CN109548055A - A kind of autonomous energy management method in ultra dense wireless network based on collection of energy - Google Patents

A kind of autonomous energy management method in ultra dense wireless network based on collection of energy Download PDF

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CN109548055A
CN109548055A CN201811377582.XA CN201811377582A CN109548055A CN 109548055 A CN109548055 A CN 109548055A CN 201811377582 A CN201811377582 A CN 201811377582A CN 109548055 A CN109548055 A CN 109548055A
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energy
wireless network
base station
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dense wireless
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CN109548055B (en
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李静磊
秦猛
杨清海
王丽萍
张帅
石岳倩
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Xidian University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W24/00Supervisory, monitoring or testing arrangements
    • H04W24/04Arrangements for maintaining operational condition
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W24/00Supervisory, monitoring or testing arrangements
    • H04W24/06Testing, supervising or monitoring using simulated traffic
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W52/00Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/02Power saving arrangements
    • H04W52/0203Power saving arrangements in the radio access network or backbone network of wireless communication networks
    • H04W52/0206Power saving arrangements in the radio access network or backbone network of wireless communication networks in access points, e.g. base stations
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02DCLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00Reducing energy consumption in communication networks
    • Y02D30/70Reducing energy consumption in communication networks in wireless communication networks

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  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

The invention belongs to wireless communication technology field, the autonomous energy management method in a kind of ultra dense wireless network based on collection of energy is disclosed;It sets in ultra dense wireless network comprising a macro base station MBS;Construct small base station SBS energy consumption model, the macro base station MBS energy consumption model of ultra dense wireless network, ultra dense wireless network collection of energy model of BTS management model in ultra dense wireless network, ultra dense wireless network;The utility function mechanism based on QoS of foundation, setting SON realize the autonomous management in wireless network as the intelligent body in ultra dense wireless network;Construct multi-arm fruit machine model;Set the optimization object function of multi-arm fruit machine model;Expense factor C is introduced, overall network value of utility is maximized;Determine the sleep mechanism strategy of optimal small base station.The present invention can promote network utility value, improving energy efficiency reduces network overhead in the priori knowledge that noenergy is collected and under conditions of without global information.

Description

A kind of autonomous energy management method in ultra dense wireless network based on collection of energy
Technical field
The invention belongs in wireless communication technology field more particularly to a kind of ultra dense wireless network based on collection of energy Autonomous energy management method.
Background technique
Currently, the prior art commonly used in the trade is such that in 5G network, with constantly climbing for mobile device quantity It rises and data is driven to main emerging service and largely rises, result in mobile data explosive growth.Therefore it provides higher Network capacity and the wider network coverage, to guarantee quality of service requirements (QoS, the quality of user Ofservice), it is significant challenge that the following 5G wireless network faces.Ultra dense wireless network (small cell network, SCN it is) a kind of emerging network technology, can be used as effective supplement of macro base station, realizes that network capacity and the effective of covering mention It rises.As the dense deployment of wireless network leads to operation management due to the space-time dynamic characteristic of network flow and business load It is more complicated, the problems such as expense is at high cost, and network load is unbalanced.With being continuously increased for the power price in power grid, energy Consumption also becomes the key factor in 5G network management operation.Therefore, in order to effectively promote network energy efficiency, design is effective Network energy administrative mechanism, reduce network energy consumption, be the key challenge in 5G network management.On how to promote nothing Efficiency problem in gauze network has caused extensive research, the main Dynamical Deployment policy mechanism including base station, power control System, sleep mechanism of base station etc. are studied.In addition, energy collection technology, can collect energy from the wireless environment of surrounding, be SCN network provides energy, collects skill as the energy supply of SCN network, such as using solar energy, wind energy and RF energy Art is that SCN network carries out collection of energy.To save network energy, dynamic of traditional energy saving research based on the base station in network Sleep mechanism.In the existing energy efficiency management research based on energy collection technology, it is all based on the energy and network overall situation letter of collection Centralized management under the premise of breath is all known needs a large amount of signaling overheads to obtain global network information.To increase Network O&M cost and network management complexity, however due to the uncertainty and collection of energy of the wireless environment around base station Random arrival characteristic, be difficult precognition collect energy size, and centralization energy efficiency management, in particular for super-intensive Wireless network, will be so that network management be more complicated and expense is huger, to need the higher energy management of complexity Algorithm.
In conclusion problem of the existing technology is: the existing energy efficiency management based on energy collection technology, which exists, to be based on Centralized management under the premise of the energy and network global information of collection are all known, needs a large amount of signaling overheads;Due to base The uncertainty of the wireless environment for surrounding of standing and the random arrival characteristic of collection of energy are difficult the energy size that precognition is collected, and And the energy efficiency management of centralization, so that network management is more complicated and expense is huger.
Solve the difficulty and meaning of above-mentioned technical problem:
With the continuous growth of user being continuously increased with business, wireless environment has the characteristic of high dynamic, so that algorithm Complexity it is high, need more dynamic EnergyPolicy.Further, since collection of energy has random arrival characteristic, need to design Effective energy dynamics model.Therefore, pass through the autonomous energy management side in ultra dense wireless network of the design based on collection of energy Method can effectively reduce network signaling overhead and network management complexity, reduce network O&M cost, promote the intelligence of network O&M ability and efficient network energy efficiency management.
Summary of the invention
In view of the problems of the existing technology, in the present invention provides a kind of ultra dense wireless network based on collection of energy Autonomous energy management method.
The invention is realized in this way the autonomous energy management side in a kind of ultra dense wireless network based on collection of energy Method, the autonomous energy management method in the ultra dense wireless network based on collection of energy include:
Step 1 is set in ultra dense wireless network comprising a macro base station MBS and Multiple Small Cell Sites SBS;Construct ultra dense nothing The small base station SBS energy consumption model of BTS management model, ultra dense wireless network in gauze network, ultra dense wireless network it is macro Base station MBS energy consumption model, ultra dense wireless network collection of energy model;
Step 2 establishes the utility function mechanism based on QoS, and SON is as the intelligent body in ultra dense wireless network for setting, Realize the autonomous management in wireless network;Small base station SBS is set as the gambling arm in model, constructs multi-arm fruit machine model;
Step 3 sets the optimization object function of multi-arm fruit machine model;Expense factor C is introduced, in multi-arm fruit machine mould It during the Optimization Learning of type, is constantly interacted between SON player, maximizes overall network value of utility;Using thomson Sampling algorithm TS obtains the upper limit of this TS strategy regret value;According to selected optimal arm, sleeping for optimal small base station is determined Dormancy mechanism policy.
Further, the BTS management model in the ultra dense wireless network of the step 1: have in entire ultra dense wireless network M small base station SBS, are expressed as S={ S1,S2,…SM, then the operation management model of small base station are as follows:
Wherein if Sm=1, then it represents that small base station is active, if Sm=0, then it represents that small base station is in suspend mode State;In the dormant state, small base station is collected into required energy and is then stored in the battery of small base station, until activation shape Under state, the energy for collecting storage is used to service user.
Further, the small base station SBS energy consumption model of the ultra dense wireless network of the step 1: in time t moment, The energy consumption model of small base station are as follows:
Wherein,Indicate total energy expense of small base station,Indicate the fixed energies consumption of small base station, ζSBS For the inverse of the efficiency power amplifier factor,Indicate small base station radio-frequency transimission power.
Further, the macro base station MBS energy consumption model of the ultra dense wireless network of the step 1:
Wherein,Indicate total energy consumption of macro base station MBS,Indicate that the fixed energies of macro base station MBS disappear Consumption,Indicate the radio frequency transmission power of macro base station.
Further, it the ultra dense wireless network collection of energy model of the step 1: in the round of jth time transmission, indicates ForDue to the stochastic behaviour of collection of energy,Be it is unknown,For independent identically distributed random change Amount.
Further, the utility function of the small base station m of selection of the step 2 are as follows:
Wherein,Indicate the maximum number of user that small base station m can be serviced in time t moment, ΞmIndicate each energy list The expense of member;Indicate energy expense required for the initialization of small base station m;Whole effect in entire ultra dense wireless network With function are as follows:
Further, the optimization object function of the multi-arm fruit machine model of the step 3 are as follows:
Wherein, Qπ(T) indicate that i.e. player SON is currently selected based on the regret value under small base station energy management strategies π The income of armWith current optimal arm incomeDifference.
Further, the use thomson sampling algorithm TS of the step 3, obtains the upper limit of this TS strategy regret value are as follows:
TS algorithm includes the exploratory stage and utilizes the stage: in the exploratory stage, carrying out attempting different arms using polling algorithm Obtain different historical knowledges;In the stage of utilizing, SON player selection has the arm of maximum return value, and after time T, TS is calculated Method converges to optimal value.
Another object of the present invention is to provide in the ultra dense wireless network described in a kind of application based on collection of energy from The mobile communication equipment of main energy management method.
Another object of the present invention is to provide in the ultra dense wireless network described in a kind of application based on collection of energy from The wireless communication system of main energy management method.
In conclusion advantages of the present invention and good effect are as follows: the present invention passes through the small base station in ultra dense wireless network Active sleep deployment strategy mechanism;In conjunction with energy collection technology, energy is collected from the wireless environment of surrounding, is ultra dense wireless Network provides energy, the energy supply as ultra dense wireless network.For ultra dense wireless network, introduce self-organizing network (SON) Intelligent body carries out autonomous distributed management, the energy supply in conjunction with energy collection technology, as base station in network.Using multi-arm Fruit machine model is solved based under the situation of no global information, how maximization network effectiveness, promote network energy efficiency management Efficiency.The present invention can be collected by comprehensively considering the actual state of current network and the actual request of user in noenergy Priori knowledge and without global information under conditions of, promoted network utility value, improving energy efficiency, reduce network overhead.By be based on The centralized energy management technology of global information is compared, can be effectively reduced herein network management complexity and network O&M at This.
In addition, the status information of the sleep mechanism demand overall situation of traditional small base station, and assume the energy collected Know;The present invention allows the carry out decision that each small base station is autonomous by distributed small base station sleep mechanism design, does not need complete The status information of office, does not need the priori knowledge of collection of energy;Pass through the interactive learning with ambient enviroment;It is gambled by multi-arm Machine model learns small base station sleep mechanism optimal out, obtains the base station energy management strategies of high energy efficiency.The present invention is by drawing Enter energy collection technology and self-organization network technology, constructs using network energy-saving as the network energy administrative model of target, in conjunction with more The study mechanism of arm fruit machine learns different network energy management strategies, ultra dense wireless network is made decisions on one's own out Optimal energy management strategies.
Detailed description of the invention
Fig. 1 is the autonomous energy management side in the ultra dense wireless network provided in an embodiment of the present invention based on collection of energy Method flow chart.
Fig. 2 is the autonomous energy management side in the ultra dense wireless network provided in an embodiment of the present invention based on collection of energy Method implementation flow chart.
In terms of Fig. 3 is network utility value provided in an embodiment of the present invention, the present invention is compared with greedy resource allocation policy Schematic diagram.
Fig. 4 is provided in an embodiment of the present invention on small base station sleep strategy, the strategy of the small base station sleep in the present invention Select schematic diagram.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to embodiments, to this hair It is bright to be further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, not For limiting the present invention.
Exist for the existing energy efficiency management based on energy collection technology and needs a large amount of signaling overheads;It is difficult precognition to receive The energy size of collection;Network management is more complicated and the huger problem of expense.The present invention opens to reduce network management Pin, key technology of the self-organizing network (self-organizing network (SON)) as autonomous network management are ultra dense The efficient management of set network provides effective approach, how to combine self-organization network technology and energy collection technology, needle The ultra dense set network changeable to dynamic, proposes that a kind of network energy administrative mechanism of high energy efficiency is the science mainly studied Problem;Autonomous energy management method in ultra dense wireless network based on collection of energy is drilled for a long time for next generation mobile communication Into system, the distribution of the user oriented actual demand of the energy harvesting and energy resource in wireless communication is solved the problems, such as.
Application principle of the invention is explained in detail with reference to the accompanying drawing.
As shown in Figure 1, the autonomous energy pipe in the ultra dense wireless network provided in an embodiment of the present invention based on collection of energy Reason method the following steps are included:
S101: it sets in ultra dense wireless network comprising a macro base station (MBS);Construct the base station in ultra dense wireless network Administrative model, the small base station SBS energy consumption model of ultra dense wireless network, ultra dense wireless network macro base station (MBS) energy disappear Consume model, ultra dense wireless network collection of energy model;
S102: establishing the utility function mechanism based on QoS, and setting SON is real as the intelligent body in ultra dense wireless network Autonomous management in existing wireless network;Construct multi-arm fruit machine model;
S103: the optimization object function of setting multi-arm fruit machine model;Expense factor C is introduced, in multi-arm fruit machine model Optimization Learning during, constantly interacted between SON player, maximize overall network value of utility;It is adopted using thomson Sample algorithm (TS) obtains the upper limit of this TS strategy regret value, in the exploratory stage, carries out attempting different arms using polling algorithm Obtain different historical knowledges;In the stage of utilizing, SON player selection has the arm of maximum return value, and after time T, TS is calculated Method can converge to optimal value.According to selected optimal arm, the sleep mechanism strategy of optimal small base station is determined.
Application principle of the invention is further described with reference to the accompanying drawing.
As shown in Fig. 2, the autonomous energy pipe in the ultra dense wireless network provided in an embodiment of the present invention based on collection of energy Reason method specifically includes the following steps:
Step 1 sets in ultra dense wireless network comprising a macro base station (MBS), guarantees the basic network coverage, M is a Small base station (SBS) provides effective support to promote the network coverage and capacity, and comprising N number of user that need to be to be serviced, is Subsequent user management and energy resource distribute offer condition.See Fig. 3, Fig. 4.
Step 2 constructs the BTS management model in ultra dense wireless network: setting in entire ultra dense wireless network has M Small base station (small cell basestation, SBS), is expressed as S={ S1,S2,…SM, then the operation management mould of small base station Type are as follows:
Wherein if Sm=1, then it represents that small base station is active, if Sm=0, then it represents that small base station is in suspend mode State.In the dormant state, small base station can be collected into required energy and be then stored in the battery of small base station, until swashing Under state living, the energy for collecting storage can be used to service user.
Step 3, the small base station SBS energy consumption model of ultra dense wireless network: in ultra dense wireless network, small base station can With dormant state or state of activation can around wireless environment in collect energy.In dormant state, in small base station Most of component will be closed that work will be turned in the component of state of activation, small base station to reducing energy consumption. Therefore in time t moment, the energy consumption model of small base station are as follows:
Wherein,Indicate total energy expense of small base station,Indicating that the fixed energies of small base station consume (includes Baseband processing circuitry and cooling unit power consumption etc.), ζSBSFor the inverse of the efficiency power amplifier factor,Indicate small base station Radio frequency transmission power.
Step 4, macro base station (MBS) energy consumption model of ultra dense wireless network:
Wherein,Indicate total energy consumption of macro base station MBS,Indicate that the fixed energies of macro base station MBS disappear Consumption,Indicate the radio frequency transmission power of macro base station.
Step 5, ultra dense wireless network collection of energy model: in ultra dense wireless network, the present invention uses storage-use Collection of energy strategy.Present invention assumes that the collection of energy process between different small base stations is independent from each other, and transmit File transmitted by J time, file is transmitted.Therefore, it in the round of jth time transmission, is expressed asSince energy is received The stochastic behaviour of collection,It is unknown, present invention assumes that beingFor independent identically distributed stochastic variable.
Step 6 establishes the utility function mechanism based on QoS: being N by m ∈ M in ultra dense wireless networkmThe N number of use of ∈ Family is serviced.User's n demandA energy unit is to meet user's QoS rate requirementThe present invention defines selection The utility function of small base station m are as follows:
Wherein,Indicate the maximum number of user that small base station m can be serviced in time t moment, ΞmIndicate each energy list The expense of member.Indicate energy expense required for the initialization of small base station m.Therefore, whole in entire ultra dense wireless network Body utility function are as follows:
Step 7, setting SON realize the autonomous management in wireless network as the intelligent body in ultra dense wireless network;Structure Multi-arm fruit machine model is built, sets arm of the small base station SBS as multi-arm fruit machine, SON intelligent body is as multi-arm fruit machine model In player.In multi-arm fruit machine model, it is primarily present two stages: the exploratory stage and utilizing stage, multi-arm fruit machine mould Player in type utilizes past historical experience knowledge maximization network effectiveness by exploring new wireless environment.
Step 8 sets the optimization object function of multi-arm fruit machine model are as follows:
Wherein, Qπ(T) indicate that (i.e. player SON is currently selected based on the regret value under small base station energy management strategies π The income of armWith current optimal arm incomeDifference).
Step 9 does not have since the small base station (arm) in multi-arm fruit machine model only has the channel state information of part Global status information, the therefore during Optimization Learning of multi-arm fruit machine model, need between SON player constantly into Row interaction, to maximize overall network value of utility, therefore present invention introduces expense factor C.
Step 10, to solve overall network value of utility maximization problems, the present invention uses thomson sampling algorithm (TS), Thus, it is possible to obtain the upper limit of this TS strategy regret value are as follows:
Step 11, TS algorithm mainly include the exploratory stage and utilize the stage: in the exploratory stage, using polling algorithm into Row attempts different arms and obtains different historical knowledges;In the stage of utilizing, SON player selection has the arm of maximum return value, warp After crossing time T, TS algorithm can converge to optimal value.According to selected optimal arm, so that it is determined that optimal small base station is slept Dormancy mechanism policy.
The present invention does not need the priori knowledge and global status information of collection of energy, can be according to the dynamic of wireless environment State variation, designs the network energy management strategy of high energy efficiency, reduces network management overhead.
Application effect of the invention is explained in detail below with reference to emulation.
As shown in figure 3, the algorithm that the present invention is mentioned can effectively improve network utility value compared to for greedy algorithm, and And convergence is quicker.In addition, the algorithm that is mentioned of the present invention only need seldom communication overhead C in the case where algorithm performance It is only second to the algorithm based on global information.
As shown in figure 4, based on multi-arm fruit machine model small base station sleep mechanism design in, base station by with it is wireless Environment constantly carries out study interaction, by the effective exploratory stage and utilizes the stage, final choice goes out optimal arm (small base Stand), to obtain optimal energy management strategies.
Simulation result shows that the present invention does not need the priori knowledge and global status information of collection of energy, being capable of basis The dynamic change of wireless environment designs the network energy management strategy of high energy efficiency, reduces network management overhead.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.

Claims (10)

1. the autonomous energy management method in a kind of ultra dense wireless network based on collection of energy, which is characterized in that described to be based on Autonomous energy management method in the ultra dense wireless network of collection of energy includes:
Step 1 is set in ultra dense wireless network comprising a macro base station MBS and Multiple Small Cell Sites SBS;Construct ultra dense wireless network The macro base station of the small base station SBS energy consumption model of BTS management model, ultra dense wireless network in network, ultra dense wireless network MBS energy consumption model, ultra dense wireless network collection of energy model;
Step 2, establishes the utility function mechanism based on QoS, and setting SON realizes nothing as the intelligent body in ultra dense wireless network Autonomous management in gauze network;Small base station SBS is set as the gambling arm in model, constructs multi-arm fruit machine model;
Step 3 sets the optimization object function of multi-arm fruit machine model;Expense factor C is introduced, in multi-arm fruit machine model It during Optimization Learning, is constantly interacted between SON player, maximizes overall network value of utility;It is sampled using thomson Algorithm TS obtains the upper limit of this TS strategy regret value;According to selected optimal arm, the sleep mechanism of optimal small base station is determined Strategy.
2. the autonomous energy management method in the ultra dense wireless network based on collection of energy as described in claim 1, feature It is, the BTS management model in the ultra dense wireless network of the step 1: there are M small base stations in entire ultra dense wireless network SBS is expressed as S={ S1,S2,…SM, then the operation management model of small base station are as follows:
Wherein if Sm=1, then it represents that small base station is active, if Sm=0, then it represents that small base station is in a dormant state; In the dormant state, small base station is collected into required energy and is then stored in the battery of small base station, waits until under state of activation, The energy of storage is collected for servicing user.
3. the autonomous energy management method in the ultra dense wireless network based on collection of energy as described in claim 1, feature It is, the small base station SBS energy consumption model of the ultra dense wireless network of the step 1: in time t moment, the energy of small base station Consumption models are as follows:
Wherein,Indicate total energy expense of small base station,Indicate the fixed energies consumption of small base station, ζSBSFor power The inverse of the efficiency of amplitude factor,Indicate small base station radio-frequency transimission power.
4. the autonomous energy management method in the ultra dense wireless network based on collection of energy as described in claim 1, feature It is, the macro base station MBS energy consumption model of the ultra dense wireless network of the step 1:
Wherein,Indicate total energy consumption of macro base station MBS,Indicate the fixed energies consumption of macro base station MBS,Indicate the radio frequency transmission power of macro base station.
5. the autonomous energy management method in the ultra dense wireless network based on collection of energy as described in claim 1, feature It is, the ultra dense wireless network collection of energy model of the step 1: in the round of jth time transmission, is expressed asDue to The stochastic behaviour of collection of energy,Be it is unknown,For independent identically distributed stochastic variable.
6. the autonomous energy management method in the ultra dense wireless network based on collection of energy as described in claim 1, feature It is, the utility function of the small base station m of selection of the step 2 are as follows:
Wherein,Indicate the maximum number of user that small base station m can be serviced in time t moment, ΞmIndicate each energy unit Expense;Indicate energy expense required for the initialization of small base station m;Overall utility function in entire ultra dense wireless network Are as follows:
7. the autonomous energy management method in the ultra dense wireless network based on collection of energy as described in claim 1, feature It is, the optimization object function of the multi-arm fruit machine model of the step 3 are as follows:
Wherein, Qπ(T) it indicates based on the regret value under small base station energy management strategies π, the i.e. receipts for the arm that player SON is currently selected BenefitWith current optimal arm incomeDifference.
8. the autonomous energy management method in the ultra dense wireless network based on collection of energy as described in claim 1, feature It is, the use thomson sampling algorithm TS of the step 3 obtains the upper limit of this TS strategy regret value are as follows:
TS algorithm includes the exploratory stage and utilizes the stage: in the exploratory stage, carrying out attempting different arm acquisitions using polling algorithm Different historical knowledges;In the stage of utilizing, SON player selection has the arm of maximum return value, and after time T, TS algorithm is received Hold back optimal value.
9. the autonomous energy in a kind of ultra dense wireless network using described in claim 1~8 any one based on collection of energy The mobile communication equipment of management method.
10. the autonomous energy in a kind of ultra dense wireless network using described in claim 1~8 any one based on collection of energy The wireless communication system of management method.
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CN112256739A (en) * 2020-11-12 2021-01-22 同济大学 Method for screening data items in dynamic flow big data based on multi-arm gambling machine
CN112256739B (en) * 2020-11-12 2022-11-18 同济大学 Method for screening data items in dynamic flow big data based on multi-arm gambling machine

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