CN115209373A - Internet of vehicles task unloading method based on bipartite graph matching strategy - Google Patents

Internet of vehicles task unloading method based on bipartite graph matching strategy Download PDF

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CN115209373A
CN115209373A CN202210808169.4A CN202210808169A CN115209373A CN 115209373 A CN115209373 A CN 115209373A CN 202210808169 A CN202210808169 A CN 202210808169A CN 115209373 A CN115209373 A CN 115209373A
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task
vehicle
algorithm
matching
vehicles
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张德干
安宏展
张捷
张婷
曹利香
曹亚辉
张志昊
张平
王法玉
陈洪涛
赵洪祥
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Tianjin University of Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/30—Services specially adapted for particular environments, situations or purposes
    • H04W4/40—Services specially adapted for particular environments, situations or purposes for vehicles, e.g. vehicle-to-pedestrians [V2P]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/22—Traffic simulation tools or models
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W28/00—Network traffic management; Network resource management
    • H04W28/16—Central resource management; Negotiation of resources or communication parameters, e.g. negotiating bandwidth or QoS [Quality of Service]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W28/00—Network traffic management; Network resource management
    • H04W28/16—Central resource management; Negotiation of resources or communication parameters, e.g. negotiating bandwidth or QoS [Quality of Service]
    • H04W28/18—Negotiating wireless communication parameters
    • H04W28/22—Negotiating communication rate

Abstract

A vehicle networking task unloading method based on a bipartite graph matching strategy is disclosed. In the vehicle network model of vehicle-oriented movement, the vehicle is configured into three vehicle subnetworks according to the turning direction at the next intersection. For each subnetwork, the vehicles communicate with each other via vehicle-to-vehicle communication and with the roadside units via vehicle-to-infrastructure communication. In addition, the method provides a task unloading method based on a bipartite matching algorithm, a vehicle network corresponding to a task unloading decision made at the current moment is constructed into a weighted bipartite, the optimal matching of the bipartite is solved through a Kuhn-Munkres algorithm, and the final purpose is to select a proper adjacent vehicle/edge server as an unloading node and minimize the task delay from the vehicle. Simulation experiment results show that the vehicle network model provided by the invention has better performance in combination with an algorithm, and can obviously reduce transmission delay and packet loss rate of the vehicle network when processing tasks and uploading data.

Description

Internet of vehicles task unloading method based on bipartite graph matching strategy
Technical Field
The invention belongs to the field of Internet of things, and particularly relates to a bipartite graph matching strategy-based vehicle networking task unloading method.
Background
The Internet of vehicles (IoV) as a typical application scenario of the 5G network has great market potential and social value, and thus becomes a hot spot for research in academic circles and industrial circles at home and abroad. The Vehicle networking system is built by means of devices such as a 5G cellular network, an RSU (road side unit), a laser/radar sensor and a camera, and a Vehicle-to-person, vehicle-to-road and network three-dimensional networking system is built, so that Vehicle-to-Vehicle (V2V), vehicle-to-infrastructure (V2I), vehicle-to-pedestrian (V2P) and Vehicle-to-network (V2N) communication is realized, the traffic safety can be greatly improved, and the traffic efficiency is improved. With the rapid development of the internet of vehicles and the increase of the number of vehicles, the generation of massive data can cause that local computing and storage resources can not effectively meet the requirements in time, and the high mobility of the vehicles can cause connection interruption and frequent network change, thereby inevitably influencing the continuity of service, and further reducing the user experience. Thus, the core problems of the internet of vehicles are: and the short-loop transmission and processing of information ultra-low delay interaction and large data volume are realized.
For entertainment applications where latency and reliability are not sensitive, traditional cloud-based working is suitable. However, since the cloud center is usually far from the vehicle, the network delay through the core network and the backbone network is high. To address these challenges, mobile Edge Computing (MEC) has been introduced into the internet of vehicles to enhance the capabilities of the internet of vehicles, thereby creating a new paradigm: vehicle Edge Computing (VEC). Computation offloading is one of key technologies of the MEC, and resources required for executing a computation-intensive and delay-sensitive application are provided to a resource-limited terminal device, so that the running speed of an application program is increased and energy consumption is reduced. Experiments have shown that offloading tasks to MECs can reduce latency by up to 88%. In addition, the coexistence of multiple communication modes in the internet of vehicles enables multiple options for the unloading mode in the internet of vehicles, and how to utilize multiple unloading modes to complete the calculation task more efficiently is also a problem worthy of intensive research.
Disclosure of Invention
The invention aims to solve the problem that due to the fact that the configuration of an unloading node discovery mechanism is too ideal, candidate unloading nodes are omitted, and unloading decisions cannot be made to optimally solve the problem that VANETs meet requirements in different application environments, and provides a bipartite graph matching strategy-based vehicle networking task unloading method. The invention aims at the mobility of the vehicle, and 1) considers that a vehicle network model VDM for the directional movement of the vehicle is provided to provide services for the vehicle in the VEC. The model can effectively utilize computing resources in the vehicle and reduce communication congestion of V2I and V2V; 2) In order to minimize the time delay of the task, a bipartite graph matching unloading algorithm by Kuhn-Munkres is provided; 3) The performance of the unloading algorithm under the VDM is evaluated through simulation experiments, and experimental results show that the bipartite graph matching algorithm can effectively reduce task time delay and packet loss rate.
The invention discloses a bipartite graph matching strategy-based vehicle networking task unloading method, which mainly comprises the following key steps:
1, constructing a system model:
1.1, establishing a vehicle and road model;
1.2, establishing a calculation and communication model;
2, algorithm design and analysis:
2.1, hungarian algorithm;
2.2, kuhn-Munkres algorithm;
and 2.3, calculating a task unloading algorithm of the vehicle network based on the bipartite graph matching algorithm.
Firstly, in step 1.1, a vehicle and road model is established, and a vehicle network model for vehicle directional movement is proposed, which is denoted as VDM, wherein vehicles with the same steering direction are configured into a sub-network, and the configuration of VDM is described as follows: is provided with
Figure BDA0003739172420000021
Are respectively a road section s j A vehicle sub-network of a middle left lane, a straight lane and a right lane, and s j The vehicles in (1) are divided into three classes according to the turning direction of the vehicles at the next intersection, and the vehicles in each class are distributed into the same vehicle subnet, specifically, the vehicles
Figure BDA0003739172420000022
If the vehicle turns right at the next intersection, the vehicle will be assigned to the next intersection
Figure BDA0003739172420000023
Similarly, if it goes straight or turns left at the next intersection, the vehicle
Figure BDA0003739172420000024
Will be assigned to
Figure BDA0003739172420000025
Or
Figure BDA0003739172420000026
All vehicles in the subnet communicate with it in the same subnet via V2VOther vehicles communicate, and all vehicles directly communicate with the RSU through a V2I communication mode; the method comprises the steps that vehicles in different subnets cannot be directly connected through V2V communication, VDMs can adapt to different intersection scenes after small adjustment, the sizes and the number of subnets need to be adjusted properly according to different scenes, the VDMs in the intersection scenes are mainly researched, in addition, the subnets in the VDMs are configured or initialized on road sections adjacent to the intersection, then, the vehicles in the same subnet are mutually connected until the vehicles drive to the road sections adjacent to the next intersection, in addition, if the vehicles drive to the coverage range of other RSUs, the feedback of tasks is unloaded from original RSUs executing the tasks to RSUs covering the vehicles at present, and then, the current RSUs unload the feedback of the tasks to the vehicles.
Step 1.2, a calculation and communication model is established, when a vehicle has a calculation requirement in the driving process, task unloading is usually adopted, a calculation task is unloaded to a scene of calculation on an RSU, data to be calculated, which is unloaded to an edge server by default, is larger than data output after calculation, and V is set R ＝{o 1 ，o 2 ，…，o n }，D＝{d 1 ，d 2 ，…，d n Are the set of vehicles generating the task and the corresponding locations where the task is performed, o i Is task r i Generated vehicles, d i Is r i For each task r i By r i ＝{b 0 ，b 1 ，t i ，o i ，d i Where i = {1,2, \8230;, n } denotes the details of the task, b 0 And b 1 The size of the upload and download data, t, of ri, respectively i Is r i Time of arrival, wherein the uploaded data is task r i Of the original size, the downloaded data being task r i Feeding back a result after the execution is finished;
let ω be the computation strength of a unit bit CPU cycle, which is the CPU cycle required to compute a relatively large or small input data, so the CPU cycle required for this task is b 0 ω, each computation task can only be on the other subnetLocal execution on one vehicle or remote execution with off-load of tasks on the edge server, assuming the vehicle computing power is the same for all vehicles, therefore, let f 0 And f 1 The CPU clock frequencies of the edge servers deployed in the vehicle and RSU respectively,
Figure BDA0003739172420000031
is the calculated delay of the execution of the task ri in the vehicle or RSU, and therefore, the calculated delay
Figure BDA0003739172420000032
Is defined as:
Figure BDA0003739172420000033
suppose that
Figure BDA0003739172420000034
And
Figure BDA0003739172420000035
respectively represent nodes o i And node d i At t i Channel loss and distance of time, for V2V communications, the channel loss is approximately equal to the deterministic path loss, thus, defining
Figure BDA0003739172420000036
Comprises the following steps:
Figure BDA0003739172420000037
in the formula A o For a suitable path loss factor, α>1 is the path loss exponent;
assuming there is no interference between different vehicle subnets, at t i At time, the channel bandwidth of V2V communication is denoted as B 0 The channel bandwidth of V2I communication is denoted as B 1 Thus, task r i Is denoted as B μ The definition is as follows:
Figure BDA0003739172420000038
let the transmission power of each vehicle be the same, let P be the transmission rate of the vehicle, and N be 0 Representing the noise power, t i Time of day, node o i To d i The uplink transmission rate of the upload task or data is recorded as
Figure BDA0003739172420000039
Node o i To d is i The downstream transmission rate of the downloaded data is recorded as
Figure BDA00037391724200000310
The uplink transmission rate may be defined as:
Figure BDA00037391724200000311
wherein the content of the first and second substances,
Figure BDA00037391724200000312
Figure BDA00037391724200000313
represents t i Time passes through a radio channel and d i A set of connected nodes;
regarding task i, let t (i) be r i The feedback of the result of (2) starts from d i Return to o i Thus, t (i) can be calculated by:
Figure BDA00037391724200000314
then task r i The downlink transmission rate at time t (i) is defined as:
Figure BDA00037391724200000315
wherein the content of the first and second substances,
Figure BDA0003739172420000041
F t(i) is to pass through a radio channel at time t (i) and o i Set of connected nodes, hypothesis
Figure BDA0003739172420000042
Is a task r i The communication delay of (2) is defined as:
Figure BDA0003739172420000043
let t total For the total delay of all unloaded tasks in a certain time period, to avoid the influence of extreme values, expressed as an average value, the total delay of the tasks in R is:
Figure BDA0003739172420000044
because the tasks on each vehicle are inseparable, one vehicle can only process one task at the same time, and in addition, the number of tasks processed in the RSUs is not limited, because each RSU is provided with an edge server which has abundant computing resources, g (k) is set to represent the loading state of a node k (k is equal to U V), the loading state of the node k is defined as the number of tasks unloaded from other vehicles to k, N = {1,2, \8230;, N }, and the expression of the decision problem is as follows:
Figure BDA0003739172420000045
Figure BDA0003739172420000046
Figure BDA0003739172420000047
Figure BDA0003739172420000048
Figure BDA0003739172420000049
Figure BDA00037391724200000410
τ∈{l,s,r},d i ∈D (17)
the goal given in equation (11) is to minimize the average response time of tasks, constraint (12) ensures that each task must be offloaded to a vehicle or a pending RSU, constraint (13) ensures that a vehicle can only process one task, constraint (14) ensures that the destination to execute a task is resource rich, and constraint (15) ensures that o is i Tasks in (a) can only be offloaded to vehicles in the same vehicle subnet or RSU;
decision making problem
Figure BDA00037391724200000411
Is a random optimization problem, if the uplink transmission rate, the download transmission rate and the vehicle position are fixed and the time of task arrival is given in advance, the decision problem is made
Figure BDA00037391724200000412
It can be solved in polynomial time, however, in a real traffic system, the position of the vehicle is rapidly changed with the passage of time, so the uplink transmission rate and the download transmission rate are changed with the passage of time, and further, the arrival of the task cannot be known in advance, and at the same time, information is difficult to predict due to the high mobility of the vehicleThus, without prior knowledge of the above information, it is difficult to determine whether a task whose decision is optimal is offloaded.
Further, the Hungarian algorithm in the step 2.1 is used for solving the maximum matching problem in bipartite graph matching;
the specific steps of algorithm 1, hungarian algorithm, are described as follows:
step 1: taking any matching from the bipartite graph G as an initial matching M, wherein M can be an empty set;
and 2, step: if all some parts in the bipartite graph are matched, the matching M at the moment is the maximum matching of G, the algorithm is terminated, if all nodes on two sides of the bipartite graph are matched, M is the perfect matching of G, otherwise, any unmatched node w in G: taking any matching from the bipartite graph G as an initial matching M, wherein M can be an empty set;
and step 3: searching for the expandable paths in the G by utilizing alternative width first search, if no expandable path can be found, the expandable paths cannot be expanded continuously, the matching M at the moment is the maximum matching of the G, and the algorithm is ended;
and 4, step 4: the edges in the found expandable path are reversed, namely the matched edges are changed into non-matched edges, the non-matched edges are changed into matched edges, the number of the non-matched edges in the expandable path is always 1 more than that of the matched edges, then the matching of the graph G is expanded, M is equal to the matching obtained by new expansion, and the step 3 is carried out;
and 5: outputting M;
wherein, the bipartite graph G (R ', P, E) represents the vehicle network to which the task offloading decision is made at the current time t, wherein R' and P are two disjoint and independent sets, respectively.
The Kuhn-Munkres algorithm in the step 2.2, the Kuhn-Munkres algorithm, referred to as KM algorithm for short, is a common algorithm for solving the optimal matching, and the optimal matching is the matching with the maximum weight sum;
the specific steps of algorithm 2Kuhn-Munkres algorithm are described as follows:
step 1: initializing the value of a topmark;
step 2: and obtaining corresponding equal subgraphs, and calling an algorithm 1 Hungarian algorithm to obtain perfect matching of the equal subgraphs. If the perfect matching exists, ending, otherwise, entering the step 3;
and 3, step 3: modifying the top mark value, and turning to the step 2;
and 4, step 4: repeating step 2 and step 3 until a perfect match of equal subgraphs is found.
Step 2.3, calculating a task offloading algorithm for the vehicle network based on the bipartite graph matching algorithm, wherein the algorithm is used for performing task offloading decisions, and a KM algorithm is utilized, and firstly, a weighted bipartite graph, namely G (R ', P, E), is constructed to represent the vehicle network corresponding to the task offloading decision made at the current time t, wherein R' and P are two disjoint and independent sets respectively; bipartite graph matching algorithm works in such a way that the KM algorithm is suitable for one-to-one matching, each RSU can assume a plurality of tasks, so that a new graph G ' = (R ', P ', E ') must first be constructed, in which P ' consists of P and n ' -1 new nodes, each of which is a virtual RSU, and E ' differ from P in the graph G in that m The connected edges are assigned to the P m And all n '-1 new nodes, so that each node in the set corresponds to a task, and the weight of the edge is marked as omega' ij, meaning that the task ri is offloaded to P j Then, in the bipartite graph matching algorithm, the maximum weight matching in G 'is obtained by adopting a KM method, and finally, the matching result is the decision of task unloading in the problem P';
algorithm 3 the specific steps of the bipartite graph matching algorithm based on Kuhn-Munkres are described as follows:
step 1: for the input G (R ', P, E) (to indicate the vehicle network for which the task offloading decision is made at the current time t), a new bipartite graph G ' = (R ', P ', E ') is first created;
and 2, step: judging the number of available nodes, and if i is less than or equal to m and is less than or equal to m + n '-1 under the premise that i is less than or equal to 1' i ＝p i Otherwise p' i ＝p m ；
And step 3: judging whether all nodes on both sides of the bipartite graph are matched, namely solving E' and p in the graph G m The connected edges are assigned to p m And all n '-1 new nodes, so that each node in the set corresponds to one task, and meanwhile, the weight of the edge is marked as omega' ij;
and 4, step 4: calling an algorithm 2, namely finding a maximum weighted match in G' by using a KM method, and returning a matching result;
and 5: calling formula (18) to calculate x ij When x is ij =1, the task ri is offloaded to p j ；
And 6: outputting X, namely a task unloading decision generated by a bipartite graph matching algorithm;
assuming η is the number of vertices in P ', i.e. η = m + n ' -1, as shown in algorithm 1, the time complexity of the algorithm is O (η), a new set P ' is created in bipartite graph G ', a new set E ' of edges is created in O (z), so the proposed algorithm runs within the time complexity O (η + z) to create G ″, and the time complexity of the KM method is O (η 3), so the time complexity of algorithm 1 to make task offload decisions at time t is also O (η |) 3 )。
The invention has the advantages and positive effects that:
the invention mainly designs a bipartite graph matching strategy-based vehicle networking task unloading method, and in the method, in order to better provide service for vehicles and traffic systems, the invention provides a directional vehicle mobile network model named as VDM. In the model, the vehicles would be configured into three vehicle subnetworks according to the direction of turn at the next intersection. The vehicles may communicate with each other via V2V and with the RSU via V2I. Meanwhile, a task unloading scheme based on a bipartite graph matching algorithm is provided for solving the optimization problem. Through simulation experiments, the influence of different factors of VEC task unloading is analyzed, and the average task completion time is smaller under the condition that the number of tasks in unit time is the same as the size of uploaded data. In addition, the packet loss rate and the transmission delay of the two algorithms provided by the invention are both smaller than those of the algorithms such as RandTO and UniTO, and the advantages are obvious.
Drawings
FIG. 1 is a graph of the number of tasks per unit time versus the average task completion time;
FIG. 2 is a graph of the relationship between the amount of data uploaded by a task and the average task completion time;
FIG. 3 is a graph of the number of CPU cycles required for task execution versus the average task completion time;
FIG. 4 is a graph of packet loss rate versus content size;
FIG. 5 is a graph of packet loss rate versus average vehicle speed;
FIG. 6 is a graph of average transmission delay versus content size;
FIG. 7 is a graph of average propagation delay versus average vehicle speed;
FIG. 8 is a flowchart of a method for offloading tasks from a vehicle networking system based on bipartite graph matching strategy in accordance with the present invention;
Detailed Description
Example 1:
the method designed by the embodiment is to build the whole experimental environment according to the simulation tool. The bipartite graph matching algorithm provided by the invention is compared with different Edge unloading strategies of V2V (unloading by adopting a V2V communication mode), onlyLocal (only local execution, namely all computing tasks are executed in a local vehicle processor without unloading), onlyEdge (only Edge unloading, namely all computing tasks are unloaded to an Edge server for execution) and Loacl & Edge (each half of local execution and Edge unloading). The implementation operation mainly involves the establishment of a simulation tool, the establishment of a simulation scene and a specific algorithm calculation process.
Referring to fig. 8, the method for unloading tasks in the internet of vehicles based on the bipartite graph matching strategy mainly includes the following key steps:
1, constructing a system model:
1.1, establishing a vehicle and road model;
1.2, establishing a calculation and communication model;
2, algorithm design and analysis:
2.1, hungarian algorithm;
2.2, kuhn-Munkres algorithm;
2.3, calculating a task unloading algorithm of the vehicle network based on the bipartite graph matching algorithm;
the invention utilizes the directional vehicle mobile network model and combines the bipartite graph matching algorithm, thereby obviously improving the load sharing rate and unloading efficiency when processing tasks and uploading data of the Internet of vehicles, and reducing the packet loss rate and transmission delay. Step 1.1, vehicle and road models are established, and a vehicle network model for vehicle directional movement is provided, which is denoted as VDM, wherein vehicles with the same steering direction are configured into a sub-network, and the configuration of VDM is described as follows
Figure BDA0003739172420000071
Respectively a road section s j The vehicle sub-networks of the middle left lane, the straight lane and the right lane are connected with s j The vehicles in (1) are divided into three classes according to the turning direction of the vehicles at the next intersection, and the vehicles in each class are distributed into the same vehicle subnet, specifically, the vehicles
Figure BDA0003739172420000072
If the vehicle turns right at the next intersection, the vehicle will be assigned to
Figure BDA0003739172420000073
Similarly, if it goes straight or turns left at the next intersection, the vehicle
Figure BDA0003739172420000074
Will be assigned to
Figure BDA0003739172420000075
Or
Figure BDA0003739172420000076
All vehicles in the subnet communicate with other vehicles in the same subnet through V2V, and simultaneously, all vehicles directly communicate with the RSU through a V2I communication mode; the vehicles in different subnets cannot be directly connected through V2V communication, the VDM can adapt to different cross scenes after small adjustment, the size and the number of the subnets need to be properly adjusted according to different scenes, and the main scheme is thatVDMs in intersection scenarios are studied, and furthermore, subnets in the VDMs are configured or initialized on road segments adjacent to an intersection, then vehicles within the same subnet remain interconnected until they travel to a road segment adjacent to the next intersection, and further, if a vehicle travels within the coverage of other RSUs, the feedback for the mission is offloaded from the original RSU performing the mission to the RSU currently covering the vehicle, which then offloads the feedback for the mission to the vehicle.
Step 1.2, a calculation and communication model is established, when a vehicle has a calculation requirement in the driving process, task unloading is usually adopted, a calculation task is unloaded to a scene of calculation on an RSU, data to be calculated, which is unloaded to an edge server by default, is larger than data output after calculation, and V is set R ＝{o 1 ，o 2 ，…，o n }，D＝{d 1 ，d 2 ，…，d n Are respectively the set of vehicles generating the task and the corresponding locations where the task is performed, o i Is task r i Generated vehicles, d i Is r i For each task r i By r, using i ＝{b 0 ，b 1 ，t i ，o i ，d i Where i = {1,2, \8230;, n } denotes the details of the task, b 0 And b 1 The size of the upload and download data, t, of ri, respectively i Is r i Time of arrival, wherein the uploaded data is task r i Of the original size, the downloaded data being task r i Feeding back a result after the execution is finished;
let ω be the computation strength of a unit bit CPU cycle, which is the CPU cycle required to compute a relatively large or small input data, so the CPU cycle required for this task is b 0 ω, each computing task can only be performed locally on another vehicle on its subnet, or remotely off-load the task on an edge server, assuming all vehicles have the same vehicle computing power, therefore, let f 0 And f 1 The CPU clock frequencies of the edge servers deployed in the vehicle and RSU respectively,
Figure BDA0003739172420000081
is the calculated delay of executing the task ri in the vehicle or RSU, and therefore, the calculated delay
Figure BDA0003739172420000082
Is defined as:
Figure BDA0003739172420000083
wherein d is i Is task r i Is assumed to be performed at
Figure BDA0003739172420000084
And
Figure BDA0003739172420000085
respectively represent nodes o i And node d i At t i Channel loss and distance at time, for V2V communication, the channel loss is approximately equal to the deterministic path loss, thus defining
Figure BDA0003739172420000086
Comprises the following steps:
Figure BDA0003739172420000087
in the formula A o For a suitable path loss coefficient, α > 1 is the path loss exponent;
assuming there is no interference between different vehicle subnets, at t i At time, the channel bandwidth of V2V communication is denoted as B 0 The channel bandwidth of V2I communication is denoted B 1 Thus, task r i Is denoted as B μ The definition is as follows:
Figure BDA0003739172420000091
let the transmission power of each vehicle be the same, let P beTransmission rate of vehicle, N 0 Representing the noise power, t i Time of day, node o i To d i The uplink transmission rate of the upload task or data is recorded as
Figure BDA0003739172420000092
Node o i To d is i The downstream transmission rate of the downloaded data is recorded as
Figure BDA0003739172420000093
The uplink transmission rate may be defined as:
Figure BDA0003739172420000094
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003739172420000095
Figure BDA0003739172420000096
denotes t i Time passes through a radio channel and d i A set of connected nodes;
about task r i Let t (i) be i, and feedback of results begin from d i Return to o i Thus, t (i) can be calculated by:
Figure BDA0003739172420000097
wherein b is 0 Is task r i The size of the data to be uploaded is,
Figure BDA0003739172420000098
is a node o i To d i The uplink transmission rate of the uploading task or data is the task r i The downlink transmission rate at his t (i) instant is defined as:
Figure BDA0003739172420000099
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00037391724200000910
F t(i) is to pass through a radio channel at time t (i) and o i Set of connected nodes, hypothesis
Figure BDA00037391724200000911
Is task r i The communication delay of (2) is defined as:
Figure BDA00037391724200000912
let t total For the total delay of all unloaded tasks in a certain time period, to avoid the influence of extreme values, expressed as an average value, the total delay of the tasks in R is:
Figure BDA00037391724200000913
because the tasks on each vehicle are inseparable, one vehicle can only process one task at the same time, and in addition, the number of tasks processed in the RSUs is not limited, because each RSU is provided with an edge server which has abundant computing resources, g (k) is set to represent the loading state of a node k (k is equal to U V), the loading state of the node k is defined as the number of tasks unloaded from other vehicles to k, N = {1,2, \8230;, N }, and the expression of the decision problem is as follows:
Figure BDA0003739172420000101
Figure BDA0003739172420000102
Figure BDA0003739172420000103
Figure BDA0003739172420000104
Figure BDA0003739172420000105
Figure BDA0003739172420000106
τ∈{l，s，r}，d i ∈D (17)
the goal given in equation (11) is to minimize the average response time of tasks, constraint (12) ensures that each task must be offloaded to a vehicle or a pending RSU, constraint (13) ensures that a vehicle can only process one task, constraint (14) ensures that the destination to execute a task is resource rich, and constraint (15) ensures that o is i Tasks in (a) can only be offloaded to vehicles in the same vehicle subnet or RSU;
attention to decision problems
Figure BDA0003739172420000107
Is a random optimization problem, if the uplink transmission rate, the download transmission rate and the vehicle position are fixed and the time of task arrival is given in advance, the decision problem is made
Figure BDA0003739172420000108
It can be solved in polynomial time, however, in a real traffic system, the position of the vehicle is rapidly changed with the passage of time, and thus the upstream transmission rate and the download transmission rate are changed with the passage of time, and further, the arrival of the task cannot be known in advanceAlso, because of the high mobility of the vehicle, the information is difficult to predict, and thus, it is difficult to determine whether to best decide to offload a task without prior knowledge of the information.
Further, the Hungarian algorithm in the step 2.1 is used for solving the maximum matching problem in bipartite graph matching;
the specific steps of algorithm 1, hungarian algorithm, are described as follows:
step 1: taking any matching from the bipartite graph G as an initial matching M, wherein M can take an empty set;
and 2, step: if all some parts in the bipartite graph are matched, the matching M at the moment is the maximum matching of G, the algorithm is terminated, if all nodes on two sides of the bipartite graph are matched, M is the perfect matching of G, otherwise, any unmatched node w in G: taking any matching from the bipartite graph G as an initial matching M, wherein M can take an empty set;
and step 3: searching for the expandable paths in the G by utilizing alternative width first search, if no expandable path can be found, the expandable paths cannot be expanded continuously, the matching M at the moment is the maximum matching of the G, and the algorithm is ended;
and 4, step 4: the edges in the found expandable path are reversed, namely the matched edges are changed into non-matched edges, the non-matched edges are changed into matched edges, the number of the non-matched edges in the expandable path is always 1 more than that of the matched edges, then the matching of the graph G is expanded, M is equal to the matching obtained by new expansion, and the step 3 is carried out;
and 5: outputting M;
wherein the bipartite graph G (R ', P, E) represents the vehicle network corresponding to the task offload decision made at the current time t, where R'
And P are two disjoint and independent sets, respectively.
The Kuhn-Munkres algorithm in the step 2.2 is a common algorithm for solving the optimal matching, and the optimal matching is the matching with the maximum weight sum;
the specific steps of algorithm 2Kuhn-Munkres algorithm are described as follows:
step 1: initializing the value of a topmark;
step 2: obtaining corresponding equal subgraphs, calling an algorithm 1 Hungarian algorithm to ask for perfect matching of the equal subgraphs, if the perfect matching exists, ending, and otherwise, entering a step 3;
and step 3: modifying the value of the vertex index, and turning to the step 2;
and 4, step 4: repeating step 2 and step 3 until a perfect match of equal subgraphs is found.
Step 2.3, calculating a task offloading algorithm for the vehicle network based on the bipartite graph matching algorithm, wherein the algorithm is used for performing task offloading decisions, and a KM algorithm is utilized, and firstly, a weighted bipartite graph, namely G (R ', P, E), is constructed to represent the vehicle network corresponding to the task offloading decision made at the current time t, wherein R' and P are two disjoint and independent sets respectively; bipartite graph matching algorithm works in such a way that the KM algorithm is suitable for one-to-one matching, each RSU being able to take on a plurality of tasks, so that a new graph G '= (R', P ', E') must first be constructed, in which graph G 'P' consists of P and n '-1 new nodes, each of which is a virtual RSU, with the difference between E and E' being that graph G is a virtual one with P m The connected edges are assigned to the P m And all n '-1 new nodes, so that each node in the set corresponds to a task, and the weight of the edge is marked as omega' ij, meaning that the task ri is offloaded to P j Then, in the bipartite graph matching algorithm, the maximum weight matching in G 'is obtained by adopting a KM method, and finally, the matching result is the decision of task unloading in the problem P';
algorithm 3 the specific steps of the bipartite graph matching algorithm based on Kuhn-Munkres are described below:
step 1: for an input G (R ', P, E) (to indicate the vehicle network to which the task offloading decision is made at the current time t), a new bipartite graph G ' = (R ', P ', E ') is first created;
step 2: judging the number of available nodes, and if i is less than or equal to m and is less than or equal to m + n '-1 under the premise that i is less than or equal to 1' i ＝p i Otherwise p' i ＝p m ；
And step 3: determine places on two sides of the bipartite graphWhether all nodes are matched, i.e. finding E', and p in graph G m The connected edges are assigned to p m And all n '-1 new nodes such that each node in the set corresponds to a task, and the weight of an edge is denoted as ω' ij ；
And 4, step 4: calling an algorithm 2, namely finding a maximum weighted match in G' by using a KM method, and returning a matching result;
and 5: calling formula (18) to calculate x ij When x is ij When =1, task r i Is unloaded to p j ；
Step 6: outputting X, namely a task unloading decision generated by a bipartite graph matching algorithm;
assuming η is the number of vertices in P ', i.e. η = m + n ' -1, as shown in algorithm 1, the time complexity of the algorithm is O (η), a new set P ' is created in bipartite graph G ', a new set E ' is created in O (z), and therefore, it is proposed that the algorithm operates within the time complexity O (η + z) to create G ″, and further, the time complexity of the KM method is O (η + z) 3 ) Thus, the time complexity of algorithm 1 in making task offload decisions at time t is also O (η) 3 )。
In the example, a simulation scene is constructed, a 250m long road section is used for testing, the number of vehicles is set to be in the range of 10-50, the channel bandwidth is 30MHz, the average size of task data is 500Kbits, the computing capacity of an edge server is 100GHz, the vehicle transmission power is set to be 2W, an IEEE 802.11p is used in an MAC layer protocol, the V2I transmission rate is 4Mb/s, the V2V transmission rate is set to be 2Mb/s, computing tasks can be generated in real time, and the computing tasks of each vehicle are considered to arrive in a Poisson distribution mode. Three simulation experiments will be performed in this environment.
1) Experiment A: the invention records the influence of the change of the factors on the average task completion time by changing the factors of the number of tasks in unit time, the size of uploaded data and the number of CPU cycles required by task execution, and compares the performances of the proposal provided by the invention with a RandTO (random task unloading) scheme, a UniTO (unified task unloading) scheme, noAny (no task unloading), GA (Genetic Algorithm) and a V2V (unloading by adopting a V2V communication mode) scheme.
2) Experiment B: according to the invention, the influence of the change of the content size and the vehicle speed provided by the Internet of vehicles system on the system packet loss rate and the transmission delay is recorded by changing the factors.
3) Experiment C: the invention analyzes the average uploading time and the average calculating time of different algorithms by changing the traffic scene.
The simulation will consider three performance indicators, which are:
1. the task completion time is averaged. The average task completion time is also called the average turnover time, the average turnover time = the total time of task turnover/the number of tasks, wherein the task turnover time = the task completion time-the task arrival time.
2. And (4) the packet loss rate. The packet loss rate is the ratio of lost packets to transmitted packets.
3. And (4) transmission delay. The transmission delay refers to the time interval from the sender of a message to the recipient of the message.
The results of the simulation experiments for this example are as follows:
1. influence of factors of the number of tasks in different unit time, the size of uploaded data and the number of CPU cycles required by task execution on average task completion time
1) Relation between number of tasks in different unit time and average task completion time
Fig. 1 shows the relationship between the number of tasks per unit time and the average task completion time. As the number of tasks in a unit time increases, the average task completion time of the six algorithms will increase. Similar to the result in an ideal scene, the bipartite graph matching algorithm can complete the task faster. The average task completion time is lower than in several other schemes. 2) Data transfer rate and average route request.
2) Relation between different uploaded data volumes and average task completion time
Fig. 2 shows an influence curve of the data volume uploaded by the task on the average task completion time, and the average task completion time increases with the increase of the uploaded data, which is in accordance with the conventional principle. The curves for the NoAny, randTO and V2V schemes are always located at the top of the figure, which means that the average task completion time for these schemes is longer with the same amount of uploaded data. On the contrary, the curve of the scheme proposed by the invention is positioned at the lowest part in the graph, namely the average task completion time of the scheme is shortest, and the scheme is superior to other five algorithm schemes.
3) Relation between CPU period number required by different task execution and average task completion time
The number of CPU cycles required for task execution is analyzed in relation to the average task completion time, as shown in fig. 3. When the number of CPU cycles is less than or equal to 0.3, the difference of the average task completion time of the six schemes is extremely small, and the curves are overlapped in the figure. And when the number of the CPU cycles is more than 0.4, the average task completion time required by RandTO, uniTO, V2V, noAny and other schemes is obviously increased and is increased faster than the scheme provided by the invention. Therefore, the average task completion time of the algorithm provided by the research scheme is shortest and is superior to other algorithm schemes.
2. Influence of different content sizes and vehicle speeds provided by the Internet of vehicles system on system packet loss rate and transmission delay
4) Relationship between packet loss rate and content size
Fig. 4 shows the relationship between the packet loss rate and the content size. As can be seen from the figure, the packet loss rate tends to increase as the content provided by the system increases. Compared with the other five algorithms, the bipartite graph matching algorithm proposed by the invention has the lowest packet loss rate, which may be due to the fact that the vehicle directly retrieves content from nearby RSUs. In several other scenarios, however, the desired vehicle is not downloaded from multiple proxy and relay vehicles for a data request, which results in frequent lane contention. Therefore, the packet loss rate of the present study is the lowest when receiving data files of the same size.
5) Relation between packet loss rate and vehicle speed
Fig. 5 shows the relationship between the packet loss rate and the vehicle speed. When the maximum request data is set to 400KB, the relation between the packet loss rate and the vehicle speed of the vehicle receiving the message can be obtained. As can be seen from the figure, the packet loss rates of the six schemes have the same packet loss tendency as the vehicle speed increases. Increasing the download success rate may allow more vehicles to participate, but may also result in higher vehicle packet loss rates.
6) Relationship between transmission delay and content size
Fig. 6 shows the average transmission delay versus the content size. As the content provided by the system increases, the average transmission delay tends to increase. Compared with the other five algorithms, the transmission delay of the bipartite graph matching algorithm is found to be relatively small.
7) Relationship between transmission delay and vehicle speed
Fig. 7 shows the relationship of the transmission delay to the vehicle speed. As can be seen from the figure, none of the six curves has obvious fluctuation and small change, which means that the vehicle speed has little influence on the average transmission delay of different schemes. In addition, the curve of the scheme proposed by the invention is positioned at the lowest part in the graph, namely the bipartite graph matching algorithm has the lowest transmission delay.
3. Average uploading time and average calculating time of different algorithms under different traffic scenes
The characteristics under different traffic scenarios are shown in table 1:
TABLE 1 traffic scene characteristics
Figure BDA0003739172420000141
8) Average upload time in different traffic scenarios
Because RanTO task uploads are randomly assigned to MEC servers and tasks have a long delay before a vehicle drives into a given server, ranTO performance is always the worst. The average uploading time of the bipartite graph matching algorithm and the GA provided by the invention is much lower than that of other algorithms. In particular, the algorithm proposed by the present invention achieves the lowest upload time in almost all service scenarios.
9) Average calculation time under different traffic scenes
The OnlyLocal scheme is much higher than other algorithms under heavy workload, possibly because of the poor computing power of the local server. The average computation time of the bipartite graph matching algorithm is lower than that of the Onlylocal, GA and RanIO. This is because the present invention proposes that the algorithm can adaptively offload tasks to the MEC or cloud depending on the real-time workload.
Simulation results show that by analyzing the influence of different factors of VEC task unloading, the average task completion time is calculated and distributed to be smaller by bipartite matching under the condition that the number of tasks in unit time is the same as the size of uploaded data. In addition, the packet loss rate and the transmission delay of the two algorithms provided by the invention are smaller than those of RandTO, uniTO and the like, and the advantages are obvious.

Claims (6)

1. A bipartite graph matching strategy-based Internet of vehicles task unloading method is characterized by mainly comprising the following steps:
1, constructing a system model:
1.1, establishing a vehicle model and a road model;
1.2, establishing a calculation and communication model;
2, algorithm design and analysis:
2.1, hungarian algorithm;
2.2, kuhn-Munkres algorithm;
and 2.3, calculating a task unloading algorithm of the vehicle network based on the bipartite graph matching algorithm.
2. The bipartite graph matching strategy-based task offloading method for internet of vehicles according to claim 1, wherein in step 1.1, vehicle and road models are established, a vehicle network model for vehicle directional movement, denoted as VDM, is proposed, wherein vehicles with the same steering direction are configured as a sub-network, and the configuration of VDM is described by setting
Figure FDA0003739172410000011
Are respectively a road section s j A vehicle sub-network of a middle left lane, a straight lane and a right lane, and s j The vehicles in (1) are divided into three classes according to the turning direction of the vehicles at the next intersection, and the vehicles in each class are distributed into the same vehicle subnet, specifically, the vehicles
Figure FDA0003739172410000012
If the vehicle turns right at the next intersection, the vehicle will be assigned to
Figure FDA0003739172410000013
Similarly, if it goes straight or turns left at the next intersection, the vehicle
Figure FDA0003739172410000014
Will be distributed to
Figure FDA0003739172410000015
Or
Figure FDA0003739172410000016
All vehicles in the subnet communicate with other vehicles in the same subnet through V2V, and simultaneously, all vehicles directly communicate with the RSU through a V2I communication mode; the method comprises the steps that vehicles in different subnets cannot be directly connected through V2V communication, the VDM can adapt to different intersection scenes after small adjustment, the size and the number of the subnets need to be adjusted properly according to different scenes, the VDM under the intersection scene is mainly researched, in addition, the subnets in the VDM are configured or initialized on road sections adjacent to an intersection, then the vehicles in the same subnet are mutually connected until the vehicles drive to the road sections adjacent to the next intersection, in addition, if the vehicles drive to the coverage range of other RSUs, the feedback of tasks is unloaded from original RSUs executing the tasks to RSUs of current covered vehicles, and then the current RSUs unload the feedback of the tasks to the vehicles.
3. The bipartite graph matching strategy-based task unloading method for the internet of vehicles according to claim 1, wherein in step 1.2, a calculation and communication model is established, when a vehicle has a calculation demand during driving, task unloading is usually adopted, calculation tasks are unloaded to a RSU for calculation, and data to be calculated, which are unloaded to an edge server by default, are unloaded to the RSUGreater than the calculated output data, set V R ＝{o 1 ,o 2 ,…,o n }，D＝{d 1 ,d 2 ,…,d n Are respectively the set of vehicles generating the task and the corresponding locations where the task is performed, o i Is task r i Generated vehicles, d i Is r i For each task r i By r i ＝{b 0 ,b 1 ,t i ,o i ,d i Where i = {1,2, \8230;, n } denotes the details of the task, b 0 And b 1 Are respectively r i Size of upload and download data of, t i Is r i Time of arrival, wherein the uploaded data is task r i Of the original size, the downloaded data being task r i Feeding back a result after the execution is finished;
let ω be the computation strength of a unit bit CPU cycle, which is the CPU cycle required to compute a relatively large or small input data, so the CPU cycle required for this task is b 0 ω, each computing task can only be performed locally on another vehicle on its subnet, or remotely off-load the task on an edge server, assuming all vehicles have the same vehicle computing power, therefore, let f 0 And f 1 The CPU clock frequencies of the edge servers deployed in the vehicle and RSU respectively,
Figure FDA0003739172410000021
is the calculated delay of the execution of the task ri in the vehicle or RSU, and therefore, the calculated delay
Figure FDA0003739172410000022
Is defined as follows:
Figure FDA0003739172410000023
suppose that
Figure FDA0003739172410000024
And
Figure FDA0003739172410000025
respectively represent nodes o i And node d i At t i Channel loss and distance of time, for V2V communications, the channel loss is approximately equal to the deterministic path loss, thus, defining
Figure FDA0003739172410000026
Comprises the following steps:
Figure FDA0003739172410000027
in the formula A o For a suitable path loss factor, α>1 is the path loss exponent;
assuming there is no interference between different vehicle subnets, at t i At time, the channel bandwidth of V2V communication is denoted as B 0 The channel bandwidth of V2I communication is denoted B 1 Thus, task r i Is denoted as B μ The definition is as follows:
Figure FDA0003739172410000028
let the transmission power of each vehicle be the same, let P be the transmission rate of the vehicle, and N be 0 Representing the noise power, t i Time of day, node o i To d i The uplink transmission rate of the upload task or data is recorded as
Figure FDA0003739172410000029
Node o i To d i The downstream transmission rate of the downloaded data is recorded as
Figure FDA00037391724100000210
The uplink transmission rate is defined as:
Figure FDA00037391724100000211
wherein the content of the first and second substances,
Figure FDA00037391724100000212
Figure FDA00037391724100000213
denotes t i Time passes through a radio channel and d i A set of connected nodes;
about task r i Let t (i) be r i The feedback of the result of (2) starts from d i Return to o i Thus, t (i) is calculated by:
Figure FDA0003739172410000031
then task r i The downlink transmission rate at his t (i) instant is defined as:
Figure FDA0003739172410000032
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003739172410000033
F t(i) is to pass through a radio channel at time t (i) and o i Set of connected nodes, hypothesis
Figure FDA0003739172410000034
Is task r i The communication delay of (2) is defined as:
Figure FDA0003739172410000035
let t total For the total delay of all unloaded tasks in a certain time period, to avoid the influence of extreme values, expressed as an average value, the total delay of the tasks in R is:
Figure FDA0003739172410000036
because the tasks on each vehicle are inseparable, one vehicle can only process one task at the same time, and in addition, the number of tasks processed in the RSUs is not limited, because each RSU is provided with an edge server which has abundant computing resources, g (k) is set to represent the loading state of a node k (k is equal to U V), the loading state of the node k is defined as the number of tasks unloaded from other vehicles to k, N = {1,2, \8230;, N }, and the expression of the decision problem is as follows:
Figure FDA0003739172410000037
Figure FDA0003739172410000038
Figure FDA0003739172410000039
Figure FDA00037391724100000310
Figure FDA00037391724100000311
Figure FDA00037391724100000312
τ∈{l,s,r},d i ∈D (17)
the goal given in equation (11) is to minimize the average response time of tasks, constraint (12) ensures that each task must be offloaded to a vehicle or a pending RSU, constraint (13) ensures that a vehicle can only process one task, constraint (14) ensures that the destination to execute a task is resource rich, and constraint (15) ensures that o is i Tasks in (a) can only be offloaded to vehicles in the same vehicle subnet or RSU;
decision problem
Figure FDA00037391724100000313
Is a random optimization problem, if the uplink transmission rate, the download transmission rate and the vehicle position are fixed and the time of task arrival is given in advance, the decision problem is made
Figure FDA0003739172410000041
The solution is achieved in polynomial time, however, in real traffic systems, the position of the vehicle is changed rapidly with the passage of time, so the uplink transmission rate and the download transmission rate are changed with the passage of time, and furthermore, the arrival of the task cannot be known in advance, and at the same time, due to the high mobility of the vehicle, the information is difficult to predict, so that it is difficult to determine whether the task unloading is decided optimally without prior knowledge of the above information.
4. The Internet of vehicles task unloading method based on bipartite graph matching strategy as claimed in claim 1, wherein Hungarian algorithm in step 2.1 is used to solve the maximum matching problem in bipartite graph matching;
the specific steps of algorithm 1, hungarian algorithm, are described as follows:
step 1: taking any matching from the bipartite graph G as an initial matching M, wherein M can take an empty set;
and 2, step: if all some parts in the bipartite graph are matched, the matching M at the moment is the maximum matching of G, the algorithm is terminated, if all nodes on two sides of the bipartite graph are matched, M is the perfect matching of G, otherwise, any unmatched node w in G: taking any matching from the bipartite graph G as an initial matching M, wherein M can take an empty set;
and step 3: searching for the expandable path in G by using alternative width first search, if the expandable path cannot be found, the expandable path cannot be expanded continuously, the matching M at the moment is the maximum matching of G, and the algorithm is ended;
and 4, step 4: the edges in the found expandable path are reversed, namely the matched edges are changed into non-matched edges, the non-matched edges are changed into matched edges, the number of the non-matched edges in the expandable path is always 1 more than that of the matched edges, then the matching of the graph G is expanded, M is equal to the matching obtained by new expansion, and the step 3 is carried out;
and 5: outputting M;
wherein the bipartite graph G (R ', P, E) represents the vehicle network for which the task offloading decision is made at the current instant t, wherein R' and P are two disjoint and independent sets, respectively.
5. The bipartite graph matching strategy-based vehicle networking task offloading method of claim 1, wherein the Kuhn-Munkres algorithm in step 2.2 is a common algorithm for solving an optimal match, which is the one with the largest sum of weights;
the specific steps of algorithm 2Kuhn-Munkres algorithm are described as follows:
step 1: initializing the value of a topmark;
step 2: obtaining corresponding equal subgraphs, calling the algorithm 1 Hungarian algorithm to evaluate the perfect matching of the equal subgraphs, if the perfect matching exists, ending, and otherwise, entering the step 3;
and 3, step 3: modifying the value of the vertex index, and turning to the step 2;
and 4, step 4: repeating step 2 and step 3 until a perfect match of equal subgraphs is found.
6. The bipartite graph matching based strategy of claim 1The task unloading method of the internet of vehicles is characterized in that in the step 2.3, a task unloading algorithm is calculated on the basis of a bipartite graph matching algorithm for vehicle networks, the algorithm is used for task unloading decision making, a KM algorithm is utilized, and firstly, a weighted bipartite graph, namely G (R ', P, E), is constructed to represent the vehicle network corresponding to the task unloading decision making at the current time t, wherein R' and P are two disjoint and independent sets respectively; bipartite graph matching algorithm works in such a way that the KM algorithm is suitable for one-to-one matching, each RSU can take on a plurality of tasks, and therefore a new graph G ' = (R ', P ', E ') must first be constructed, in which P ' consists of P and n ' -1 new nodes, each of which is a virtual RSU, and E ' differ from P in graph G m The connected edges are assigned to the group P m And all n '-1 new nodes, so that each node in the set corresponds to a task, and the weight of the edge is marked as omega' ij, meaning that the task ri is offloaded to P j Then, in the bipartite graph matching algorithm, the maximum weight matching in G 'is obtained by adopting a KM method, and finally, the matching result is the decision of task unloading in the problem P';
algorithm 3 the specific steps of the bipartite graph matching algorithm based on Kuhn-Munkres are described as follows:
step 1: for an input G (R ', P, E) (to indicate the vehicle network to which the task offloading decision is made at the current time t), a new bipartite graph G ' = (R ', P ', E ') is first created;
step 2: judging the number of available nodes, and if i is less than or equal to m and is less than or equal to m + n '-1 under the premise that i is less than or equal to 1' i ＝p i Otherwise p' i ＝p m ；
And step 3: judging whether all nodes on both sides of the bipartite graph are matched, namely solving E' and p in the graph G m The connected edges are assigned to p m And all n '-1 new nodes, so that each node in the set corresponds to one task, and meanwhile, the weight of the edge is marked as omega' ij;
and 4, step 4: calling an algorithm 2, namely finding a maximum weighted match in G' by using a KM method, and returning a matching result;
and 5: calling formula (18) to calculate x ij When x is ij When =1, task r i Is unloaded to p j ；
And 6: outputting X, namely a task unloading decision generated by a bipartite graph matching algorithm;
assuming η is the number of vertices in P ', i.e. η = m + n ' -1, as shown in algorithm 1, the time complexity of the algorithm is O (η), a new set P ' is created in bipartite graph G ', a new set E ' of edges is created in O (z), so it is proposed that the algorithm operates within the time complexity O (η + z) to create G ", and furthermore, the time complexity of the KM method is O (η + z) 3 ) Thus, the time complexity of algorithm 1 in making task offload decisions at time t is also O (η) 3 )。
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Application publication date: 20221018