CN111614571B - Distributed key task end-to-end time delay optimization method and system - Google Patents

Distributed key task end-to-end time delay optimization method and system Download PDF

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CN111614571B
CN111614571B CN202010340849.9A CN202010340849A CN111614571B CN 111614571 B CN111614571 B CN 111614571B CN 202010340849 A CN202010340849 A CN 202010340849A CN 111614571 B CN111614571 B CN 111614571B
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model
variable
demand
virtual path
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CN111614571A (en
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王莹
陈源彬
汪洋
王智慧
汤亿则
王彦波
孟萨出拉
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State Grid Corp of China SGCC
Beijing University of Posts and Telecommunications
China Electric Power Research Institute Co Ltd CEPRI
Information and Telecommunication Branch of State Grid Zhejiang Electric Power Co Ltd
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State Grid Corp of China SGCC
Beijing University of Posts and Telecommunications
China Electric Power Research Institute Co Ltd CEPRI
Information and Telecommunication Branch of State Grid Zhejiang Electric Power Co Ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L47/00—Traffic control in data switching networks
    • H04L47/10—Flow control; Congestion control
    • H04L47/18—End to end
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L47/00—Traffic control in data switching networks
    • H04L47/10—Flow control; Congestion control
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L47/00—Traffic control in data switching networks
    • H04L47/10—Flow control; Congestion control
    • H04L47/28—Flow control; Congestion control in relation to timing considerations
    • H04L47/283—Flow control; Congestion control in relation to timing considerations in response to processing delays, e.g. caused by jitter or round trip time [RTT]

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Abstract

The invention provides a distributed key task end-to-end time delay optimization method and a system, comprising the following steps: constructing a weight directed graph of a bottom layer core network according to an end-to-end network; taking a link congestion factor as an optimization variable, and considering a link-path flow recovery design when a link has a fault, constructing a time delay optimization model; and solving the time delay optimization model by adopting Benders decomposition based on an alternative direction multiplier to obtain a distributed link-path flow planning scheme. The embodiment of the invention adopts a simple method to design the bottom core network, creates a problem model aiming at minimizing the maximum link congestion factor, and adopts Benders decomposition based on the alternative direction multiplier to solve the model so as to obtain a distributed link-path flow planning scheme, thereby minimizing the end-to-end key task time delay, considering the flow recovery design of the link-path and effectively improving the optimization efficiency and precision.

Description

Distributed key task end-to-end time delay optimization method and system
Technical Field
The invention relates to the technical field of communication, in particular to a distributed key task end-to-end time delay optimization method and system.
Background
With the rapid development of network technologies, the 5G communication network needs to strictly guarantee QoS end-to-end service delivery of the internet of things device, so that the end-to-end service delivery is required to have characteristics of customization and delay sensitivity, and provide finer-grained service quality for internet of things communication. Typical application scenarios of the internet of things include smart power grids, large-scale mobile social networks, industrial automation and intelligent transportation systems and the like. For end-to-end service delivery, data packets from the radio access network side (RAN) are aggregated and grouped into traffic flows according to service type and then forwarded over a backhaul link to an edge router of the core network.
The QoS requirements required by diversified power services are different as a typical vertical industry of the smart grid. Some time-critical machine-to-machine communication services in the smart grid require networks with ultra-high reliability and low delay; services such as real-time control and dynamic process automatic scheduling need the communication network with extremely high delay capability, and the services can be called as critical task communication in the power grid. For example, for distribution automation with low delay requirements, fault judgment and accurate positioning of distribution network line sections or distribution network equipment can be quickly realized by detecting state information of distribution network lines or equipment, which plays a very important role in power communication, the reliability requirement of the distribution network line sections or the distribution network equipment reaches 99.999%, a high-precision time synchronization requirement and a low delay requirement are required, and the end-to-end transmission delay requirement of communication is less than 10ms or even lower.
The end-to-end power network may include a Radio Access (RAN) portion and a Core Network (CN) portion. On the CN side, each of the partitioned, logically isolated CNs can be made to share underlying network infrastructure (e.g., routes, switches and wired links, etc.) using Software Defined Networking (SDN) and Network Function Virtualization (NFV). Meanwhile, in the core network, VNFs can be flexibly placed in the network, and can dynamically request and release corresponding resources. A set of VNFs and the virtual links connecting them form a logical VNF chain, called Service Function Chain (SFC), representing a specific sequence of network functions that traffic flows need to traverse for E2E service provisioning.
In the face of different kinds of mission critical, the SFC serving the mission critical traffic flows will be composed of VNFs differently set on the routing nodes. For mission critical, the E2E packet delay of delay sensitive traffic flows through SFC is the primary metric indicating slicing performance. However, mission critical communications are still in the early standardization phase of 5G, which brings about many unsolved research issues.
In most existing studies, the E2E packet delay for each traffic flow is calculated as the sum of the packet transmission delays on each physical link, without considering the packet processing delay due to CPU processing on the NFV node. Therefore, how to build an analysis model to evaluate the average packet delay of a traffic flow through SFC is a challenging task and has important significance to the key task of implementing the delay perception of SFC formation.
Disclosure of Invention
The embodiment of the invention provides a distributed end-to-end time delay optimization method and a distributed end-to-end time delay optimization system for key tasks, which are used for overcoming the defects of low calculation efficiency, poor precision calculation, more constraint conditions and the like caused by the fact that the packet transmission delay on each physical link is obtained and the sum of the transmission delays is calculated when the end-to-end time delay optimization calculation is carried out in the prior art.
In a first aspect, an embodiment of the present invention provides a distributed end-to-end latency optimization method for a key task, which mainly includes:
s1, constructing a weight directed graph of a bottom-layer core network according to the distributed key task end-to-end network; s2, according to the weight directed graph, taking a link congestion factor as an optimization variable, considering a link-path flow recovery design when a link has a fault, and constructing a time delay optimization model for minimizing the congestion factor; s3, solving the time delay optimization model by adopting Benders decomposition based on the alternative direction multiplier to obtain a distributed link-path flow planning scheme, so that the time delay of the end-to-end key task is minimized.
Optionally, the step S1 of constructing a weight directed graph of the underlying core network according to the distributed mission-critical end-to-end network may include:
determining a set of physical nodes for a mission-critical end-to-end network
Figure BDA0002468409060000021
A link set epsilon, a processing capacity set V of a node supporting a VNF function, and a link capacity set C; constructing a weight directed graph of a bottom core network according to a physical node set, a link set, a processing capacity set of nodes supporting VNF functions and the link capacity set
Figure BDA0002468409060000031
Optionally, the above-mentioned time delay optimization model for minimizing the congestion factor is constructed by taking the congestion factor of the link as an optimization variable and considering the link-path traffic recovery design when the link has a fault according to the weight directed graph, and its objective function is:
Figure BDA0002468409060000032
the constraint conditions of the time delay optimization model are as follows:
C1-1：
Figure BDA0002468409060000033
C1-2：
Figure BDA0002468409060000034
C1-3:
Figure BDA0002468409060000035
C1-4:
Figure BDA0002468409060000036
C1-5:
Figure BDA0002468409060000037
C1-6:
Figure BDA0002468409060000038
wherein r is a link congestion factor, and e represents a link; p represents a virtual path, h represents the amount of demand between node pairs, d represents the number of demands, hdRepresenting the demanded quantity of the d-th service; s represents the fault state of the link e, wherein s-0 represents that the link e normally operates, and s-e represents that the link e fails;
Figure BDA0002468409060000039
a set of virtual paths feasible for demand d;
Figure BDA00024684090600000310
is a business requirement set;
Figure BDA00024684090600000311
is a link state set; h isd0Indicating the demanded quantity of the d-th service in a normal state; h isdsIndicating the demanded quantity of the d-th service in the state s;xdp0indicating the flow of the demand d on the virtual path p under the normal condition; x is the number ofdpsIndicating the flow of the demand d on the virtual path p in the state s; deltaedpFor a binary constant as a path-link indicator, δ if link e is on virtual path p, for demand d edp1, otherwise δedp＝0；udp0To indicate whether the demand d uses the binary variable of the virtual path p under normal conditions, if the virtual path p is used, u dp01, otherwise, alldp0＝0；udpsTo indicate whether the demand d uses the binary variable of the virtual path p in state s, if the virtual path p is used, u dps1, otherwise, alldps＝0；θdpsA binary constant that is indicative of the availability of the virtual path p of demand d in state s; x is the number ofdpsA recovery flow variable of the virtual path p for the demand d in the state s; x is the number ofdp0Recovering the flow variable of the virtual path p which is the demand d under the normal condition; y iseIs the load on link e; alpha is alphaesIs a binary constant that indicates whether link e is in a failed state s.
Optionally, in the step S3, solving the time-delay optimization model by using Benders' decomposition based on the alternating direction multiplier method may include the following steps:
s3.1, decomposing the time delay optimization model into a first problem model P2 and a main problem model P6 based on Benders decomposition;
s3.2, carrying out feasibility test on the first problem model P2;
s3.3, if the first problem model P2 is feasible, performing P2 solution on the first problem model based on an alternating direction multiplier method to obtain the optimal cut and upper bound information of the Lagrangian multiplier, and feeding back the optimal cut of the Lagrangian multiplier to the main problem model P6;
s3.4, based on the branch-and-bound method, solving the main problem model P6 according to the optimal cut of the Lagrange multiplier so as to update the binary variable u of the initial problem model P2dp0、udpsAnd acquiring lower bound information;
and S3.5, iteratively executing S3.2-S3.4 until the first problem model P2 is judged to be infeasible, and acquiring the load of each link and the flow variable of each virtual path to determine a distributed link-path flow planning scheme.
Optionally, in the step S3.1, decomposing the delay optimization model into a first problem model P2 and a main problem model P6 based on Benders' decomposition may include the following steps:
binary variable u at the time of determining the v-th iterationdp0And udpsThen, acquiring a first problem model P2 according to the time delay optimization model; the objective function of the first problem model P2 is:
Figure BDA0002468409060000041
the constraints of the first problem model P2 are:
C2-1:
Figure BDA0002468409060000051
C2-2:
Figure BDA0002468409060000052
C2-3:
Figure BDA0002468409060000053
C2-4:
Figure BDA0002468409060000054
the objective function of the master problem model P6 is:
Figure BDA0002468409060000055
the constraints of the main problem model P6 are:
C6-1:
Figure BDA0002468409060000056
C6-2:
Figure BDA0002468409060000057
C6-3:
Figure BDA0002468409060000058
C6-4:
Figure BDA0002468409060000059
wherein, V1+V2V is the total number of iterations, V1When the first problem is feasible, solving the iteration times of the first problem; v2To solve l when the first problem is not feasible1-number of iterations in min problem;
Figure BDA00024684090600000510
are respectively the V th1The recovery flow variable of the virtual path p of the demand d in the state s during the secondary iteration;
Figure BDA00024684090600000511
is the V th1Load on link e at the time of the second iteration;
Figure BDA00024684090600000512
is the V th1Lagrange multipliers at a second iteration;
Figure BDA00024684090600000513
a Lagrangian function when the Lagrangian multiplier is optimally cut;
Figure BDA00024684090600000514
and
Figure BDA00024684090600000515
respectively, a Vth corresponding to the optimal cut of the Lagrangian multiplier2And in the secondary iteration, the recovery flow variable of the virtual path p of the demand d in the state s, the load on the link e and the Lagrangian multiplier are required.
Optionally, in S3.3, if the first problem model P2 is feasible, solving the first problem model P2 based on an alternating direction multiplier method specifically includes the following steps:
s3.3.1, obtaining Lagrangian function of the first problem model P2
Figure BDA00024684090600000516
Figure BDA0002468409060000061
Wherein λ ═ λ (λ)1,λ2,λ3,λ4) In order to be a lagrange multiplier,
Figure BDA0002468409060000062
indicating whether the demand d uses a binary variable of the virtual path p in the state s for the vth iteration;
Figure BDA0002468409060000063
indicating whether the demand d uses a binary variable of the virtual path p in a normal state for the Vth iteration;
s3.3.2, based on Lagrangian function
Figure BDA0002468409060000064
Obtaining a Dual model P2-Dual of the first problem model P2: the objective function of the Dual model P2-Dual is:
Figure BDA0002468409060000065
the constraints of the Dual model P2-Dual are:
λ≥0；
s3.3.3, decomposing the Dual model P2-Dual into an inner minimization model P3 and an outer maximization model P4, wherein the solution variable of the inner minimization model is a binary variable xdps、yeThe solving variable of the outer-layer maximization model is Lagrange multiplier lambda ═ lambda (lambda)1,λ2,λ3,λ4)；
The inner minimization model P3 is an unconstrained model whose objective function is:
Figure BDA0002468409060000066
the objective function of the outer maximization model P4 is:
Figure BDA0002468409060000067
the constraints of the outer-layer maximization model P4 are:
λ≥0；
wherein the content of the first and second substances,
Figure BDA0002468409060000068
respectively obtaining the optimal solution of each link load and each flow variable of each virtual path in the inner layer optimization;
s3.3.4, solving the inner layer minimization model P3 based on an alternating direction multiplier method;
s3.3.5, updating the Lagrange multiplier in the initial problem model P2, and completing the solution of the outer layer maximization model P4.
Alternatively, the S3.3.4 solving the inner-layer minimization model P3 based on the alternating direction multiplier method includes, but is not limited to, the following steps:
introducing an auxiliary variable feAs a load variable y on link eeObtaining augmented Lagrangian function of the first problem model P2
Figure BDA0002468409060000071
Figure BDA0002468409060000072
Wherein, mueIs the lagrange multiplier corresponding to this equality constraint, ρ is a penalty parameter; e is the total number of links;
obtaining a converted inner-layer minimization model P3':
Figure BDA0002468409060000073
wherein the variable ye，fe，xdpsAnd multiplier mueThe updating modes of (1) are respectively as follows:
Figure BDA0002468409060000074
Figure BDA0002468409060000075
Figure BDA0002468409060000076
μe[t+1]＝μe[t]+ρ(fe-ye)
wherein t is the current update times.
Optionally, in the S3.3.5, in updating the lagrangian multiplier in the first problem model P2 and completing the solution of the outer-layer maximization model P4, the step of updating the lagrangian multiplier is:
Figure BDA0002468409060000077
wherein the content of the first and second substances,
Figure BDA0002468409060000078
step size at the o-th iteration, i the number of updates, operator [ x]+＝max{0,x}。
Optionally, in S3.5, obtaining the load of each link and the flow variable of each virtual path until it is determined that the first problem model P2 is not feasible includes:
if the first problem model P2 is judged to be not feasible, a feasible segmentation determination model l is created1-min；
Feasible cut determination model l1The objective function for min is:
Figure BDA0002468409060000081
feasible cut determination model l1The constraint of min is:
C5-1:
Figure BDA0002468409060000082
C5-2:
Figure BDA0002468409060000083
C5-3:
Figure BDA0002468409060000084
C5-4:
Figure BDA0002468409060000085
wherein q isjAnd (4) destroying variables for newly introduced constraints, wherein the variables are used for relaxing the constraint conditions of the first problem when no feasible solution meets the first problem.
Determining a model l from the feasible cut1-min, obtaining the optimal cut of the Lagrangian multiplier
Figure BDA0002468409060000086
Figure BDA0002468409060000087
Wherein the content of the first and second substances,
Figure BDA0002468409060000088
is with qjCorresponding toA lagrange multiplier;
optimal cut according to lagrange multiplier
Figure BDA0002468409060000089
The current load per link and the flow variables per virtual path are determined.
In a second aspect, an embodiment of the present invention provides a distributed end-to-end latency optimization system for a critical task, which mainly includes: the device comprises a topological structure construction unit, a time delay optimization model unit and a model operation unit, wherein:
the topological structure construction unit is mainly used for constructing a weight directed graph of a bottom-layer core network according to a distributed key task end-to-end network; the time delay optimization model unit is used for constructing a time delay optimization model for minimizing the congestion factor by taking the link congestion factor as an optimization variable according to the weight directed graph; the model operation unit is mainly used for solving the delay optimization model by adopting Benders decomposition based on an alternative direction multiplier to obtain a distributed link-path flow planning scheme, so that the delay of an end-to-end key task is minimized.
In a third aspect, an embodiment of the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, where the processor implements the steps of the distributed mission-critical end-to-end latency optimization method according to any one of the first aspect when executing the program.
In a fourth aspect, an embodiment of the present invention provides a non-transitory computer readable storage medium, on which a computer program is stored, which when executed by a processor, implements the steps of the distributed mission-critical end-to-end latency optimization method according to any one of the first aspect.
The distributed key task end-to-end delay optimization method and system provided by the embodiment of the invention adopt a concise method to design a bottom core network, create a problem model aiming at minimizing the maximum link congestion factor, and solve the model by adopting Benders decomposition based on an alternative direction multiplier to obtain a distributed link-path flow planning scheme, so that the end-to-end key task delay is minimized, the flow recovery design of a link-path is considered, and the optimization efficiency and precision are effectively improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a distributed end-to-end time delay optimization method for a key task according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a distributed end-to-end network architecture for critical tasks according to an embodiment of the present invention;
fig. 3 is a schematic diagram of an underlying network model according to an embodiment of the present invention;
FIG. 4 is a graph illustrating average delay and link utilization in the prior art;
fig. 5 is a framework diagram of a distributed end-to-end latency optimization method for a critical task according to an embodiment of the present invention;
fig. 6 is a schematic model diagram of an ADMM implementing method according to an embodiment of the present invention;
fig. 7 is a schematic structural diagram of a distributed end-to-end latency optimization system for a critical task according to an embodiment of the present invention;
fig. 8 is a physical structure diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a schematic flow chart of a distributed end-to-end delay optimization method for a critical task according to an embodiment of the present invention, as shown in fig. 1, the method includes, but is not limited to, the following steps:
s1, constructing a weight directed graph of a bottom-layer core network according to the distributed key task end-to-end network;
s2, according to the weight directed graph, taking the link congestion factor as an optimization variable, and considering the link-path flow recovery design when the link has a fault, constructing a time delay optimization model for minimizing the congestion factor;
s3, solving the time delay optimization model by adopting Benders decomposition based on the alternative direction multiplier to obtain a distributed link-path flow planning scheme, so that the time delay of the end-to-end key task is minimized.
Specifically, as an alternative embodiment, for the design of a distributed mission-critical end-to-end network, for example, a power underlying core network, any software-defined network (SDN)/Network Function Virtualization (NFV) technology supported software-based network is considered as a model. On this underlay network, Virtual Network Function (VNF) instances (e.g., VNF1, VNF2, etc.) are created on the actual data forwarding nodes. Alternatively, VNF instances of the same type may be deployed on multiple physical nodes in order to approach end users and achieve load balancing, and each physical node may deploy multiple VNF instances.
In particular, the processing power of an NFV-capable node refers to a collection of computing resources, which may include CPU cores, memory and storage, and the like.
Wherein the node sets
Figure BDA0002468409060000111
Can be divided into a set of forwarding nodes that do not require processing capacity
Figure BDA0002468409060000112
And a set of nodes supporting a VNF
Figure BDA0002468409060000113
Because certain service requirements exist among node pairs, data streams forming the service requirements can pass through nodes and links on an underlying network, a plurality of preset virtual paths are arranged among each demand node pair, and the preset virtual paths serve actual key communication tasks. In the embodiment of the present invention, it is assumed that only the node where the VNF is deployed will handle the corresponding traffic demand, and it can determine how the flow (including the normal leave and restore flow) traverses other nodes or links of the underlying network, while the ordinary node only needs to complete the store-and-forward function of the data packet. Data streams typically need to be processed by Service Function Chains (SFCs), so each SFC is an ordered VNF sequence.
Assuming that VNF instances supported by the underlying network infrastructure are represented by the set pi ═ pi | pi ═ 1, 2.. and N }, fig. 2 illustrates a mission-critical end-to-end network architecture provided by the embodiment of the present invention, and fig. 3 illustrates an underlying network model corresponding to fig. 2 provided by the embodiment of the present invention, as shown in fig. 2 and 3, end-to-end requirements from a source node S to a destination node D may be served by an SFC composed of { VNF1, VNF2, VNF3, and VNF4 }.
It should be noted that VNFs may be created in the source node and the destination node of the traffic demand, and may also be used as VNFs in the relay node to process traffic flows from the previous flow segment, i.e. a subset of the SFC sequence { VNF1, VNF2, VNF3, VNF4} may also be a long SFC sequence { VNF1, …, VNF N }.
Meanwhile, in the construction of the distributed key task end-to-end network, the embodiment of the invention can further combine the recovery design problem of the fault in the core network, namely, the embodiment of the invention not only aims at the normal operation state of the network, but also aims at a state set corresponding to a group of selected fault conditions. Where different failure situations are specified by the availability status of the links and nodes, and also by the amount of demand required for a particular situation. Therefore, the distributed key task end-to-end delay optimization method provided by the embodiment of the invention can have the capability of recovering the fault by modeling and analyzing the distributed key task end-to-end network constructed by the method, and effectively improve the robustness of the delay optimization model, so that the network can bear corresponding requirements even if part of network resources temporarily fail.
As an alternative embodiment, in step S1, the constructing a weight directed graph of an underlying core network according to a distributed mission-critical end-to-end network in consideration of a link-path traffic restoration design when a link has a failure may include:
determining a set of physical nodes for a mission-critical end-to-end network
Figure BDA0002468409060000121
A link set epsilon, a processing capacity set V of a node supporting a VNF function, and a link capacity set C;
constructing a weight directed graph of a bottom core network according to a physical node set, a link set, a processing capacity set of nodes supporting VNF functions and the link capacity set
Figure BDA0002468409060000122
Specifically, in the embodiment of the present invention, the following method may be adopted to construct the weight directed graph of the underlying core network:
denote a node by i, a link by e, a virtual path by p, a demand between pairs of nodes by h, and the number of demands by d, i.e. hdAnd d represents the size of the d-th service demand, s represents the fault state of the link e, wherein s-0 represents that the link e normally operates, and s-e represents that the link e fails.
Thus, a set of nodes can be defined as
Figure BDA0002468409060000123
Link set is ═ 1,2,. E; the set of virtual paths available for demand d is
Figure BDA0002468409060000124
The demand set is
Figure BDA0002468409060000125
Set of states as
Figure BDA0002468409060000126
Further, in the embodiment of the present invention, a link congestion factor is used as an optimization variable, and a delay optimization model for minimizing the congestion factor is constructed, based on the following considerations:
the transmission of key tasks in the power network needs a network with extremely high delay capability, for example, an intelligent distributed power distribution automation service in a power grid, the maximum end-to-end delay of the network should not exceed 10ms, and the end-to-end delay requirement of an application layer needs to be realized by reasonably designing a bottom layer physical network, so that the delay requirement of end-to-end key task communication can be met by reasonably designing the topology flow in a bottom layer network. Furthermore, how to minimize the delay of the data packet through the network is a technical problem to be solved by the embodiments of the present invention. It should be noted that the computational focus on the latency of the network is not a specific packet, but the average latency of the flow of the entire packet between the source and the target (demand), or even the average behavior of the entire packet.
To further illustrate the advantage of selecting the link congestion factor as the optimization variable in the embodiment of the present invention, the following description will be made in conjunction with the relationship between the system average delay and the link congestion factor.
To illustrate the delay behavior of a typical network, it can be intuitively known from the graph of the average delay and the link utilization rate recorded in the prior art shown in fig. 4: when the utilization rate of a link is higher, the traffic carried on the link is more, i.e., the link is more congested. Therefore, in the embodiment of the present invention, a Link congestion factor (Link congestion factor) is selected to replace the Link utilization (Link utilization) in fig. 4. In calculating the end-to-end delay, it is important that the delay components need to be added due to the instantaneous store and forward nature of the network routes, so that the average delay on each link/network is kept as low as possible. In summary, for the purpose of network design consideration, the substitute standard for adopting the maximum link congestion factor as the delay standard is in accordance with objective rules, and an optimal distributed link-path traffic planning scheme is determined by constructing a delay optimization model for minimizing the congestion factor, so that the determination efficiency of the delay minimization of the end-to-end key task is improved.
Furthermore, when the time delay optimization model is solved, the method and the device adopt the combination of the alternating direction multiplier (ADMM) and Benders decomposition, solve the problem that the original initial problem usually takes a large amount of time and resources due to the constraint on model decoupling related to all users, and can save end-to-end communication time and resources by dividing the problem into small problems, thereby having high solving speed and good convergence performance.
The distributed key task end-to-end delay optimization method provided by the embodiment of the invention adopts a concise method to design a bottom core network, creates a problem model aiming at minimizing the maximum link congestion factor, and adopts Benders decomposition based on an alternative direction multiplier to solve the model so as to obtain a distributed link-path flow planning scheme, so that the end-to-end key task delay is minimized, the flow recovery design of a link-path is considered, and the optimization efficiency and precision are effectively improved.
Based on the content of the foregoing embodiment, as an optional embodiment, in the foregoing S22, a delay optimization model for minimizing the congestion factor is constructed according to the weight directed graph and with the link congestion factor as an optimization variable, and an objective function of the delay optimization model may be:
P1：
Figure BDA0002468409060000131
the constraint conditions of the time delay optimization model are set as follows:
C1-1：
Figure BDA0002468409060000141
C1-2：
Figure BDA0002468409060000142
C1-3:
Figure BDA0002468409060000143
C1-4:
Figure BDA0002468409060000144
C1-5:
Figure BDA0002468409060000145
C1-6:
Figure BDA0002468409060000146
wherein r is a link congestion factor, and e represents a link; p represents a virtual path, h represents the amount of demand between node pairs, d represents the number of demands, hdRepresenting the demanded quantity of the d-th service; s represents the fault state of the link e, wherein s-0 represents that the link e normally operates, and s-e represents that the link e fails;
Figure BDA0002468409060000147
a set of virtual paths feasible for demand d;
Figure BDA0002468409060000148
is a business requirement set;
Figure BDA0002468409060000149
is a link state set; h isd0Indicating the demanded quantity of the d-th service in a normal state; h isdsIndicating the demanded quantity of the d-th service in the state s; x is the number ofdp0Indicating the flow of the demand d on the virtual path p under the normal condition; x is the number ofdpsIndicating the flow of the demand d on the virtual path p in the state s; deltaedpFor a binary constant as a path-link indicator, for a requirement d, if link e is inOn the virtual path p, then δedp1, otherwise δedp＝0；udp0To indicate whether the demand d uses the binary variable of the virtual path p under normal conditions, if the virtual path p is used, udp01, otherwise, alldp0＝0；udpsTo indicate whether the demand d uses the binary variable of the virtual path p in state s, if the virtual path p is used, udps1, otherwise, alldps＝0；θdpsA binary constant that is indicative of the availability of the virtual path p of demand d in state s; x is the number ofdpsA recovery flow variable of the virtual path p for the demand d in the state s; x is the number ofdp0Recovering the flow variable of the virtual path p which is the demand d under the normal condition; y iseIs the load on link e; alpha is alphaesIs a binary constant that indicates whether link e is in a failed state s.
Specifically, in the embodiment of the present invention, not only the demanded quantity h of the d-th service when the link is normal is consideredd0Meanwhile, the demanded quantity h of the d-th service under various state links is considereddsThe accuracy of the model is effectively improved.
Further, the capacity of link e is ceAnd let the actual load of link e be ye，xdp0Representing the flow of the demand d on the virtual path p under normal conditions, xdpsRepresenting the traffic of the demand d on the virtual path p in state s. Let a binary constant deltaedpAs a path-link indicator, for demand d, if link e is on virtual path p, δedpOtherwise, it is 0. Introduction of a binary variable udp0And udpsIndicating respectively whether the demand d uses the virtual path p in normal conditions and in state s, if this path is used, udp0＝1、udpsOtherwise, all are 0.
In the embodiment of the present application, the actual load on each link is yeDefining a link congestion factor of
Figure BDA0002468409060000151
Since the average delay of packets in a network is difficult to characterize, optimization is employedThe problem is converted into a congestion factor for reducing the most congested link in the network slice, so that the optimization problem is formulated into an objective function of the time delay optimization model
Since the traffic flow of the whole network under normal conditions does not branch, that is, the sum of the virtual paths p opened for the requirement d should be equal to 1, the constraint C1-1 can be constructed.
Due to the fact that
Figure BDA0002468409060000152
The actual load of link e needs to satisfy the constraint C1-2 under normal conditions.
Since at most one additional recovery flow of demand d is allowed in the fault state s, this extra flow is needed when the existing normal flow is not sufficient to fulfill the demand. So a binary variable udpsThe constraint C1-3 should be satisfied.
Due to xdpsIs an a priori unknown recovery stream, the above constraint C1-4 needs to be satisfied.
Further, a binary constant α is introduced in the present embodimentes∈{0,1}α es1 indicates whether the link e is in the failure state s, if the link is normal, then alpha es1, otherwise α es0. To describe the availability of a certain virtual path p of a demand d in a state s, a binary constant is introduced
Figure BDA0002468409060000153
It can be known that when all links of the path are in normal state (i.e. alpha)esWhen 1), θ dps1. The demand d considering the survival in the fault state s is
Figure BDA0002468409060000154
The flow of all paths p in state s to meet the demand d should meet the constraint C1-5 described above.
Finally, for link e, the above constraint C1-6 should also be satisfied. It should be noted that, in the following description,
Figure BDA0002468409060000155
indicating the capacity (i.e., free capacity) on link e in state s that is not occupied by normal flows, the constraint is to limit the amount of protection traffic on link e in state s to be less than or equal to the free capacity in link e in state s.
Based on the content of the foregoing embodiment, as an optional embodiment, in the foregoing S3, the solution of the delay optimization model is performed by using Benders decomposition based on an alternating direction multiplier method, which includes, but is not limited to, the following steps:
s3.1, decomposing the time delay optimization model into a first problem model P2 and a main problem model P6 based on Benders decomposition;
s3.2, carrying out feasibility test on the first problem model P2;
s3.3, if the first problem model P2 is feasible, performing P2 solution on the first problem model based on an alternating direction multiplier method to obtain the optimal cut and upper bound information of the Lagrangian multiplier, and feeding back the optimal cut of the Lagrangian multiplier to the main problem model P6;
s3.4, based on the branch-and-bound method, solving the main problem model P6 according to the optimal cut of the Lagrange multiplier so as to update the binary variable u of the initial problem model P2dp0、udpsAnd acquiring lower bound information;
and S3.5, iteratively executing S3.2-S3.4 until the first problem model P2 is judged to be infeasible, and acquiring the load of each link and the flow variable of each virtual path to determine a distributed link-path flow planning scheme.
Specifically, the problem of minimizing the average delay of the end-to-end critical task involved in this embodiment is to optimize the load y on each link by using the link congestion factor as an optimization variableeAt the same time, we also introduced protective design constraints (C1-3 to C1-6). Meanwhile, the optimization variable also takes the path indicating variable u under the normal condition and the state s into considerationdp0And udpsAnd the flow variable x of the path p in the state sdps. Through the analysis of the constructed time delay optimization model, it can be seen that u isdp0And udpsIs binary, so that the problem is a mixed integer programming (MILP)And (5) problems are solved.
As shown in fig. 5, in the embodiment of the present invention, the solution problem of the time delay optimization model is still an MILP problem, which includes integer and continuous variables. The render Decomposition (BD) is an iterative algorithm that effectively solves such problems. The basic principle of BD decomposition is to decompose the original MILP problem into a first problem and a main problem, and to perform mutual iterative solution using the solutions of the two problems in each step. The first problem related to the original problem needs a fixed binary variable, and for solving the first problem, upper bound information of a delay optimization model (the original problem is a min problem) can be obtained, and information of a Lagrange multiplier related to inequality constraint can be obtained.
In the embodiment of the invention, the solution of the main problem is derived and solved by using a dual theory and a Lagrangian multiplier obtained from the initial problem. For the solution of the main problem, the lower bound information of the delay optimization model (the original problem is the min problem) can be obtained, and the information of the binary variable of the first problem of the next iteration can be obtained.
Based on the content of the foregoing embodiment, as an optional embodiment, in combination with the schematic diagram of the ADMM implementation method shown in fig. 6, S3.1 decomposes the delay optimization model into a first problem model P2 and a main problem model P6 based on Benders decomposition, and specifically may include:
binary variable u at the time of determining the v-th iterationdp0And udpsThen, obtaining the first problem model P2 according to the time delay optimization model, wherein:
the objective function of the first problem model P2 is:
Figure BDA0002468409060000171
the constraints of the first problem model P2 are:
C2-1:
Figure BDA0002468409060000172
C2-2:
Figure BDA0002468409060000173
C2-3:
Figure BDA0002468409060000174
C2-4:
Figure BDA0002468409060000175
the objective function of the main problem model P6 is:
Figure BDA0002468409060000176
the constraints of the main problem model P6 are:
C6-1:
Figure BDA0002468409060000177
C6-2:
Figure BDA0002468409060000178
C6-3:
Figure BDA0002468409060000181
C6-4:
Figure BDA0002468409060000182
wherein, V1+V2V is the total number of iterations, V1When the first problem is feasible, solving the iteration times of the first problem; v2To solve l when the first problem is not feasible1-number of iterations in min problem;
Figure BDA0002468409060000183
are respectively the V th1The recovery flow variable of the virtual path p of the demand d in the state s during the secondary iteration;
Figure BDA0002468409060000184
is the V th1Load on link e at the time of the second iteration;
Figure BDA0002468409060000185
is the V th1Lagrange multipliers at a second iteration;
Figure BDA0002468409060000186
a Lagrangian function when the Lagrangian multiplier is optimally cut;
Figure BDA0002468409060000187
and
Figure BDA0002468409060000188
respectively, a Vth corresponding to the optimal cut of the Lagrangian multiplier2And in the secondary iteration, the recovery flow variable of the virtual path p of the demand d in the state s, the load on the link e and the Lagrangian multiplier are required.
Since the first problem based on Benders' decomposition contains only continuous variables, the binary variable u at the v-th iteration is givendp0And udpsThen the first question P2 described above can be obtained.
Further, in the first problem P2, the flow variable x on the virtual path P is required d only in the state s due to the optimization variabledpsAnd the actual load y of each link eeMeanwhile, constraints C2-1 to C2-4 are all linear constraints, so the problem P2 is a linear programming problem.
Further, after the initial problem P2 is determined, the objective function and its constraint of the main problem model P6 can be determined accordingly for the main problems of the Benders decomposition.
Further, in the distributed end-to-end time delay optimization method for the key tasks provided in the embodiment of the present invention, in S3.3, if the first problem model P2 is feasible, the first problem model P2 is solved based on an alternating direction multiplier method, including but not limited to the following steps:
s3.3.1, get itLagrange function of the first problem model P2
Figure BDA0002468409060000189
Figure BDA00024684090600001810
Wherein λ ═ λ (λ)1,λ2,λ3,λ4) In order to be a lagrange multiplier,
Figure BDA00024684090600001811
indicating whether the demand d uses a binary variable of the virtual path p in the state s for the vth iteration;
Figure BDA0002468409060000191
indicating whether the demand d uses a binary variable of the virtual path p in a normal state for the Vth iteration;
s3.3.2 based on the Lagrangian function
Figure BDA0002468409060000192
Obtaining a Dual model P2-Dual of the first problem model P2: the objective function of the Dual model P2-Dual is:
Figure BDA0002468409060000193
the constraint conditions of the Dual model P2-Dual are as follows:
λ≥0；
s3.3.3, decomposing the Dual model P2-Dual into an inner minimization model P3 and an outer maximization model P4, wherein the solution variable of the inner minimization model is a binary variable xdps、yeThe solving variable of the outer layer maximization model is Lagrange multiplier lambda ═ lambda (lambda)1,λ2,λ3,λ4)；
The inner layer minimization model P3 is an unconstrained model, and the objective function of the unconstrained model is as follows:
Figure BDA0002468409060000194
the objective function of the outer-layer maximization model P4 is as follows:
Figure BDA0002468409060000195
the constraint conditions of the outer-layer maximization model P4 are as follows:
λ≥0；
wherein the content of the first and second substances,
Figure BDA0002468409060000196
respectively obtaining the optimal solution of each link load and each flow variable of each virtual path in the inner layer optimization;
s3.3.4, solving the inner layer minimization model P3 based on an alternating direction multiplier method;
s3.3.5, updating the Lagrange multiplier in the first problem model P2, and completing the solution of the outer layer maximization model P4.
Specifically, in the process of solving the first problem model P2, the embodiment of the present invention first determines the lagrangian function of P2
Figure BDA0002468409060000197
Based on this, a Dual problem P2-Dual of problem P2 can be further determined.
For the problem P2-Dual, in this embodiment, it can be separated into an inner minimization problem and an outer maximization problem. Wherein, the solving variable of the inner-layer minimization problem is a flow variable x of the demand d on the virtual path p under the state sdpsAnd the actual load y of each link ee(ii) a The solution variable for the outer maximization problem is then the lagrange multiplier λ ═ λ (λ)1,λ2,...)。
Specifically, the solving step of the inner-layer minimization problem may be:
question P2-When the Dual decomposition obtains the inner layer minimization problem P3, the objective function of the inner layer minimization problem model P3 is
Figure BDA0002468409060000201
The problem P3 is an unconstrained minimization problem, and the optimization variable is xdpsAnd yeThe solution can be performed by using ADMM (alternating direction multiplier).
ADMM is widely used to decouple constraints involving all users. It usually takes a lot of time and resources for the original initial problem, but with the aid of ADMM, end-to-end communication time and resources can be saved by dividing the problem into small ones.
A general problem can be represented by the following problem:
Figure BDA0002468409060000202
Figure BDA0002468409060000203
where x is a variable coupled by an equality constraint.
The augmented lagrangian function for the original problem can be expressed as:
Figure BDA0002468409060000204
where γ is the corresponding lagrange multiplier and μ is a penalty parameter.
The variable update process may proceed in the following order:
Figure BDA0002468409060000205
Figure BDA0002468409060000206
therefore, in the present embodiment, since the lagrangian function has been determined, the variables in the problem P3 need to be updated in the way the ADMM variables are updated.
It should be noted that before solving problem P3, problem P3 needs to be first transformed into a separable form to facilitate the distributed solution:
first, an auxiliary variable f is introducedeAs variable yeIs copied as a global variable of the first question P2. The auxiliary variable feThe introduction of (2) is equivalent to adding an equality constraint newly, and the following formula needs to be satisfied:
Figure BDA0002468409060000211
then the objective function in problem P3 needs to be further adapted to add the equality constraint to the objective function, i.e. the augmented lagrangian function of problem P2.
Wherein, mueIs the lagrange multiplier corresponding to this equality constraint, and the coefficient p is a penalty parameter.
Wherein the global replication variable feProcessed by a global SDN controller, and the original variable yeIt is processed in parallel by each link (processed by routing node or NFV) so the problem P3 can be further transformed into the inner minimization model P3' and the variable y is obtained at the same timee，fe，xdpsAnd multiplier mueThe update method of (1).
Based on the content of the foregoing embodiment, as an optional embodiment, in the step S3.3.5, updating the lagrangian multiplier in the first problem model P2, and completing the solution of the outer-layer maximization model P4, the step of updating the lagrangian multiplier is:
Figure BDA0002468409060000212
wherein the content of the first and second substances,
Figure BDA0002468409060000213
step size at the o-th iteration, i is the number of updates, operator
Figure BDA0002468409060000214
Since the outer-layer maximization problem is mainly an update of the lagrangian multiplier in P2, the objective function of the maximization model P4 can be obtained, wherein,
Figure BDA0002468409060000215
and
Figure BDA0002468409060000216
is the optimal solution of the load of each link and the flow variables of each virtual path obtained in the inner layer optimization.
Based on the above implementation, in the embodiment of the present invention, when the Benders decomposition based on the alternating direction multiplier method is adopted, in the process of each iteration, the binary value at the time of the v-th iteration is used
Figure BDA0002468409060000217
And
Figure BDA0002468409060000218
the first problem usually does not necessarily have a feasible solution, and therefore, our discussion of the solvability of the first problem herein requires a feasibility test on the first problem model P2 to ensure convergence of the iteration.
If at the time of the v-th iteration the first problem is feasible, its solution can provide information on the actual load of each link and the flow variables on path p for demand d at state s. On this basis, then the lagrange multiplier optimal cut α can be obtained and added to the main problem that follows:
Figure BDA0002468409060000221
if the first problem is not feasible at the time of the v-th iteration, then a feasible cut determination model/needs to be created1-min。
Wherein the feasible cut determines the model l1The objective function for min is:
Figure BDA0002468409060000222
feasible cut determination model l1The constraint of min is:
C5-1:
Figure BDA0002468409060000223
C5-2:
Figure BDA0002468409060000224
C5-3:
Figure BDA0002468409060000225
C5-4:
Figure BDA0002468409060000226
wherein q isjAnd (4) destroying variables for newly introduced constraints, wherein the variables are used for relaxing the constraint conditions of the first problem when no feasible solution meets the first problem.
Further, the model/may be determined from the feasible cut1-min, obtaining the optimal cut of the Lagrangian multiplier
Figure BDA0002468409060000227
Figure BDA0002468409060000228
Wherein the content of the first and second substances,
Figure BDA0002468409060000229
is with qjA corresponding lagrange multiplier;
finally, the optimal cut is based on the Lagrangian multiplier
Figure BDA00024684090600002210
The current load per link and the flow variables per virtual path are determined. Furthermore, lagrange multipliers for infeasible solutions should suffice
Figure BDA00024684090600002211
The embodiment of the present invention provides a distributed end-to-end time delay optimization system for key tasks, as shown in fig. 7, including but not limited to a topology structure building unit 1, a time delay optimization model unit 2, and a model operation unit 3, where:
the topological structure construction unit 1 is mainly used for constructing a weight directed graph of a bottom-layer core network according to a distributed key task end-to-end network; the delay optimization model unit 2 is mainly used for constructing a delay optimization model for minimizing a congestion factor by taking a link congestion factor as an optimization variable according to a weight directed graph and considering a link-path flow recovery design when a link has a fault; the model operation unit 3 is mainly used for solving the time delay optimization model by adopting Benders decomposition based on an alternative direction multiplier to obtain a distributed link-path flow planning scheme, so that the time delay of an end-to-end key task is minimized.
It should be noted that, in a specific operation process of the distributed end-to-end time delay optimization system for a key task according to the embodiment of the present invention, the distributed end-to-end time delay optimization method for a key task according to any of the above embodiments may be executed, and details of this embodiment are not described herein.
The distributed key task end-to-end time delay optimization system provided by the embodiment of the invention adopts a simple method to design a bottom core network, creates a problem model aiming at minimizing the maximum link congestion factor, and adopts Benders decomposition based on an alternative direction multiplier to solve the model so as to obtain a distributed link-path flow planning scheme, so that the end-to-end key task time delay is minimized, the flow recovery design of a link-path is considered, and the optimization efficiency and precision are effectively improved.
Fig. 8 illustrates a physical structure diagram of an electronic device, and as shown in fig. 8, the electronic device may include: a processor (processor)310, a communication Interface (communication Interface)320, a memory (memory)330 and a communication bus 340, wherein the processor 310, the communication Interface 320 and the memory 330 communicate with each other via the communication bus 340. The processor 310 may call logic instructions in the memory 330 to perform the following method: s1, constructing a weight directed graph of a bottom-layer core network according to the distributed key task end-to-end network; s2, according to the weight directed graph, taking the link congestion factor as an optimization variable, and constructing a time delay optimization model for minimizing the congestion factor; s3, solving the time delay optimization model by adopting Benders decomposition based on the alternative direction multiplier to obtain a distributed link-path flow planning scheme, so that the time delay of the end-to-end key task is minimized.
Furthermore, the logic instructions in the memory 330 may be implemented in software functional units and stored in a computer readable storage medium when sold or used as a stand-alone data set. Based on such understanding, the technical solution of the present invention or a part thereof, which essentially contributes to the prior art, can be embodied in the form of a software data set, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
In another aspect, an embodiment of the present invention further provides a non-transitory computer-readable storage medium, on which a computer program is stored, where the computer program is implemented to perform the optimization method provided in the foregoing embodiments when executed by a processor, and for example, the method includes: s1, constructing a weight directed graph of a bottom-layer core network according to the distributed key task end-to-end network; s2, according to the weight directed graph, taking the link congestion factor as an optimization variable, and constructing a time delay optimization model for minimizing the congestion factor; s3, solving the time delay optimization model by adopting Benders decomposition based on the alternative direction multiplier to obtain a distributed link-path flow planning scheme, so that the time delay of the end-to-end key task is minimized.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above technical solutions may be embodied in the form of a software data set, which may be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method according to the embodiments or some parts of the embodiments.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. A distributed end-to-end time delay optimization method for key tasks is characterized by comprising the following steps:
s1, constructing a weight directed graph of a bottom-layer core network according to the distributed key task end-to-end network;
s2, according to the weight directed graph, taking a link congestion factor as an optimization variable, and considering a link-path flow recovery design when a link has a fault, constructing a time delay optimization model for minimizing the congestion factor;
s3, solving the time delay optimization model by adopting Benders decomposition based on an alternative direction multiplier to obtain a distributed link-path flow planning scheme so as to minimize the time delay of the end-to-end key task;
the S1, constructing a weight directed graph of the underlying core network according to the distributed key task end-to-end network, includes:
determining a set of physical nodes of the mission-critical end-to-end network
Figure FDA0003346460790000011
A link set epsilon, a processing capacity set V of a node supporting a VNF function, and a link capacity set C;
constructing a weight directed graph of the bottom core network according to the physical node set, the link set, the processing capacity set of the nodes supporting the VNF function and the link capacity set
Figure FDA0003346460790000012
The S2, according to the weight directed graph, taking a link congestion factor as an optimization variable, and considering a link-path flow recovery design when a link has a fault, constructing a time delay optimization model P1 for minimizing the congestion factor;
the objective function of the time delay optimization model P1 is as follows:
Figure FDA0003346460790000013
the constraint conditions of the time delay optimization model P1 are as follows:
C1-1：
Figure FDA0003346460790000021
C1-2：
Figure FDA0003346460790000022
C1-3:
Figure FDA0003346460790000023
C1-4:
Figure FDA0003346460790000024
C1-5:
Figure FDA0003346460790000025
C1-6:
Figure FDA0003346460790000026
wherein r is a link congestion factor, and e represents a link; p represents a virtual path, h represents the amount of demand between node pairs, d represents the number of demands, hdRepresenting the demanded quantity of the d-th service; s represents the fault state of the link e, wherein s-0 represents that the link e normally operates, and s-e represents that the link e fails;
Figure FDA0003346460790000027
virtual way feasible for demand dA path set;
Figure FDA0003346460790000028
is a business requirement set;
Figure FDA0003346460790000029
is a link state set; h isd0Indicating the demanded quantity of the d-th service in a normal state; h isdsIndicating the demanded quantity of the d-th service in the state s; x is the number ofdp0Indicating the flow of the demand d on the virtual path p under the normal condition; deltaedpFor a binary constant as a path-link indicator, δ if link e is on virtual path p, for demand dedp1, otherwise δedp＝0；udp0To indicate whether the demand d uses the binary variable of the virtual path p under normal conditions, if the virtual path p is used, udp01, otherwise, alldp0＝0；udpsTo indicate whether the demand d uses the binary variable of the virtual path p in state s, if the virtual path p is used, udps1, otherwise, alldps＝0；θdpsA binary constant that is indicative of the availability of the virtual path p of demand d in state s; x is the number ofdpsA recovery flow variable of the virtual path p for the demand d in the state s; x is the number ofdp0Recovering the flow variable of the virtual path p which is the demand d under the normal condition; y iseIs the load on link e; alpha is alphaesIs a binary constant that indicates whether link e is in a failed state s.
2. The distributed key-type task end-to-end delay optimization method of claim 1, wherein the S3, solving the delay optimization model by using Benders' decomposition based on an alternating direction multiplier method, comprises:
s3.1, decomposing the time delay optimization model into a first problem model P2 and a main problem model P6 based on Benders decomposition;
s3.2, carrying out feasibility test on the first problem model P2;
s3.3, if the first problem model P2 is feasible, performing P2 solution on the first problem model based on an alternating direction multiplier method to obtain the optimal cut and upper bound information of the Lagrangian multiplier, and feeding back the optimal cut of the Lagrangian multiplier to the main problem model P6;
s3.4, solving the main problem model P6 according to the optimal cut of the Lagrange multiplier based on a branch-and-bound method so as to update the binary variable u of the initial problem model P2dp0、udpsAnd acquiring lower bound information;
and S3.5, iteratively executing S3.2-S3.4 until the first problem model P2 is judged to be infeasible, and acquiring the load of each link and the flow variable of each virtual path to determine the distributed link-path flow planning scheme.
3. The distributed mission-critical end-to-end delay optimization method of claim 2, wherein the S3.1, based on Benders' decomposition, decomposes the delay optimization model into a first problem model P2 and a main problem model P6, including:
binary variable u in determining the v-th iterationdp0And udpsThen, acquiring the first problem model P2 according to the time delay optimization model;
the objective function of the first problem model P2 is:
Figure FDA0003346460790000031
the constraint conditions of the first problem model P2 are as follows:
C2-1:
Figure FDA0003346460790000032
C2-2:
Figure FDA0003346460790000033
C2-3:
Figure FDA0003346460790000034
C2-4:
Figure FDA0003346460790000035
the objective function of the main problem model P6 is:
Figure FDA0003346460790000041
the constraint conditions of the main problem model P6 are as follows:
C6-1:
Figure FDA0003346460790000042
C6-2:
Figure FDA0003346460790000043
C6-3:
Figure FDA0003346460790000044
C6-4:
Figure FDA0003346460790000045
wherein, V1+V2V is the total number of iterations, V1When the first problem is feasible, solving the iteration times of the first problem; v2To solve l when the first problem is not feasible1-number of iterations in min problem;
Figure FDA0003346460790000046
are respectively the V th1The recovery flow variable of the virtual path p of the demand d in the state s during the secondary iteration;
Figure FDA0003346460790000047
is the V th1Sub-iterative time linke, the load on the rotor;
Figure FDA0003346460790000048
is the V th1Lagrange multipliers at a second iteration;
Figure FDA0003346460790000049
a Lagrangian function when the Lagrangian multiplier is optimally cut;
Figure FDA00033464607900000410
Figure FDA00033464607900000411
and
Figure FDA00033464607900000412
respectively, a Vth corresponding to the optimal cut of the Lagrangian multiplier2And in the secondary iteration, the recovery flow variable of the virtual path p of the demand d in the state s, the load on the link e and the Lagrangian multiplier are required.
4. The distributed key-type task end-to-end delay optimization method of claim 3, wherein, in step S3.3, if the initial problem model P2 is feasible, solving the initial problem model P2 based on an alternative direction multiplier method includes:
s3.3.1, obtaining Lagrangian function of the first problem model P2
Figure FDA00033464607900000413
Figure FDA0003346460790000051
Wherein λ ═ λ (λ)1,λ2,λ3,λ4) In order to be a lagrange multiplier,
Figure FDA0003346460790000052
indicating whether the demand d uses a binary variable of the virtual path p in the state s for the vth iteration;
Figure FDA0003346460790000053
indicating whether the demand d uses a binary variable of the virtual path p in a normal state for the Vth iteration;
s3.3.2 based on the Lagrangian function
Figure FDA0003346460790000054
Obtaining a Dual model P2-Dual of the first problem model P2: the objective function of the Dual model P2-Dual is:
Figure FDA0003346460790000055
the constraint conditions of the Dual model P2-Dual are as follows:
λ≥0；
s3.3.3, decomposing the Dual model P2-Dual into an inner minimization model P3 and an outer maximization model P4, wherein the solution variable of the inner minimization model is a binary variable xdps、yeThe solving variable of the outer layer maximization model is Lagrange multiplier lambda ═ lambda (lambda)1,λ2,λ3,λ4)；
The inner-layer minimization problem P3 is an unconstrained model, and the objective function of the unconstrained model is as follows:
Figure FDA0003346460790000056
the objective function of the outer-layer maximization model P4 is as follows:
Figure FDA0003346460790000057
the constraint conditions of the outer-layer maximization model P4 are as follows:
λ≥0；
wherein the content of the first and second substances,
Figure FDA0003346460790000058
respectively obtaining the optimal solution of each link load and each flow variable of each virtual path in the inner layer optimization;
s3.3.4, solving the inner layer minimization model P3 based on an alternating direction multiplier method;
s3.3.5, updating the Lagrange multiplier in the first problem model P2, and completing the solution of the outer layer maximization model P4.
5. The distributed mission-critical end-to-end delay optimization method of claim 4, wherein the S3.3.4 solving the inner minimization model P3 based on an alternating direction multiplier method comprises:
introducing an auxiliary variable feAs a load variable y on link eeObtaining augmented Lagrangian function of the first problem model P2
Figure FDA0003346460790000061
Figure FDA0003346460790000062
Wherein, mueIs the lagrange multiplier corresponding to this equality constraint, ρ is a penalty parameter; e is the total number of links;
obtaining a converted inner-layer minimization model P3':
Figure FDA0003346460790000063
wherein the variable ye，fe，xdpsAnd multiplier mueThe updating modes of (1) are respectively as follows:
Figure FDA0003346460790000064
Figure FDA0003346460790000065
Figure FDA0003346460790000066
μe[t+1]＝μe[t]+ρ(fe-ye)
wherein t is the current update times.
6. The distributed key task end-to-end delay optimization method of claim 4, wherein at S3.3.5, the lagrangian multiplier in the first problem model P2 is updated, and the solution to the outer maximization model P4 is completed, and the lagrangian multiplier is updated by the steps of:
Figure FDA0003346460790000067
wherein the content of the first and second substances,
Figure FDA0003346460790000068
step size at the o-th iteration, i the number of updates, operator [ x]+＝max{0,x}。
7. The distributed end-to-end latency optimization method of a critical task according to claim 4, wherein in the step S3.5, obtaining the load of each link and the flow variable of each virtual path until it is determined that the first problem model P2 is not feasible includes:
if the first problem model P2 is judged to be not feasible, a feasible cutting determination model is createdl1-min；
The feasible cut determines the model l1The objective function for min is:
Figure FDA0003346460790000071
the feasible cut determines the model l1The constraint of min is:
C5-1:
Figure FDA0003346460790000072
C5-2:
Figure FDA0003346460790000073
C5-3:
Figure FDA0003346460790000074
C5-4:
Figure FDA0003346460790000075
wherein q isjBreaking variables for newly introduced constraints, wherein the constraint breaking variables are used for relaxing constraint conditions on the first problem when no feasible solution meets the first problem;
determining a model l from the feasible cut1-min, obtaining the optimal cut of the Lagrangian multiplier
Figure FDA0003346460790000076
Figure FDA0003346460790000077
Wherein the content of the first and second substances,
Figure FDA0003346460790000081
is with qjCorresponding toA lagrange multiplier;
according to the Lagrange multiplier optimal cut
Figure FDA0003346460790000082
The current load per link and the flow variables per virtual path are determined.
8. A distributed mission-critical end-to-end delay optimization system, comprising:
the topological structure construction unit is used for constructing a weight directed graph of a bottom-layer core network according to the distributed key task end-to-end network;
the time delay optimization model unit is used for constructing a time delay optimization model for minimizing the congestion factor by taking the congestion factor of the link as an optimization variable and considering the link-path flow recovery design when the link has a fault according to the weight directed graph;
the model operation unit is used for solving the time delay optimization model by adopting Benders decomposition based on an alternative direction multiplier to obtain a distributed link-path flow planning scheme so as to minimize the time delay of the end-to-end key task;
the method comprises the following steps of constructing a weight directed graph of a bottom layer core network according to a distributed key type task end-to-end network, wherein the weight directed graph comprises the following steps:
determining a set of physical nodes of the mission-critical end-to-end network
Figure FDA0003346460790000083
A link set epsilon, a processing capacity set V of a node supporting a VNF function, and a link capacity set C;
constructing a weight directed graph of the bottom core network according to the physical node set, the link set, the processing capacity set of the nodes supporting the VNF function and the link capacity set
Figure FDA0003346460790000084
According to the weight directed graph, a link congestion factor is used as an optimization variable, a link-path flow recovery design when a link has a fault is considered, and a time delay optimization model P1 for minimizing the congestion factor is constructed;
the objective function of the time delay optimization model P1 is as follows:
Figure FDA0003346460790000085
the constraint conditions of the time delay optimization model P1 are as follows:
C1-1：
Figure FDA0003346460790000091
C1-2：
Figure FDA0003346460790000092
C1-3:
Figure FDA0003346460790000093
C1-4:
Figure FDA0003346460790000094
C1-5:
Figure FDA0003346460790000095
C1-6:
Figure FDA0003346460790000096
wherein r is a link congestion factor, and e represents a link; p represents a virtual path, h represents the amount of demand between node pairs, d represents the number of demands, hdRepresenting the demanded quantity of the d-th service; s represents the fault state of the link e, wherein s-0 represents that the link e normally operates, and s-e represents that the link e occursA failure;
Figure FDA0003346460790000097
a set of virtual paths feasible for demand d;
Figure FDA0003346460790000098
is a business requirement set;
Figure FDA0003346460790000099
is a link state set; h isd0Indicating the demanded quantity of the d-th service in a normal state; h isdsIndicating the demanded quantity of the d-th service in the state s; x is the number ofdp0Indicating the flow of the demand d on the virtual path p under the normal condition; deltaedpFor a binary constant as a path-link indicator, δ if link e is on virtual path p, for demand dedp1, otherwise δedp＝0；udp0To indicate whether the demand d uses the binary variable of the virtual path p under normal conditions, if the virtual path p is used, udp01, otherwise, alldp0＝0；udpsTo indicate whether the demand d uses the binary variable of the virtual path p in state s, if the virtual path p is used, udps1, otherwise, alldps＝0；θdpsA binary constant that is indicative of the availability of the virtual path p of demand d in state s; x is the number ofdpsA recovery flow variable of the virtual path p for the demand d in the state s; x is the number ofdp0Recovering the flow variable of the virtual path p which is the demand d under the normal condition; y iseIs the load on link e; alpha is alphaesIs a binary constant that indicates whether link e is in a failed state s.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the distributed mission-critical end-to-end latency optimization method according to any one of claims 1 to 7 when executing the program.
10. A non-transitory computer readable storage medium having stored thereon a computer program, which when executed by a processor, performs the steps of the distributed mission-critical end-to-end latency optimization method of any one of claims 1 to 7.
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