CN111263419A - Unmanned aerial vehicle-based dynamic routing method for stereo heterogeneous network in emergency scene - Google Patents

Unmanned aerial vehicle-based dynamic routing method for stereo heterogeneous network in emergency scene Download PDF

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CN111263419A
CN111263419A CN202010053783.5A CN202010053783A CN111263419A CN 111263419 A CN111263419 A CN 111263419A CN 202010053783 A CN202010053783 A CN 202010053783A CN 111263419 A CN111263419 A CN 111263419A
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CN111263419B (en
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曲桦
赵季红
罗媛媛
岳鹏程
常晨
徐晓芸
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Xian Jiaotong University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W40/00Communication routing or communication path finding
    • H04W40/02Communication route or path selection, e.g. power-based or shortest path routing
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B7/00Radio transmission systems, i.e. using radiation field
    • H04B7/14Relay systems
    • H04B7/15Active relay systems
    • H04B7/185Space-based or airborne stations; Stations for satellite systems
    • H04B7/18502Airborne stations
    • H04B7/18506Communications with or from aircraft, i.e. aeronautical mobile service
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W28/00Network traffic management; Network resource management
    • H04W28/02Traffic management, e.g. flow control or congestion control
    • H04W28/08Load balancing or load distribution
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W40/00Communication routing or communication path finding
    • H04W40/02Communication route or path selection, e.g. power-based or shortest path routing
    • H04W40/22Communication route or path selection, e.g. power-based or shortest path routing using selective relaying for reaching a BTS [Base Transceiver Station] or an access point

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Abstract

The invention relates to a dynamic routing method of a stereo heterogeneous network in an emergency scene based on an unmanned aerial vehicle, which can adapt to a fusion network with dynamic topological change, wherein the unmanned aerial vehicle is used as a relay node to form a relay node, nodes in the same region do not communicate, nodes in different regions communicate and are relayed by the unmanned aerial vehicle node, a ground node is only used as a terminal node in the route, and in each communication process, the method comprises the following steps of A, respectively carrying out scene modeling on the unmanned aerial vehicle node and the ground node, and B, carrying out link weight improvement on the basis of the traditional OLSR protocol, and selecting a routing path with cost of α × ETT + β × Ei+ (1- α - β) x T as benchmark(ii) a And C: the core idea of the OLSR routing protocol is to select an MPR set, so as to reduce routing overhead, and the improved LBMRE-OLSR discards a classical MPR set selection algorithm, and selects an MPR set according to the expected transmission time of a node, node energy, and node congestion degree.

Description

Unmanned aerial vehicle-based dynamic routing method for stereo heterogeneous network in emergency scene
Technical Field
The invention belongs to the technical field of network communication, and particularly relates to a dynamic routing method of a stereo heterogeneous network in an emergency scene based on an unmanned aerial vehicle.
Background
Under the condition of sudden natural disasters and public events, a plurality of nodes communicate simultaneously, ground communication facilities are possibly destroyed, ground networks are seriously congested, the original communication mode is difficult to continue communicating, and therefore the communication under the emergency scene is very important. The air-space-ground integrated heterogeneous network can solve the problem of network congestion and can enable the network to have wider coverage, better connectivity and stronger survivability.
On the basis of a traditional air-space-ground integrated network structure, the invention carries out layered control on a ground network, a near space network and a satellite network, and introduces the concept of separation of control and forwarding in an SDN framework into a three-layer heterogeneous network framework. As shown in fig. 1, an SDN architecture is deployed in each layer, an SDN controller is configured in each layer, a plurality of application programs run on the controller, and states and multidimensional resources in a network are uniformly managed through an OpenFlow protocol. The SDN controllers between the three layers communicate through east-west interfaces, so that the routing of the air-ground integrated network and the distribution of multidimensional resources are coordinated uniformly, and the connectivity and survivability of the network are enhanced.
The traditional space-ground integrated network architecture has larger time delay due to longer distance. The space-air-ground integrated network depends on a near space platform, can realize rapid and flexible deployment and networking, and becomes the best choice for constructing an emergency communication network. In general, close space platform vehicles are deployed in areas difficult to be covered by ground and satellites for communication in remote zones; and in emergency, the platform is deployed or moved to the upper space of the disaster area to supplement or replace the service of the ground communication system. In the invention, the satellite network is supposed to have only a scheduling function without data transmission, and an SDN controller is added on each layer of the original network structure, so that a uniform protocol and a programming interface are arranged between the layers, and the management is convenient. In order to seamlessly connect the adjacent space network and the ground equipment, the possible network congestion and bottleneck between the space equipment and the ground equipment need to be solved, wherein the efficient and reliable load balancing dynamic routing based on multidimensional resources is one of the important technical contents for building the air-ground network.
Currently, Ad hoc routing protocols are classified into static routing protocols, proactive routing protocols, reactive routing protocols, and hybrid routing protocols. The static routing protocol does not update the routing table during task execution, and due to this limitation, it is not suitable for running in dynamic scenarios. The Proactive Routing Protocol (PRP) can update the routing table in time, correctly reflect the topological structure of the network, has the advantage of small time delay of obtaining the routing, and is more suitable for application with real-time requirements. But because of the continuous interaction of routing messages between nodes, a large consumption of bandwidth and node energy is caused. At present, proactive routing protocols commonly used in mobile ad hoc networks mainly include an Optimized Link State Routing (OLSR) protocol, a Destination Sequence Distance Vector (DSDV) protocol, and the like. The reactive routing protocol starts a route discovery program only when needed, the required route information cache is small, and the overhead of the reactive routing protocol is far smaller than that of a proactive routing protocol under the condition that the network load is not large, and the commonly used reactive routing protocol is an active dynamic routing (DSR) protocol, an ad hoc on-demand distance vector (AODV) protocol and the like. As the name implies, the hybrid routing protocol combines proactive and reactive routing, employs proactive routing between neighboring nodes and reactive routing algorithms between distant nodes, thereby finding a balance between cost and delay. However, the hybrid routing protocol also faces many difficulties, such as large traffic problems in the network, selection and maintenance of clusters, selection of proactive and reactive routes, etc. The most representative hybrid routing protocol is the Zone Routing Protocol (ZRP).
The prior art has the following disadvantages:
1. the 'integrated' routing of the air-space-ground network in the true sense is not realized, and more is the layered routing.
2. The characteristic that the unmanned aerial vehicle moves along with the airplane in the adjacent space network is not fully grasped, and the used routing protocol cannot well realize the dynamic change of the network topology.
3. Multidimensional resources (including link states and node states) between different layers are not considered when routing.
4. The routing in the traditional mobile ad hoc network is not suitable for unmanned aerial vehicle nodes moving at high speed and unmanned aerial vehicle networks with frequently changing topology.
Disclosure of Invention
The invention aims to provide a dynamic routing method of a stereo heterogeneous network in an emergency scene based on an unmanned aerial vehicle, which analyzes and improves the characteristics of the air-ground integrated network routing problem in the emergency scene, reduces the end-to-end time delay and the packet loss rate, and simultaneously reduces the network congestion degree. The invention realizes the integrated routing between the two layers of networks by modeling the near space platform and the ground network, realizes the load balancing dynamic routing based on multidimensional resources and energy, improves the communication efficiency of the network routing and ensures the reasonable utilization of the resources.
The invention is realized by adopting the following technical scheme:
the method can adapt to a fusion network with dynamic topological change, an unmanned aerial vehicle is used as a relay node to form the relay node, nodes in the same area do not communicate, nodes in different areas communicate through the unmanned aerial vehicle node relay route, a ground node is only used as a terminal node in the route, and in each communication process, the method comprises the following steps:
step A: respectively carrying out scene modeling on unmanned aerial vehicle nodes and ground nodes, wherein the data rates of a node transmitter and a node receiver are both 1Mb/s, the initial energy of each node is the same and is set to be 0.2J, the unmanned aerial vehicle nodes are 25m/s, and the ground nodes are 3 m/s;
step B, improving the link weight on the basis of the traditional OLSR protocol, and selecting a routing path with cost of α × ETT + β × Ei+ (1- α - β) x T as benchmark;
and C: the core idea of the OLSR routing protocol is to select an MPR set, so as to reduce routing overhead, and the improved LBMRE-OLSR discards a classical MPR set selection algorithm, and selects an MPR set according to the expected transmission time of a node, node energy, and node congestion degree.
The invention has the further improvement that the specific calculation process of the step B is as follows:
201) ETT Link metrics
The transmission times required by ETX for successfully transmitting a data packet, i.e. the expected transmission times for a node to correctly receive the required data packet at the receiving end, include retransmissions:
Figure BDA0002372115300000041
wherein d isfFor forward transmission probability, drIs the reverse transmission probability;
ETT is the expected transmission time, and simultaneously takes the retransmission of data into consideration, and represents the average time required for successfully transmitting a data packet;
Figure BDA0002372115300000042
wherein S is the average size of the data packet and B is the link bandwidth;
202) node consuming energy
EiFor the energy consumed by the node, the received data power of the node i is set as P1The transmission data power is P2(ii) a Receiving a data packet of duration T1The duration of the transmitted data packet is T2(ii) a Receiving data packetLength of L1The length of the transmission data packet is L2Data reception rate of V1Data transmission rate is V2Then the energy consumed by node i in this route is:
Figure BDA0002372115300000043
203) node MAC layer congestion level
T is the average queuing delay of the MAC layer, and in a set period, the queuing time of the data packets at the interface of the node MAC layer is sampled on the assumption that the MAC layer reaches N data packets in the period; recording the time when the data packet i reaches the MAC layer
Figure BDA0002372115300000044
And leave the MAC layer at a time of
Figure BDA0002372115300000045
Averaging the residence time of the N data packets in the MAC layer;
Figure BDA0002372115300000046
204) defining routing comprehensive weight
cost=α×ETT+β×Ei+(1-α-β)×T (5)
The above formula is a comprehensive parameter of link weight measurement, wherein α is 0.3, β is 0.4, and 1- α - β is 0.3, multidimensional resource and energy perception is introduced into the improved routing protocol and load balancing is realized, the mobile node will continue updating its link weight after receiving the HELLO packet, the link weight set will contain multidimensional resource and energy and load information of its neighbors, after receiving the TC packet, the MPR will update the topology table, and the topology table also includes multidimensional resource and energy and load information.
A further improvement of the invention is that let S1 be the neighbor set of node A, S2 be the set of 2-hop neighbors of node A, MPR be the set of multipoint relays of node A, ETT be the expected transmission time, EiIf the energy consumed by the node is T, and the average queuing delay of the node is T, the specific implementation process of the step C is as follows:
301) starting from the MPR set of all N1 members with all willingness of N1 equal to wide _ ALWAYS;
302) adding those nodes in N1 to the MPR set, which is the only node providing reachability to the nodes in N2; nodes are removed from N2, which are now covered by nodes in the MPR set;
303) although there are nodes in N2, at least one node in the MPR set does not cover these nodes;
for each node in N1, equation (5) is calculated, adding the N1 node with the smallest Cost to the MPR;
304) if the Cost values are the same, arranging the Cost values from small to large according to the ETT; if ETT is equal, arranging according to E from small to large; if E is the same, sorting according to T from small to large;
305) nodes are removed from N2, which are now covered by nodes in the MPR set;
306) the MPR is obtained by repeating the above steps 301) to 305).
The invention has the following beneficial technical effects:
the invention integrates the SDN controller on the traditional air-space-ground integrated network architecture, realizes convenient and visual unified allocation of the three-dimensional heterogeneous network architecture and improves the operation efficiency of the whole network. And on the basis of an emergency scene, the node congestion degree is considered to realize load balancing, an improved routing protocol is provided, and a comprehensive parameter based on multidimensional resources is defined as a link weight. Simulation experiments prove that the improved routing algorithm is more suitable for dynamic routing of an air-space-ground integrated network under an unmanned-aerial-vehicle-based emergency scene, and the end-to-end time delay and the packet loss rate are optimized.
Drawings
FIG. 1 is an aerospace-ground integrated network diagram in an emergency scenario according to the invention.
Fig. 2 is an air-space-ground integrated network diagram based on an SDN architecture in the present invention.
Fig. 3 is a schematic diagram of a multi-drone relay network.
Fig. 4 is a graph of average end-to-end delay versus load.
Fig. 5 is a graph of packet loss rate versus load.
Fig. 6 is a graph of packet loss rate over time.
Fig. 7 is a graph of end-to-end delay over time.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in fig. 1 to 3, the method for dynamically routing a stereoheterogeneous network in an emergency scene based on an unmanned aerial vehicle according to the present invention is capable of adapting to a fusion network with dynamic topology change, wherein the unmanned aerial vehicle is used as a relay node to form a relay node, nodes in the same area do not communicate, nodes in different areas communicate via the unmanned aerial vehicle node relay route, a ground node is only used as a terminal node in the route, and the method includes the following steps in each communication process:
step A: respectively carrying out scene modeling on unmanned aerial vehicle nodes and ground nodes, wherein the data rates of a node transmitter and a node receiver are both 1Mb/s, the initial energy of each node is the same and is set to be 0.2J, the unmanned aerial vehicle nodes are 25m/s, and the ground nodes are 3 m/s;
step B, improving the link weight on the basis of the traditional OLSR protocol, and selecting a routing path with cost of α × ETT + β × Ei+ (1- α - β) multiplied by T is taken as a reference, and the specific calculation process is as follows:
201) ETT Link metrics
The transmission times required by ETX for successfully transmitting a data packet, i.e. the expected transmission times for a node to correctly receive the required data packet at the receiving end, include retransmissions:
Figure BDA0002372115300000061
wherein d isfFor forward transmission probability, drIs the reverse transmission probability;
ETT is the expected transmission time, and simultaneously takes the retransmission of data into consideration, and represents the average time required for successfully transmitting a data packet;
Figure BDA0002372115300000071
wherein S is the average size of the data packet and B is the link bandwidth;
202) node consuming energy
EiFor the energy consumed by the node, the received data power of the node i is set as P1The transmission data power is P2(ii) a Receiving a data packet of duration T1The duration of the transmitted data packet is T2(ii) a Receiving a packet of data of length L1The length of the transmission data packet is L2Data reception rate of V1Data transmission rate is V2Then the energy consumed by node i in this route is:
Figure BDA0002372115300000072
203) node MAC layer congestion level
T is the average queuing delay of the MAC layer, and in a set period, the queuing time of the data packets at the interface of the node MAC layer is sampled on the assumption that the MAC layer reaches N data packets in the period; recording the time when the data packet i reaches the MAC layer
Figure BDA0002372115300000073
And leave the MAC layer at a time of
Figure BDA0002372115300000074
Averaging the residence time of the N data packets in the MAC layer;
Figure BDA0002372115300000075
204) defining routing comprehensive weight
cost=α×ETT+β×Ei+(1-α-β)×T (5)
The above formula is a comprehensive parameter of link weight measurement, wherein α is 0.3, β is 0.4, and 1- α - β is 0.3, multidimensional resource and energy perception is introduced into the improved routing protocol and load balancing is realized, the mobile node will continue updating its link weight after receiving the HELLO packet, the link weight set will contain multidimensional resource and energy and load information of its neighbors, after receiving the TC packet, the MPR will update the topology table, and the topology table also includes multidimensional resource and energy and load information.
And C: the core idea of the OLSR routing protocol is to select an MPR set, so as to reduce routing overhead, and the improved LBMRE-OLSR discards a classical MPR set selection algorithm, and selects an MPR set according to the expected transmission time of a node, node energy, and node congestion degree. Let S1 be the neighbor set of node A, S2 be the set of 2-hop neighbors of node A, MPR be the set of multipoint relays of node A, ETT be the expected transmission time, EiIf the energy consumed by the node is T, and the average queuing delay of the node is T, the specific implementation process of the step C is as follows:
301) starting from the MPR set of all N1 members with all willingness of N1 equal to wide _ ALWAYS;
302) adding those nodes in N1 to the MPR set, which is the only node providing reachability to the nodes in N2; nodes are removed from N2, which are now covered by nodes in the MPR set;
303) although there are nodes in N2, at least one node in the MPR set does not cover these nodes;
for each node in N1, equation (5) is calculated, adding the N1 node with the smallest Cost to the MPR;
304) if the Cost values are the same, arranging the Cost values from small to large according to the ETT; if ETT is equal, arranging according to E from small to large; if E is the same, sorting according to T from small to large;
305) nodes are removed from N2, which are now covered by nodes in the MPR set;
306) the MPR is obtained by repeating the above steps 301) to 305).
The application of the invention has the following advantages:
1. the invention adopts a new link weight value measurement method, namely, the invention sets that most of the resources on the links between different layers are related to the resources of the nodes at the same time. And the end-to-end time delay and the packet loss rate are reduced to a certain extent.
2. From the network load perspective, a random number function is adopted to realize load balance, and congestion on a link with the optimal link weight and overload of a certain node are avoided. If the buffer queue is full, the data packet is lost and retransmitted, so the invention effectively controls the aspect.
3. From the perspective of a network architecture, an SDN technology is introduced on the basis of a traditional air-space-ground integrated network architecture, and a satellite unified control center is added to form a dispatching and commanding effect on unmanned aerial vehicle formation and a ground network. Meanwhile, the SDN controllers of all layers facilitate unified coordination and management of the whole heterogeneous network.
To be more specific, the multidimensional resource and energy based load balancing routing algorithm is as follows:
Figure BDA0002372115300000091
the advantages of the algorithm are as follows:
the outstanding problem in the air-space-ground integrated network under the emergency scene is solved:
1) the topology changes rapidly.
2) The network load is unbalanced.
3) The node energy is limited.
Meanwhile, in terms of architecture, compared with a satellite network or a ground network only: adding the empty base layer reduces latency. The space communication system built on the aerial platform provides another mode of the ground communication system than the satellite communication system: compared with a satellite communication system, the distance between the aerial platform and the ground is short, the link loss is small, the propagation delay is small, and the aerial platform can be rapidly deployed at a lower price compared with a satellite; compared with a ground communication system, the aerial platform can provide wider signal coverage, has good survivability and flexible deployment, and is not limited by the environment.
In the invention, the traditional space-air-ground integrated network architecture is fused with the SDN controller, so that the complex three-dimensional heterogeneous network architecture is conveniently and intuitively deployed in a unified manner, and the operation efficiency of the whole network is improved. And multidimensional resources are considered on the basis of the traditional OLSR algorithm, an improved routing protocol is provided, and a comprehensive parameter based on the multidimensional resources is defined as an objective function. Simulation experiments prove that the improved routing algorithm is more suitable for dynamic routing of an air-space-ground integrated network under an unmanned-aerial-vehicle-based emergency scene, and the end-to-end time delay and the packet loss rate are optimized.
The invention realizes the routing of the air-space-ground integrated network and improves the network communication efficiency; the link weight is comprehensively measured by relating to multidimensional resources, so that the data success rate is higher; by calculating the node energy, the link interruption caused by selecting a node with lower energy is avoided; the load of the node is measured, and a route with lower load and stability is selected, so that the load balance is better realized, and the end-to-end time delay is reduced.
A simulation section:
and (3) simulating OLSR and LBMRE-OLSR routing protocols by using an OPNET model 14.5 as a simulation tool under a Windows 7 operating system. OPNET can be written in C + +, can simulate different network transmission protocols, and can be added with various routing protocols.
TABLE 1 simulation parameters
Figure BDA0002372115300000101
Figure BDA0002372115300000111
Simulation result
The 2 indexes of the packet loss rate and the data end-to-end delay of the network data are selected under different scenes to compare and improve the performance of the former and later OLSR routing protocols.
1) Simulation result of load gradual increase
The comparison of the end-to-end delay and the packet loss rate before and after the improvement is shown in fig. 4 and fig. 5. When the data packet sending speed continues to be improved, the end-to-end delay and the packet loss rate are respectively increased, but the end-to-end delay and the packet loss rate of the improved LBMRE-OLSR routing protocol are improved. These two performances are significantly better than the conventional OLSR protocol.
2) Simulation results over time
As the network simulation time increases, the end-to-end delay variation and the packet loss rate are shown in fig. 6 and fig. 7. The overall performance of the improved LBMRE-OLSR protocol is superior to the conventional OLSR protocol.

Claims (3)

1. The method is characterized in that the method can adapt to a fusion network with dynamic topological change, an unmanned aerial vehicle is used as a relay node to form the relay node, nodes in the same area do not communicate, nodes in different areas communicate through the unmanned aerial vehicle node relay route, a ground node is only used as a terminal node in the route, and in each communication process, the method comprises the following steps:
step A: respectively carrying out scene modeling on unmanned aerial vehicle nodes and ground nodes, wherein the data rates of a node transmitter and a node receiver are both 1Mb/s, the initial energy of each node is the same and is set to be 0.2J, the unmanned aerial vehicle nodes are 25m/s, and the ground nodes are 3 m/s;
step B, improving the link weight on the basis of the traditional OLSR protocol, and selecting a routing path with cost of α × ETT + β × Ei+ (1- α - β) x T as benchmark;
and C: the core idea of the OLSR routing protocol is to select an MPR set, so as to reduce routing overhead, and the improved LBMRE-OLSR discards a classical MPR set selection algorithm, and selects an MPR set according to the expected transmission time of a node, node energy, and node congestion degree.
2. The dynamic routing method for the stereoheterogeneous network in the emergency scene based on the unmanned aerial vehicle of claim 1, wherein the specific calculation process of the step B is as follows:
201) ETT Link metrics
The transmission times required by ETX for successfully transmitting a data packet, i.e. the expected transmission times for a node to correctly receive the required data packet at the receiving end, include retransmissions:
Figure FDA0002372115290000011
wherein d isfFor forward transmission probability, drIs the reverse transmission probability;
ETT is the expected transmission time, and simultaneously takes the retransmission of data into consideration, and represents the average time required for successfully transmitting a data packet;
Figure FDA0002372115290000012
wherein S is the average size of the data packet and B is the link bandwidth;
202) node consuming energy
EiFor the energy consumed by the node, the received data power of the node i is set as P1The transmission data power is P2(ii) a Receiving a data packet of duration T1The duration of the transmitted data packet is T2(ii) a Receiving a packet of data of length L1The length of the transmission data packet is L2Data reception rate of V1Data transmission rate is V2Then the energy consumed by node i in this route is:
Figure FDA0002372115290000021
203) node MAC layer congestion level
T is the average queuing delay of the MAC layer, and in a set period, the queuing time of the data packets at the interface of the node MAC layer is sampled on the assumption that the MAC layer reaches N data packets in the period; recording the time when the data packet i reaches the MAC layer
Figure FDA0002372115290000023
And leave the MAC layer at a time of
Figure FDA0002372115290000024
Averaging the residence time of the N data packets in the MAC layer;
Figure FDA0002372115290000022
204) defining routing comprehensive weight
cost=α×ETT+β×Ei+(1-α-β)×T (5)
The above formula is a comprehensive parameter of link weight measurement, wherein α is 0.3, β is 0.4, and 1- α - β is 0.3, multidimensional resource and energy perception is introduced into the improved routing protocol and load balancing is realized, the mobile node will continue updating its link weight after receiving the HELLO packet, the link weight set will contain multidimensional resource and energy and load information of its neighbors, after receiving the TC packet, the MPR will update the topology table, and the topology table also includes multidimensional resource and energy and load information.
3. The dynamic routing method for the stereoheterogeneous network in the emergency scenario based on UAV of claim 2, wherein S1 is the neighbor set of node A, S2 is the set of 2-hop neighbors of node A, MPR is the set of multi-point relays of node A, ETT is the expected transmission time, EiIf the energy consumed by the node is T, and the average queuing delay of the node is T, the specific implementation process of the step C is as follows:
301) starting from the MPR set of all N1 members with all willingness of N1 equal to wide _ ALWAYS;
302) adding those nodes in N1 to the MPR set, which is the only node providing reachability to the nodes in N2;
nodes are removed from N2, which are now covered by nodes in the MPR set;
303) although there are nodes in N2, at least one node in the MPR set does not cover these nodes;
for each node in N1, equation (5) is calculated, adding the N1 node with the smallest Cost to the MPR;
304) if the Cost values are the same, arranging the Cost values from small to large according to the ETT; if ETT is equal, arranging according to E from small to large; if E is the same, sorting according to T from small to large;
305) nodes are removed from N2, which are now covered by nodes in the MPR set;
306) the MPR is obtained by repeating the above steps 301) to 305).
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