the objective function is to maximize computing power resource utilization as the optimization goal, and the constraints include computing power resource constraints, frequency slot resource constraints, spectrum resource constraints, spectrum trading credit constraints, and computing power trading credit constraints;

[0030] Wherein, solving the business deployment model to obtain a computing power business deployment solution includes:

[0031] According to the computing power resource constraints, the frequency slot resource constraints, and the spectrum resource constraints, a destination node is selected from the destination node candidate list of the computing power service;

[0032] If the destination node and the starting node belong to the same operator, the computing power services are directly deployed using the computing power resources within the operator. If the destination node and the starting node do not belong to the same operator, it is determined whether the computing power transaction credit constraints are met. If so, computing power transaction is carried out to deploy computing power services. If spectrum resources are lacking during the direct deployment of computing power services, it is determined whether the spectrum transaction credit constraints are met. If so, spectrum transaction is carried out to deploy computing power services. If spectrum resources are lacking during the computing power transaction process, it is determined whether the spectrum transaction credit constraints are met. If so, spectrum transaction is carried out to deploy computing power services.

[0033] As a preferred technical solution of the present invention, the filtering out of the destination node from the destination node candidate list of the computing power service according to the computing power resource constraint, the frequency slot resource constraint, and the spectrum resource constraint includes:

[0034] The nodes whose remaining idle computing power resources are not less than 0 in the target node candidate list are screened out by the computing power resource constraint, which is expressed as:

[0035] ;

[0036] in, Indicates the computing power of the nodes in the destination node candidate list, It represents the set of virtual links where the starting node is located, S represents the set of computing power services s, Indicates the amount of computing resources required for the computing business. Indicates that the computing power business s is deployed successfully, otherwise it is 0. N represents the set of starting nodes z, and T represents the set of time t;

[0037] After screening, the Dijstra algorithm is used to determine the path from the starting node to the node with a remaining idle computing power resource of not less than 0, in order to calculate the number of frequency slots required for the computing power business;

[0038] The spectrum resources corresponding to the path are traversed in the virtual optical network controlled by the operator to which the starting node belongs, and the node with the shortest path that meets the frequency slot resource constraints and spectrum resource constraints is selected as the destination node.

[0039] As a preferred technical solution of the present invention, the frequency slot resource constraints include frequency slot usage constraints, frequency slot quantity constraints, frequency slot unallocated constraints, and frequency slot non-overlap constraints;

[0040] The frequency slot usage constraint is expressed as:

[0041] ;

[0042] ;

[0043] ;

[0044] in, Indicates the starting node Transmit computing power services through virtual link k The starting index of the occupied frequency slot, Indicates the starting node Transmit computing power services through virtual link k The occupied frequency slot end index, Indicates the frequency slot start index of the virtual link, Indicates the frequency slot end index of the virtual link, It means using the computing power resources within the operator to directly deploy computing power services. Indicates computing power business Deployment was successful;

[0045] The frequency slot quantity constraint is expressed as:

[0046] ;

[0047] ;

[0048] ;

[0049] in, Indicates the number of frequency slots occupied by computing power business transmission, represents a positive minimum;

[0050] The frequency slot unassignment constraint is expressed as:

[0051] ;

[0052] in, Indicates that the physical link The index on If the frequency slot is not allocated, , represents the frequency slot set, Indicates the physical link that virtual link k passes through A collection of Indicates a positive maximum value;

[0053] The frequency slot non-overlap constraint is expressed as:

[0054] ;

[0055] ;

[0056] ;

[0057] in, Indicates that at the starting node Through virtual link Transmission computing power business When computing power business The starting index of the occupied frequency slot is greater than the computing power business The starting index of the occupied frequency slot, then , Indicates that at the starting node Through virtual link Transmission computing power business When computing power business The starting index of the occupied frequency slot is greater than the computing power business The starting index of the occupied frequency slot, then ;

[0058] The spectrum resource constraints include virtual link capacity constraints and spectrum non-overlap constraints;

[0059] The virtual link capacity constraint is expressed as:

[0060] ;

[0061] The spectrum non-overlap constraint is used to prevent spectrum overlap when computing services are transmitted on different virtual links over the same physical link. It is expressed as:

[0062] ;

[0063] ;

[0064] ;

[0065] ;

[0066] in, Indicates at time Starting Node Transmit computing power services through virtual links , the starting node passes the virtual link Transmission computing power business , the two virtual links pass through the same physical link, computing power business The occupied starting frequency slot range index is greater than the computing power business The occupied starting frequency slot range index is , otherwise 0, Indicates a virtual link and Through the same physical link, Indicates the starting node Through virtual link Transmission computing power business The starting index of the occupied frequency slot, Indicates the starting node Through virtual link Transmission computing power business End index of the occupied frequency slot.

[0067] As a preferred technical solution of the present invention, if the destination node and the starting node do not belong to the same operator, determining whether the computing power transaction credit constraint is satisfied, and if the computing power transaction credit constraint is satisfied, performing computing power transaction to deploy computing power services, including:

[0068] If the destination node and the starting node do not belong to the same operator, determine whether the cumulative credit threshold of the starting node at time t is not less than the minimum threshold, the cumulative credit threshold of the starting node Expressed as:

[0069] ;

[0070] ;

[0071] ;

[0072] ;

[0073] in, Indicates the credit value paid by the starting node as the computing power demander, Indicates the credit value obtained by the destination node as a supplier, represents the cumulative credit threshold of the starting node, Indicates the starting credit threshold of the starting node, Indicates the computing power required by the computing business. Indicates that the starting node and the destination node belong to the same operator, otherwise it is 0. It means deploying computing power business through spectrum trading. Indicates the deployment of computing power business through computing power trading;

[0074] The computing power transaction credit constraints include:

[0075] ;

[0076] ;

[0077] ;

[0078] ;

[0079] ;

[0080] ;

[0081] in, Indicates the starting node Transmit computing power services through virtual link k The starting index of the occupied frequency slot, Indicates the starting node Transmit computing power services through virtual link k The occupied frequency slot end index, Indicates the frequency slot start index of the virtual link, Indicates the frequency slot end index of the virtual link, Indicates the minimum threshold of the cumulative credit threshold of the starting node, represents the positive maximum value, represents a positive minimum, Indicates that the cumulative credit threshold of the starting node is not less than the minimum threshold, Representation node With Virtual Link Virtual optical network Belong to the same operator.

[0082] As a preferred technical solution of the present invention, if spectrum resources are lacking during the direct deployment of computing power services, determining whether spectrum trading credit constraints are met, and if so, conducting spectrum trading to deploy computing power services; if spectrum resources are lacking during the computing power trading process, determining whether spectrum trading credit constraints are met, and if so, conducting spectrum trading to deploy computing power services, includes:

[0083] When spectrum resources are insufficient during direct deployment or computing power trading deployment, determine whether spectrum trading credit constraints are met, including virtual link frequency slot status constraints, physical link frequency slot status constraints, spectrum trading request constraints, spectrum credit threshold constraints, and spectrum trading credit constraints.

[0084] The virtual link frequency slot state constraint is expressed as:

[0085] ;

[0086] ;

[0087] ;

[0088] ;

[0089] in, Indicates the starting node Transmit computing power services through virtual link k The starting index of the occupied frequency slot, Indicates the starting node Transmit computing power services through virtual link k The occupied frequency slot end index, represents a positive minimum, Indicates computing power business Deployment is successful. represents the frequency slot index, represents the positive maximum value, Indicates the index in the frequency slot Not less than the starting index Its value is 1 when , otherwise it is 0. Indicates the index in the frequency slot Not greater than the ending index Its value is 1 when , otherwise it is 0;

[0090] The physical link frequency slot state constraint is expressed as:

[0091] ;

[0092] ;

[0093] ;

[0094] in, Indicates the frequency slot usage status of the physical link. Indicates the actual usage status of the physical link. represents the frequency slot set, represents the set of physical links that virtual link k passes through, Indicates the set of physical links that the virtual link does not pass through. represents the set of all physical links, T represents the time set, Represents a set of virtual links;

[0095] The spectrum trading request constraint is expressed as:

[0096] ;

[0097] in, Indicates that if the computing power business requests spectrum trading, its value is 1, otherwise it is 0;

[0098] The spectrum credit threshold constraint is expressed as:

[0099] ;

[0100] ;

[0101] ;

[0102] ;

[0103] in, Indicates the spectrum credit value of the virtual optical network to which the destination node belongs at the starting time. represents the cumulative spectrum credit value of the virtual optical network to which the destination node belongs at time t, represents the threshold of the cumulative spectrum credit value, Indicates the frequency slot start index of the virtual link, Indicates the frequency slot end index of the virtual link, Indicates that the cumulative spectrum credit value is not less than the threshold , Indicates at time Virtual Link The left endpoint of Deploy the left endpoint computing power business to the right endpoint for the starting node The number of frequency slots required, Indicates virtual link The right endpoint The left endpoint of the starting node Deploy the right endpoint service The number of frequency slots required;

[0104] The spectrum trading credit constraint is expressed as:

[0105] ;

[0106] ;

[0107] in, It means deploying computing power business through spectrum trading. Indicates a virtual link Virtual optical network At the current moment Whether the spectrum credit meets the requirements, if yes, it is 1, otherwise 0, Indicates the starting node With Virtual Link Virtual optical network belongs to the same operator, otherwise 0, Indicates that the starting node z and the destination node belong to the same operator, Indicates that the cumulative credit threshold of the starting node is not less than the minimum threshold;

[0108] Traverse the virtual optical networks managed by other operators to find a virtual link with the same physical path as the current virtual link, and determine whether its idle frequency slot can meet the spectrum trading credit constraints. If so, spectrum trading is carried out. Spectrum trading satisfies:

[0109] ;

[0110] ;

[0111] ;

[0112] ;

[0113] ;

[0114] ;

[0115] in, Indicates the maximum index of the frequency slot.

[0116] As a preferred technical solution of the present invention, the deployment computing power business meets the following requirements:

[0117] ;

[0118] ;

[0119] ;

[0120] ;

[0121] in, Indicates computing power business Deployment is successful. It means using the computing power resources within the operator to directly deploy computing power services. Indicates the deployment of computing power business through computing power transactions. It means deploying computing power business through spectrum trading. Indicates that the starting node and the destination node belong to the same operator, otherwise it is 0. Indicates the starting node With Virtual Link Virtual optical network Belong to the same operator.

[0122] Compared with the prior art, the present invention has the following beneficial effects:

[0123] The present invention provides a computing power service deployment method for a distributed intelligent computing center network, which realizes flexible allocation of multi-dimensional resources based on the distribution of computing power resources within and outside operators in the network and the amount of network spectrum resources, efficiently couples the computing power resources of different operators with the network resource allocation and transaction process, and improves the working efficiency of the distributed intelligent computing center network by enhancing the degree of coordination between computing and network. BRIEF DESCRIPTION OF THE DRAWINGS

[0124] Figure 1 This is a flowchart of a computing power service deployment algorithm method according to an embodiment of the present invention;

[0125] Figure 2 It is a flowchart of the computing power business deployment model method in an embodiment of the present invention. DETAILED DESCRIPTION

[0126] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0127] The present invention provides a computing power service deployment method for a distributed intelligent computing center network, including an algorithm deployment method and a model deployment method. The algorithm deployment method is applicable to actual system deployment services, and the model deployment method is applicable to solving the theoretical optimal deployment method. In a distributed intelligent computing center network, multiple operators independently manage their own computing power resources and spectrum resources and deploy services through their own virtual optical network (VON).

[0128] Example 1

[0129] This embodiment provides a computing power service deployment method for a distributed intelligent computing center network, which uses an algorithm for deployment.

[0130] like Figure 1 As shown, the method includes:

[0131] Step 1: Obtain several computing services of the distributed intelligent computing center network, which include a list of starting nodes and destination nodes to be selected.

[0132] The computing power business is represented as ;

[0133] in, Indicates the computing power required by the computing business. Indicates the traffic required by the computing business. Indicates the starting node of the computing power business. Indicates the computing power business on the starting node Through virtual link The destination node for deployment.

[0134] Step 2: Determine the destination node based on the idle computing resources of the nodes in the destination node candidate list and the routing status with the starting node.

[0135] All nodes in the destination node candidate list are traversed, and the idle computing power resources of each node are used as the initial state score of each node.

[0136] Determine whether the starting node and the nodes in the target node candidate list belong to the same operator. If they do not, deduct the node's starting status score. In this embodiment, if they belong to the same operator, the starting status score remains unchanged; if they do not belong to the same operator, the status score is updated to 0.85 * starting status score.

[0137] The Dijstra algorithm is used to determine the number of hops from the starting node to the destination node in the candidate list. The final state score is updated based on the number of hops. The final state score = current state score * (1 - 0.15 * number of hops).

[0138] The higher the final state score, the more compatible the node is with the business to be processed in terms of computing power resources and spectrum resources. The node with the highest final state score will be used as the destination node.

[0139] Step 3: Based on the starting node and the destination node, deploy computing power services through spectrum trading, computing power trading, or joint trading.

[0140] Allocate sufficient spectrum resources for the computing service on the routing-related physical links, and allocate sufficient computing resources for the computing service at the destination node to complete the computing service deployment. If either resource requirement is not met, the computing service deployment is considered a failure and the next computing service deployment is carried out.

[0141] Before deploying computing power services through spectrum trading, computing power trading or joint trading, select different modulation formats such as BPSK, QPSK, 8-QAM according to the routing distance, and select the bandwidth and modulation format efficiency required by the business. , calculate the number of frequency slots required for computing power business, expressed as:

[0142] ;

[0143] in, represents the number of frequency slots, Indicates the traffic required by the computing business. represents the frequency slot bandwidth, Indicates the modulation format efficiency of the path.

[0144] (1) The spectrum trading includes:

[0145] The spectrum resources corresponding to the path are traversed within the virtual optical network controlled by the operator to which the starting node belongs. If a frequency slot that meets the service requirements exists, the system determines whether the starting and destination nodes belong to the same operator. If so, the computing service is deployed. If not, the computing service is added to the blocking queue and the next computing service in the queue is prepared for deployment. Based on the resource requirements of the computing service, equal resources are allocated at the destination node and on the associated route. After resource allocation, the computing service deployment is complete, and the next computing service in the queue is executed, continuing until there are no more undeployed computing services in the sequence.

[0146] The service requirements are spectrum continuity and non-overlapping, and the length of the idle spectrum block to be searched must be greater than the minimum number of frequency slots required by the service.

[0147] (2) The computing power transaction includes:

[0148] Traverse the spectrum resources corresponding to the path in the virtual optical network controlled by the operator to which the starting node belongs. If there is a frequency gap that meets the service requirements, determine whether the starting node and the destination node belong to the same operator. If they are the same, deploy computing power services. If they are different, determine the cumulative credit threshold of the starting node. Is it not less than the minimum threshold? If the conditions are met, the starting node will pay the supply node a computing power credit value equal to the transaction resource volume. After the starting node and the supply node update the accumulated credit value, the computing power business will be deployed.

[0149] (3) The joint transaction includes:

[0150] Traverse the spectrum resources corresponding to the path in the virtual optical network controlled by the operator to which the starting node belongs. If there is a frequency gap that meets the business requirements, determine whether the starting node and the destination node belong to the same operator. If they are the same, deploy computing power services. If they are different, conduct computing power transactions to deploy computing power services. If there is no frequency gap that meets the business requirements, determine the accumulated spectrum credit value of the virtual optical network to which the destination node belongs. Is it not less than the threshold of the cumulative spectrum credit value? ,in Virtual optical network At the moment If the credit threshold is met, the system traverses the virtual optical networks managed by other operators to find a virtual link with the same physical path as the current virtual link, and determines whether its idle frequency slot can meet the service requirements. If so, the system updates the accumulated spectrum credit value of both virtual optical networks and deploys computing power services.

[0151] Example 2

[0152] This embodiment provides a computing power service deployment method for a distributed intelligent computing center network, which adopts a model for deployment.

[0153] like Figure 2 As shown, the method includes:

[0154] Step 1: Obtain several computing services of the distributed intelligent computing center network, which include a list of starting nodes and destination nodes to be selected.

[0155] The computing power business is represented as ;

[0156] in, Indicates the computing power required by the computing business. Indicates the traffic required by the computing business. Indicates the starting node of the computing power business. Indicates the computing power business on the starting node Through virtual link The destination node for deployment.

[0157] Step 2: Input the computing power business into a pre-built business deployment model including an objective function and constraints, and solve the business deployment model to obtain a computing power business deployment plan; wherein, the objective function takes the maximum computing power resource utilization as the optimization goal, and the constraints include computing power resource constraints, frequency slot resource constraints, spectrum resource constraints, spectrum trading credit constraints, and computing power trading credit constraints.

[0158] Wherein, solving the business deployment model to obtain a computing power business deployment solution includes:

[0159] Step 2.1: According to the computing power resource constraints, the frequency slot resource constraints, and the spectrum resource constraints, a destination node is selected from the destination node candidate list of the computing power service.

[0160] Selecting the destination node requires ensuring the current time The total computing power demand of all businesses carried by the node does not exceed the maximum load of the node, that is, the remaining idle computing power resources of the node are not less than 0.

[0161] The nodes whose remaining idle computing power resources are not less than 0 in the target node candidate list are screened out by the computing power resource constraint, which is expressed as:

[0162] ;

[0163] in, Indicates the computing power of the nodes in the destination node candidate list, It represents the set of virtual links where the starting node is located, S represents the set of computing power services s, Indicates the amount of computing resources required for the computing business. Indicates that the computing power business s is deployed successfully, otherwise it is 0. N represents the set of starting nodes z, and T represents the set of time t.

[0164] After screening, the Dijstra algorithm is used to determine the path from the starting node to the node with a remaining idle computing power resource of not less than 0. Different modulation formats such as BPSK, QPSK, and 8-QAM are selected based on the path distance and their corresponding modulation format efficiency to calculate the number of frequency slots required for the computing power service, which is expressed as:

[0165] ;

[0166] in, represents the number of frequency slots, Indicates the traffic required by the computing business. represents the frequency slot bandwidth, Indicates the modulation format efficiency of the path.

[0167] Traverse the spectrum resources corresponding to the path in the virtual optical network controlled by the operator to which the starting node belongs. Service transmission requires spectrum continuity. The length of the idle spectrum block searched must be greater than the number of frequency slots required for service transmission. The total number of frequency slots used by services carried by each link cannot exceed the maximum capacity of each link. Spectrum overlap and unallocated spectrum resources must be avoided between different services on the same virtual link, and between different services on different virtual links but traversing the same physical link. The node with the shortest path that meets both frequency slot and spectrum resource constraints is selected as the destination node.

[0168] (1) The frequency slot resource constraints include frequency slot usage constraints, frequency slot quantity constraints, frequency slot unallocated constraints, and frequency slot non-overlap constraints.

[0169] The frequency slot usage constraint is that the start index of the occupied frequency slot is less than the end index, the service frequency slot deployed without spectrum trading cannot exceed the link range, and the occupied frequency slots are continuously available, which can be expressed as:

[0170] ;

[0171] ;

[0172] ;

[0173] in, Indicates the starting node Transmit computing power services through virtual link k The starting index of the occupied frequency slot, Indicates the starting node Transmit computing power services through virtual link k The occupied frequency slot end index, Indicates the frequency slot start index of the virtual link, Indicates the frequency slot end index of the virtual link, It means using the computing power resources within the operator to directly deploy computing power services. Indicates computing power business Deployment successful.

[0174] The frequency slot quantity constraint is the number of frequency slots occupied by the service Not less than the number of frequency slots required for business transmission , expressed as:

[0175] ;

[0176] ;

[0177] ;

[0178] in, Indicates the number of frequency slots occupied by computing power business transmission, Indicates a positive minimum.

[0179] The frequency slot unassignment constraint is to not use the unassigned frequency slots, which is expressed as:

[0180] ;

[0181] in, Indicates that the physical link The index on If the frequency slot is not allocated, , represents the frequency slot set, Indicates the physical link that virtual link k passes through A collection of Indicates a positive maximum value.

[0182] The frequency slot non-overlap constraint means that the frequency slots occupied by different services on the same virtual link do not overlap, which is expressed as:

[0183] ;

[0184] ;

[0185] ;

[0186] in, Indicates that at the starting node Through virtual link Transmission computing power business When computing power business The starting index of the occupied frequency slot is greater than the computing power business The starting index of the occupied frequency slot, then , Indicates that at the starting node Through virtual link Transmission computing power business When computing power business The starting index of the occupied frequency slot is greater than the computing power business The starting index of the occupied frequency slot, then , otherwise 0.

[0187] (2) The spectrum resource constraints include virtual link capacity constraints and spectrum non-overlap constraints.

[0188] The virtual link capacity constraint means that the spectrum occupied by all services does not exceed the bearer link capacity, which is expressed as:

[0189] ;

[0190] The spectrum non-overlap constraint is used to prevent spectrum overlap when computing services are transmitted on different virtual links over the same physical link. It is expressed as:

[0191] ;

[0192] ;

[0193] ;

[0194] ;

[0195] in, Indicates at time Starting Node Through virtual link Transmission computing power business , starting node Through virtual link Transmission computing power business , the two virtual links pass through the same physical link, computing power business The occupied starting frequency slot range index is greater than the computing power business The occupied starting frequency slot range index is , otherwise 0, Indicates a virtual link and Through the same physical link, Indicates the starting node Through virtual link Transmission computing power business The starting index of the occupied frequency slot, Indicates the starting node Through virtual link Transmission computing power business End index of the occupied frequency slot.

[0196] Step 2.2: If the destination node and the starting node belong to the same operator, the computing power service is directly deployed using the computing power resources within the operator. If the destination node and the starting node do not belong to the same operator, determine whether the computing power transaction credit constraints are met. If so, conduct a computing power transaction to deploy the computing power service. If spectrum resources are lacking during the direct deployment of the computing power service, determine whether the spectrum transaction credit constraints are met. If so, conduct a spectrum transaction to deploy the computing power service. If spectrum resources are lacking during the computing power transaction, determine whether the spectrum transaction credit constraints are met. If so, conduct a spectrum transaction to deploy the computing power service.

[0197] Determine whether the current starting node and destination node belong to the same operator. If they are the same, the computing power resources within the operator can be used to directly deploy the service. Otherwise, determine the time Cumulative credit threshold of the next starting node Is it greater than the minimum threshold? If the computing power resources required by the business are met, the starting node pays the supply node an amount of computing power credit equal to the transaction resource amount, updates the accumulated computing power credit value, and conducts computing power transactions.

[0198] Specifically, if the destination node and the starting node do not belong to the same operator, it is determined whether the cumulative credit threshold of the starting node at time t is not less than the minimum threshold. Expressed as:

[0199] ;

[0200] ;

[0201] ;

[0202] ;

[0203] in, Indicates the credit value paid by the starting node as the computing power demander, Indicates the credit value obtained by the destination node as a supplier, represents the cumulative credit threshold of the starting node, Indicates the starting credit threshold of the starting node, Indicates the computing power required by the computing business. Indicates that the starting node and the destination node belong to the same operator, otherwise it is 0. It means deploying computing power business through spectrum trading. Indicates deploying computing power business through computing power trading.

[0204] The computing power transaction credit constraints include:

[0205] ;

[0206] ;

[0207] ;

[0208] ;

[0209] ;

[0210] ;

[0211] in, Indicates the starting node Transmit computing power services through virtual link k The starting index of the occupied frequency slot, Indicates the starting node Transmit computing power services through virtual link k The occupied frequency slot end index, Indicates the frequency slot start index of the virtual link, Indicates the frequency slot end index of the virtual link, Indicates the minimum threshold of the cumulative credit threshold of the starting node, represents the positive maximum value, represents a positive minimum, Indicates that the cumulative credit threshold of the starting node is not less than the minimum threshold, Representation node With Virtual Link Virtual optical network Belong to the same operator.

[0212] When spectrum resources are lacking during direct deployment or computing power trading deployment, it is determined whether the spectrum trading credit constraints are met, including virtual link frequency slot status constraints, physical link frequency slot status constraints, spectrum trading request constraints, spectrum credit threshold constraints, and spectrum trading credit constraints.

[0213] The virtual link frequency slot state constraint determines the usage state of each frequency slot on the virtual link, which is expressed as:

[0214] ;

[0215] ;

[0216] ;

[0217] ;

[0218] in, Indicates the starting node Transmit computing power services through virtual link k The starting index of the occupied frequency slot, Indicates the starting node Transmit computing power services through virtual link k The occupied frequency slot end index, represents a positive minimum, Indicates computing power business Deployment is successful. represents the frequency slot index, represents the positive maximum value, Indicates the index in the frequency slot Not less than the starting index Its value is 1 when , otherwise it is 0. Indicates the index in the frequency slot Not greater than the ending index Its value is 1 when , otherwise it is 0.

[0219] The physical link frequency slot state constraint is expressed as:

[0220] ;

[0221] ;

[0222] ;

[0223] in, Indicates the frequency slot usage status of the physical link. Indicates the actual usage status of the physical link. Indicates it is occupied, otherwise it is idle. represents the frequency slot set, represents the set of physical links that virtual link k passes through, Indicates the set of physical links that the virtual link does not pass through. represents the set of all physical links, T represents the time set, Indicates a set of virtual links.

[0224] Determine the virtual optical network VON to which the current destination node belongs at the current moment The accumulated spectrum credit value If it is greater than the minimum threshold Limit, traverse the virtual optical networks managed by other operators, and search for virtual links that are related to the current virtual link The virtual links with the same physical path are searched to see if their idle frequency slots can meet the service requirements. If they meet the service requirements, spectrum trading is carried out. The accumulated credit value of the virtual optical network of both parties is updated according to the number of frequency slots traded. Otherwise, the service is blocked. The spectrum trading request constraint is to attempt spectrum trading for services that have failed to deploy in other ways, which is expressed as:

[0225] ;

[0226] in, Indicates that if the computing power business requests spectrum trading, its value is 1, otherwise it is 0.

[0227] The spectrum credit threshold constraint is expressed as:

[0228] ;

[0229] ;

[0230] ;

[0231] ;

[0232] in, Indicates the spectrum credit value of the virtual optical network to which the destination node belongs at the starting time. represents the cumulative spectrum credit value of the virtual optical network to which the destination node belongs at time t, represents the threshold of the cumulative spectrum credit value, Indicates the frequency slot start index of the virtual link, Indicates the frequency slot end index of the virtual link, Indicates that the cumulative spectrum credit value is not less than the threshold , Indicates at time Virtual Link The left endpoint of Deploy the left endpoint computing power business to the right endpoint for the starting node The number of frequency slots required, Indicates virtual link The right endpoint The left endpoint of the starting node Deploy the right endpoint service The number of frequency slots required.

[0233] The spectrum trading credit constraint is expressed as:

[0234] ;

[0235] ;

[0236] Among them, spectrum trading allows two nodes within an operator to trade spectrum, and also allows two nodes to conduct computing power trading and spectrum trading at the same time. It means deploying computing power business through spectrum trading. Indicates a virtual link Virtual optical network At the current moment Whether the spectrum credit meets the requirements, if yes, it is 1, otherwise 0, Indicates the starting node With Virtual Link Virtual optical network belongs to the same operator, otherwise 0, Indicates that the starting node z and the destination node belong to the same operator, Indicates that the cumulative credit threshold of the starting node is not less than the minimum threshold.

[0237] Traverse the virtual optical networks managed by other operators to find a virtual link with the same physical path as the current virtual link, and determine whether its idle frequency slots can meet the spectrum trading credit constraints. If so, spectrum trading is carried out and the accumulated credit values ​​of both parties' VONs are updated according to the number of frequency slots traded. Spectrum trading satisfies:

[0238] ;

[0239] ;

[0240] ;

[0241] ;

[0242] ;

[0243] ;

[0244] in, Indicates the maximum index of the frequency slot.

[0245] Regardless of whether direct deployment, computing power trading deployment, or spectrum trading deployment is used, services are deployed based on the occupied computing power resource destination node and the spectrum resources of the relevant routes. After the resources are allocated, the service deployment ends and the next computing power service in the queue is executed until all computing power services are deployed. The deployed computing power service meets the following requirements:

[0246] ;

[0247] ;

[0248] ;

[0249] ;

[0250] in, Indicates computing power business Deployment is successful. It means using the computing power resources within the operator to directly deploy computing power services. Indicates the deployment of computing power business through computing power transactions. It means deploying computing power business through spectrum trading. Indicates that the starting node and the destination node belong to the same operator, otherwise it is 0. Indicates the starting node With Virtual Link Virtual optical network Belong to the same operator.

[0251] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0252] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0253] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0254] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0255] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A computing power service deployment method for a distributed intelligent computing center network, characterized in that: include: Obtaining several computing services of the distributed intelligent computing center network, wherein the computing services include a list of start nodes and destination nodes to be selected; Determine the destination node based on the idle computing resources of the nodes in the destination node candidate list and the routing status with the starting node; Based on the starting node and the destination node, computing power services are deployed through spectrum trading, computing power trading or joint trading.

2. The computing power service deployment method for a distributed intelligent computing center network according to claim 1 is characterized in that: The computing power business is represented as ; in, Indicates the computing power required by the computing business. Indicates the traffic required by the computing power business. Indicates the starting node of the computing power business. Indicates the computing power business on the starting node Through virtual link The destination node for deployment.

3. The computing power service deployment method for a distributed intelligent computing center network according to claim 1 is characterized in that: The determining of the destination node according to the idle computing resources of the nodes in the destination node candidate list and the routing status with the starting node includes: Traversing all nodes in the target node candidate list, and using the idle computing power resources of each node as the starting state score of each node; Determine whether the starting node and the nodes in the destination node candidate list belong to the same operator. If they are different, deduct the starting status score of the node; Determine the number of routing hops from the starting node to the nodes in the destination node candidate list according to the Dijstra algorithm, and update the final state score according to the number of routing hops; The node with the highest final state score is taken as the destination node.

4. The computing power service deployment method for a distributed intelligent computing center network according to claim 1 is characterized in that: The deployment of computing power services based on the starting node and the destination node through spectrum trading, computing power trading, or combined trading includes: Before deploying computing power services through spectrum trading, computing power trading, or joint trading, calculate the number of frequency slots required for the computing power service, expressed as: ； in, represents the number of frequency slots, Indicates the traffic required by the computing power business. represents the frequency slot bandwidth, Indicates the modulation format efficiency of the path; The spectrum trading includes: Traverse the spectrum resources corresponding to the path in the virtual optical network controlled by the operator to which the starting node belongs. If there is a frequency gap that meets the service requirements, determine whether the starting node and the destination node belong to the same operator. If they do, deploy computing power services; The computing power transaction includes: Traverse the spectrum resources corresponding to the path in the virtual optical network controlled by the operator to which the starting node belongs. If there is a frequency gap that meets the service requirements, determine whether the starting node and the destination node belong to the same operator. If they are the same, deploy computing power services. If they are different, determine the cumulative credit threshold of the starting node. Is it not less than the minimum threshold? If the conditions are met, the starting node pays the supply node a computing power credit equal to the transaction resource volume. After the starting node and the supply node update the accumulated credit value, the computing power business is deployed. The joint transaction includes: Traverse the spectrum resources corresponding to the path in the virtual optical network controlled by the operator to which the starting node belongs. If there is a frequency gap that meets the business requirements, determine whether the starting node and the destination node belong to the same operator. If they are the same, deploy computing power services. If they are different, conduct computing power transactions to deploy computing power services. If there is no frequency gap that meets the business requirements, determine the accumulated spectrum credit value of the virtual optical network to which the destination node belongs. Is it not less than the threshold of the cumulative spectrum credit value? ,in Virtual optical network At the moment If the credit threshold is met, the system traverses the virtual optical networks managed by other operators to find a virtual link with the same physical path as the current virtual link, and determines whether its idle frequency slot can meet the service requirements. If so, the system updates the accumulated spectrum credit value of both virtual optical networks and deploys computing power services.

5. A computing power service deployment method for a distributed intelligent computing center network, characterized in that: include: Obtaining several computing services of the distributed intelligent computing center network, wherein the computing services include a list of start nodes and destination nodes to be selected; The computing power service is input into a pre-built service deployment model including an objective function and constraints, and the service deployment model is solved to obtain a computing power service deployment plan; wherein the objective function is to maximize computing power resource utilization as the optimization goal, and the constraints include computing power resource constraints, frequency slot resource constraints, spectrum resource constraints, spectrum trading credit constraints, and computing power trading credit constraints; Wherein, solving the business deployment model to obtain a computing power business deployment solution includes: According to the computing power resource constraints, the frequency slot resource constraints, and the spectrum resource constraints, a destination node is selected from the destination node candidate list of the computing power service; If the destination node and the starting node belong to the same operator, the computing power services are directly deployed using the computing power resources within the operator. If the destination node and the starting node do not belong to the same operator, it is determined whether the computing power transaction credit constraints are met. If so, computing power transaction is carried out to deploy computing power services. If spectrum resources are lacking during the direct deployment of computing power services, it is determined whether the spectrum transaction credit constraints are met. If so, spectrum transaction is carried out to deploy computing power services. If spectrum resources are lacking during the computing power transaction process, it is determined whether the spectrum transaction credit constraints are met. If so, spectrum transaction is carried out to deploy computing power services.

6. The computing power service deployment method for a distributed intelligent computing center network according to claim 5 is characterized in that: The selecting a destination node from the destination node candidate list of the computing service according to the computing power resource constraint, the frequency slot resource constraint, and the spectrum resource constraint includes: The nodes in the target node candidate list with the remaining idle computing power resources not less than 0 are selected by using the computing power resource constraint, which is expressed as: ； in, Indicates the computing power of the nodes in the destination node candidate list, It represents the set of virtual links where the starting node is located, S represents the set of computing power services s, Indicates the amount of computing resources required for the computing business. Indicates that the computing power business s is deployed successfully, otherwise it is 0. N represents the set of starting nodes z, and T represents the set of time t; After screening, the Dijstra algorithm is used to determine the path from the starting node to the node with a remaining idle computing power resource of not less than 0, in order to calculate the number of frequency slots required for the computing power business; The spectrum resources corresponding to the path are traversed in the virtual optical network controlled by the operator to which the starting node belongs, and the node with the shortest path that meets the frequency slot resource constraints and spectrum resource constraints is selected as the destination node.

7. The computing power service deployment method for a distributed intelligent computing center network according to claim 6 is characterized in that: The frequency slot resource constraints include frequency slot usage constraints, frequency slot quantity constraints, frequency slot unallocated constraints, and frequency slot non-overlap constraints; The frequency slot usage constraint is expressed as: ； ； ； in, Indicates the starting node Transmit computing power services through virtual link k The starting index of the occupied frequency slot, Indicates the starting node Transmit computing power services through virtual link k The occupied frequency slot end index, Indicates the frequency slot start index of the virtual link, Indicates the frequency slot end index of the virtual link, It means using the computing power resources within the operator to directly deploy computing power services. Indicates computing power business Deployment was successful; The frequency slot quantity constraint is expressed as: ； ； ； in, Indicates the number of frequency slots occupied by computing power business transmission, represents a positive minimum; The frequency slot unassignment constraint is expressed as: ； in, Indicates that the physical link The index on If the frequency slot is not allocated, , represents the frequency slot set, Indicates the physical link that virtual link k passes through A collection of Indicates a positive maximum value; The frequency slot non-overlap constraint is expressed as: ； ； ； in, Indicates that at the starting node Through virtual link Transmission computing power business When computing power business The starting index of the occupied frequency slot is greater than the computing power business The starting index of the occupied frequency slot, then , Indicates that at the starting node Through virtual link Transmission computing power business If the computing power business The starting index of the occupied frequency slot is greater than the computing power business The starting index of the occupied frequency slot, then ; The spectrum resource constraints include virtual link capacity constraints and spectrum non-overlap constraints; The virtual link capacity constraint is expressed as: ； The spectrum non-overlap constraint is used to prevent spectrum overlap when computing services are transmitted on different virtual links over the same physical link. It is expressed as: ； ； ； ； in, Indicates at time Starting Node Through virtual link Transmission computing power business , starting node Through virtual link Transmission computing power business , the two virtual links pass through the same physical link, computing power business The occupied starting frequency slot range index is greater than the computing power business The occupied starting frequency slot range index is , otherwise 0, Indicates a virtual link and Through the same physical link, Indicates the starting node Through virtual link Transmission computing power business The starting index of the occupied frequency slot, Indicates the starting node Through virtual link Transmission computing power business End index of the occupied frequency slot.

8. The computing power service deployment method for a distributed intelligent computing center network according to claim 5, characterized in that: If the destination node and the starting node do not belong to the same operator, determining whether the computing power transaction credit constraint is satisfied. If the computing power transaction credit constraint is satisfied, performing computing power transaction to deploy computing power services includes: If the destination node and the starting node do not belong to the same operator, determine whether the cumulative credit threshold of the starting node at time t is not less than the minimum threshold, the cumulative credit threshold of the starting node Expressed as: ； ； ； ； in, Indicates the credit value paid by the starting node as the computing power demander, Indicates the credit value obtained by the destination node as a supplier, represents the cumulative credit threshold of the starting node, Indicates the starting credit threshold of the starting node, Indicates the computing power required by the computing business. Indicates that the starting node and the destination node belong to the same operator, otherwise it is 0. It means deploying computing power business through spectrum trading. Indicates the deployment of computing power business through computing power trading; The computing power transaction credit constraints include: ； ； ； ； ； ； in, Indicates the starting node Transmit computing power services through virtual link k The starting index of the occupied frequency slot, Indicates the starting node Transmit computing power services through virtual link k The occupied frequency slot end index, Indicates the frequency slot start index of the virtual link, Indicates the frequency slot end index of the virtual link, Indicates the minimum threshold of the cumulative credit threshold of the starting node, represents the positive maximum value, represents a positive minimum, Indicates that the cumulative credit threshold of the starting node is not less than the minimum threshold, Representation node With Virtual Link Virtual optical network Belong to the same operator.

9. The computing power service deployment method for a distributed intelligent computing center network according to claim 5, characterized in that: If spectrum resources are lacking during the direct deployment of computing power services, determining whether spectrum transaction credit constraints are met, and if so, conducting spectrum transactions to deploy computing power services; If spectrum resources are insufficient during computing power transactions, the system determines whether the spectrum transaction credit constraints are met. If so, spectrum transactions are conducted to deploy computing power services, including: When spectrum resources are insufficient during direct deployment or computing power trading deployment, determine whether spectrum trading credit constraints are met, including virtual link frequency slot status constraints, physical link frequency slot status constraints, spectrum trading request constraints, spectrum credit threshold constraints, and spectrum trading credit constraints. The virtual link frequency slot state constraint is expressed as: ； ； ； ； in, Indicates the starting node Transmit computing power services through virtual link k The starting index of the occupied frequency slot, Indicates the starting node Transmit computing power services through virtual link k The occupied frequency slot end index, represents a positive minimum, Indicates computing power business Deployment is successful. represents the frequency slot index, represents the positive maximum value, Indicates the index in the frequency slot Not less than the starting index Its value is 1 when , otherwise it is 0. Indicates the index in the frequency slot Not greater than the ending index Its value is 1 when , otherwise it is 0; The physical link frequency slot state constraint is expressed as: ； ； ； in, Indicates the frequency slot usage status of the physical link. Indicates the actual usage status of the physical link. represents the frequency slot set, represents the set of physical links that virtual link k passes through, Indicates the set of physical links that the virtual link does not pass through. represents the set of all physical links, T represents the time set, Represents a set of virtual links; The spectrum trading request constraint is expressed as: ； in, Indicates that if the computing power business requests spectrum trading, its value is 1, otherwise it is 0; The spectrum credit threshold constraint is expressed as: ； ； ； ； in, Indicates the spectrum credit value of the virtual optical network to which the destination node belongs at the starting time. represents the cumulative spectrum credit value of the virtual optical network to which the destination node belongs at time t, represents the threshold of the cumulative spectrum credit value, Indicates the frequency slot start index of the virtual link, Indicates the frequency slot end index of the virtual link, Indicates that the cumulative spectrum credit value is not less than the threshold , Indicates at time Virtual Link The left endpoint of Deploy the left endpoint computing power business to the right endpoint for the starting node The number of frequency slots required, Indicates virtual link The right endpoint The left endpoint of the starting node Deploy right endpoint services The number of frequency slots required; The spectrum trading credit constraint is expressed as: ； ； in, It means deploying computing power business through spectrum trading. Indicates a virtual link Virtual optical network At the current moment Whether the spectrum credit meets the requirements, if yes, it is 1, otherwise 0, Indicates the starting node With Virtual Link Virtual optical network belongs to the same operator, otherwise 0, Indicates that the starting node z and the destination node belong to the same operator, Indicates that the cumulative credit threshold of the starting node is not less than the minimum threshold; Traverse the virtual optical networks managed by other operators to find a virtual link with the same physical path as the current virtual link, and determine whether its idle frequency slot can meet the spectrum trading credit constraints. If so, spectrum trading is carried out. Spectrum trading satisfies: ； ； ； ； ； ； in, Indicates the maximum index of the frequency slot.

10. The computing power service deployment method for a distributed intelligent computing center network according to claim 5, characterized in that: The deployment computing power business meets the following requirements: ； ； ； ； in, Indicates computing power business Deployment is successful. It means using the computing power resources within the operator to directly deploy computing power services. Indicates the deployment of computing power business through computing power transactions. It means deploying computing power business through spectrum trading. Indicates that the starting node and the destination node belong to the same operator, otherwise it is 0. Indicates the starting node With Virtual Link Virtual optical network Belong to the same operator.

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