CN107070817A - A kind of uploading bandwidth optimization method applied to the live platform of cloud - Google Patents

A kind of uploading bandwidth optimization method applied to the live platform of cloud Download PDF

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Publication number
CN107070817A
CN107070817A CN201710351125.2A CN201710351125A CN107070817A CN 107070817 A CN107070817 A CN 107070817A CN 201710351125 A CN201710351125 A CN 201710351125A CN 107070817 A CN107070817 A CN 107070817A
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mrow
msub
msubsup
msup
uploader
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CN107070817B (en
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吴迪
叶国桥
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National Sun Yat Sen University
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National Sun Yat Sen University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L47/00Traffic control in data switching networks
    • H04L47/70Admission control; Resource allocation
    • H04L47/80Actions related to the user profile or the type of traffic
    • H04L47/805QOS or priority aware
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14Network analysis or design
    • H04L41/142Network analysis or design using statistical or mathematical methods
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14Network analysis or design
    • H04L41/145Network analysis or design involving simulating, designing, planning or modelling of a network
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/50Network service management, e.g. ensuring proper service fulfilment according to agreements
    • H04L41/5003Managing SLA; Interaction between SLA and QoS
    • H04L41/5019Ensuring fulfilment of SLA
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L47/00Traffic control in data switching networks
    • H04L47/70Admission control; Resource allocation
    • H04L47/80Actions related to the user profile or the type of traffic
    • H04L47/808User-type aware

Abstract

Angle of the present invention from the live platform of cloud, in the case where uploading bandwidth is limited, the bandwidth cost of uploader is reduced, while ensureing the good viewing experience of user, and consider the viewing number of users of different uploaders, Consumer's Experience as well as possible can be provided while campus network is reduced.The present invention is based on NBS(That is Nash Bargaining solution, receive assorted agreed-upon price solution)Optimization Framework, can be in the case where uploading bandwidth be limited, it is contemplated that the different viewing numbers of users of different uploaders, it is fair effectively to distribute uploading bandwidth to each participant, realize global optimum while realizing that individual interests are optimal.

Description

A kind of uploading bandwidth optimization method applied to the live platform of cloud
Technical field
The present invention relates to multi-media network and cloud computing resources management domain, cloud is applied to more particularly, to one kind straight Broadcast the uploading bandwidth optimization method of platform.
Background technology
The rise of extensive covering and internet high bandwidth consumption application with video frequency terminal apparatus, the live platform phase of cloud After the network traffics for occurring and bringing jumbo growth.In recent years, the live platform of many clouds has been emerged in large numbers both at home and abroad, and has been carried out Many successful practices.The popular live platform of cloud of domestic contrast has the live platform of bucket fish, the live platform of protruding canine teeth and imperial pearl live Platform.The external more popular live platform of cloud has Twitch.tv, YouTube, Azubu.tv.The content of the live platform of cloud is covered Lid is extensive, be related to that game content is live, amusement variety is live, sports cast it is live etc..
The live platform architecture of cloud relates generally to three different colonies:The live platform of video flowing uploader, cloud and spectators.On Biography person can use various terminal equipment (such as PC, smart mobile phone, tablet personal computer etc.) uploaded videos stream in real time, and cloud is live Platform receives the video flowing that uploader is uploaded, and provides transcoding service, then distributes the video flowing after transcoding to spectators.Uploader All parts of the world can be distributed in spectators.
In the framework of the live platform of cloud, the transmission of video flowing mainly includes three aspects:Uploader uploaded videos are flowed to The live platform of cloud, the transmission of video of the live platform interior of cloud, the live platform of cloud distributes video flowing to spectators.The portion that the present invention is paid close attention to Divide the upload part of mainly video flowing.
With being continuously increased for the Internet, applications, bandwidth turns into a kind of limited resource, how it is sufficiently effective using and Distribute the problem of bandwidth is one important.For the live platform of cloud, uploading bandwidth is limited, with uploader quantity Constantly increase, uploading bandwidth will turn into a bottleneck of the live platform of cloud.For a user, user's uploaded videos may Cause campus network, and different campus network will be triggered using different code checks (i.e. different video flow qualities). Then, among the current existing live platform architecture of cloud, uploader can arbitrarily set upload code check, and this will cause Pass the waste of bandwidth resources.In addition, among the service of the live platform of cloud, the video that different uploaders are uploaded has different Spectator attendance, and the quality of uploader uploaded videos very big will influence the Consumer's Experience of spectators.Therefore, how band is being uploaded The code check of uploader uploaded videos is selected in the case that width is limited, and considers spectators' Consumer's Experience of each uploader simultaneously, with And the campus network that rationally reduction uploaded videos are brought, the problem of this is one challenging.
The content of the invention
The present invention for solve uploading bandwidth distribution that the live platform of existing cloud is present and using irrational problem there is provided A kind of uploading bandwidth optimization method applied to the live platform of cloud, this method is being uploaded from the angle of the live platform of cloud In the case that bandwidth is limited, the bandwidth cost of uploader is reduced, while ensureing the good viewing experience of user, and difference is considered The viewing number of users of uploader, can provide Consumer's Experience as well as possible while campus network is reduced.
To realize above goal of the invention, the technical scheme of use is:
A kind of uploading bandwidth optimization method applied to the live platform of cloud, comprises the following steps:
S1. definition set u={ u1, u2..., uNUploader colony is represented,Represent uploader group The set that the upload code check of each uploader selection in body is formed,Wherein, b represents that the live platform of cloud is maximum Uploading bandwidth;Make rminWithTo represent that the minimum uploading bandwidth of each uploader is limited and maximum uploading bandwidth limitation, i.e.,:
S2. the bandwidth cost C of i-th of uploader is definediFor:
Ci=ci*ri
Wherein ciRepresent that unit bandwidth consumes triggered campus network;
S3. the QoE models for defining the viewing user of i-th of uploader are:
Define i-th of uploader using minimum uploading bandwidth upload when its watch user QoE models as:
S4. utility models are defined and are come to current upload with reference to the bandwidth cost of i-th of uploader and the QoE of viewing user Code check is evaluated:
Wherein, k represents the weight of bandwidth cost;
Define i-th of uploader using minimum uploading bandwidth upload when its utility models as:
S5. the utility models and the viewing number of users Vi of i-th of uploader obtained with reference to S4 define i-th uploader Utility function is:
S6. to set u={ u1, u2..., uNIn each uploader perform step S1~S5 operation and obtain each The utility function of individual uploader;
S7. the optimization problem of uploading bandwidth is defined as receiving assorted agreed-upon price problem, definition receives assorted agreed-upon price problem and is:
Wherein gatherThe upload code check of different uploader selections is represented, that is, needs the target of optimization;
S8. the corresponding P2 problems of P1 problem definitions are combined:
S9. Lagrangian conversion is carried out to P2 problems, the Lagrangian for obtaining P2 problems is:
Whereinγ is Lagrange multiplier;
S10. Lagrangian is decomposed, Lagrangian is rewritten as:
Wherein
S11. each is made on liThe inverse of Lagrangian be 0, obtain corresponding uploader and upload code check Optimal selection, i.e.,:
WhereinRepresent to upload code check most by receiving each uploader that assorted agreed-upon price decision-making obtains It is preferred that selecting the set of composition.
In specific implementation process, the optimal of code check is uploaded obtaining each uploader using uploading bandwidth optimization method , it is necessary to Lagrange multiplier after selectionγ is updated iteration, its specific process It is as follows:
Many decomposition are carried out to P2 problems, P3 problems are converted to:
P3:Maxg(α, beta, gamma)
WhereinFor dual function, the strategy based on Sub-gradient can To obtain the more new strategy of Lagrange multiplier:
(1) Lagrange multiplierMore new strategy be:
(2) Lagrange multiplierMore new strategy be:
(3) Lagrange multiplier γ more new strategy is:
Wherein, s represents the order of iteration, and ξ represents the step-length of iteration each time;When satisfaction | g (s+1)-g (s) | during≤∈ No longer to Lagrange multiplierγ is updated, and wherein ∈ is the constant of setting.
Compared with prior art, the beneficial effects of the invention are as follows:
The present invention, in the case where uploading bandwidth is limited, reduces the bandwidth of uploader from the angle of the live platform of cloud Expense, while ensureing the good viewing experience of user, and considers the viewing number of users of different uploaders, can be in reduction stream Consumer's Experience as well as possible is provided while amount expense.The present invention based on NBS (i.e. Nash Bargaining solution, Receive assorted agreed-upon price solution) Optimization Framework, can be in the case where uploading bandwidth be limited, it is contemplated that the difference of different uploaders Number of users is watched, it is fair effectively to distribute uploading bandwidth to each participant, realized while realizing that individual interests are optimal Global optimum.
Brief description of the drawings
Fig. 1 is the schematic flow sheet of method.
Embodiment
Accompanying drawing being given for example only property explanation, it is impossible to be interpreted as the limitation to this patent;
Below in conjunction with drawings and examples, the present invention is further elaborated.
Embodiment 1
As shown in figure 1, the method that the present invention is provided specifically includes following steps:
S1. definition set u={ u1, u2..., uNUploader colony is represented,Represent uploader group The set that the upload code check of each uploader selection in body is formed,Wherein, b represents that the live platform of cloud is maximum Uploading bandwidth;Make rminWithTo represent that the minimum uploading bandwidth of each uploader is limited and maximum uploading bandwidth limitation, i.e.,:
S2. the bandwidth cost C of i-th of uploader is definediFor:
Ci=ci*ri
Wherein ciRepresent that unit bandwidth consumes triggered campus network;
S3. the QoE models for defining the viewing user of i-th of uploader are:
Define i-th of uploader using minimum uploading bandwidth upload when its watch user QoE models as:
S4. utility models are defined and are come to current upload with reference to the bandwidth cost of i-th of uploader and the QoE of viewing user Code check is evaluated:
Wherein, k represents the weight of bandwidth cost;
Define i-th of uploader using minimum uploading bandwidth upload when its utility models as:
S5. with reference to the obtained utility models of S4 and the viewing number of users V of i-th of uploaderiDefine i-th uploader Utility function is:
S6. to set u={ u1, u2..., uNIn each uploader perform step S1~S5 operation and obtain each The utility function of individual uploader;
S7. the optimization problem of uploading bandwidth is defined as receiving assorted agreed-upon price problem, definition receives assorted agreed-upon price problem and is:
Wherein gatherThe upload code check of different uploader selections is represented, that is, needs the target of optimization;
S8. the corresponding P2 problems of P1 problem definitions are combined:
S9. Lagrangian conversion is carried out to P2 problems, the Lagrangian for obtaining P2 problems is:
Whereinγ is Lagrange multiplier;ri-rminri- b represents three constraints corresponding with Lagrange multiplier, including bandwidth can not be more than maximum bandwidth, Bandwidth, which can not be less than minimum bandwidth, total bandwidth, can not be more than total uploading bandwidth of system.
S10. Lagrangian is decomposed, Lagrangian is rewritten as:
Wherein
S11. each is made on liThe inverse of Lagrangian be 0, obtain corresponding uploader and upload code check Optimal selection, i.e.,:
WhereinRepresent to upload code check most by receiving each uploader that assorted agreed-upon price decision-making obtains It is preferred that selecting the set of composition.
In such scheme, the method that the present invention is provided is substantially carried out the optimization of uploading bandwidth, it is not intended that the live platform of cloud Part to spectators of transcoding and transmitting video-frequency flow.Therefore, the present invention defines the video code rate that the QoE of user is uploaded by uploader To determine, it can be understood as after uploader is with a code check uploaded videos, it, which watches user, can have an opportunity with this code Rate carries out viewing video.
In such scheme, the present invention is using NBS's (i.e. NashBargainingsolution, receive assorted agreed-upon price solution) Optimisation strategy.NBS inherent thought is, in the case of it is assumed that the selection strategy of other participants is constant, single participant His optimal selection can be calculated, and when other participants do not change their selection strategy, any participant is Higher effectiveness can not be obtained using others selection.This is a kind of resource allocation policy based on game theory, it is ensured that Fairness and validity, while ensure that individual interests are optimal, it is ensured that the maximization that the overall situation is utilized.
In specific implementation process, the optimal of code check is uploaded obtaining each uploader using uploading bandwidth optimization method , it is necessary to Lagrange multiplier after selectionγ is updated iteration, its specific process It is as follows:
Many decomposition are carried out to P2 problems, P3 problems are converted to:
P3:Max g (α, beta, gamma)
WhereinFor dual function, the strategy based on Sub-gradient can To obtain the more new strategy of Lagrange multiplier:
(1) Lagrange multiplierMore new strategy be:
(2) Lagrange multiplierMore new strategy be:
(3) Lagrange multiplier γ more new strategy is:
Wherein, s represents the order of iteration, and ξ represents the step-length of iteration each time;When satisfaction | g (s+1)-g (s) | during≤∈ No longer to Lagrange multiplierγ is updated, and wherein ∈ is the constant of setting.
Wherein, the false code for the optimization method that the present invention is provided is as follows:
Obviously, the above embodiment of the present invention is only intended to clearly illustrate example of the present invention, and is not pair The restriction of embodiments of the present invention.For those of ordinary skill in the field, may be used also on the basis of the above description To make other changes in different forms.There is no necessity and possibility to exhaust all the enbodiments.It is all this Any modifications, equivalent substitutions and improvements made within the spirit and principle of invention etc., should be included in the claims in the present invention Protection domain within.

Claims (2)

1. a kind of uploading bandwidth optimization method applied to the live platform of cloud, it is characterised in that:Comprise the following steps:
S1. definition setUploader colony is represented,Represent in uploader colony The selection of each uploader the set that is formed of upload code check,Wherein, b represents the upper of the live platform maximum of cloud Pass bandwidth;Make rminWithTo represent that the minimum uploading bandwidth of each uploader is limited and maximum uploading bandwidth limitation, i.e.,:
<mrow> <msup> <mi>r</mi> <mi>min</mi> </msup> <mo>&amp;le;</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>&amp;le;</mo> <msubsup> <mi>r</mi> <mi>i</mi> <mi>max</mi> </msubsup> </mrow>
S2. the bandwidth cost C of i-th of uploader is definediFor:
Ci=ci*ri
Wherein ciRepresent that unit bandwidth consumes triggered campus network;
S3. the QoE models for defining the viewing user of i-th of uploader are:
<mrow> <msubsup> <mi>Q</mi> <mi>i</mi> <mi>o</mi> </msubsup> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>,</mo> <msup> <mi>r</mi> <mi>min</mi> </msup> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <msub> <mi>r</mi> <mi>i</mi> </msub> <msup> <mi>r</mi> <mi>min</mi> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow>
Define i-th of uploader using minimum uploading bandwidth upload when its watch user QoE models as:
<mrow> <msubsup> <mi>Q</mi> <mi>i</mi> <mi>b</mi> </msubsup> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>r</mi> <mi>min</mi> </msup> <mo>,</mo> <msup> <mi>r</mi> <mi>min</mi> </msup> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>a</mi> <mo>=</mo> <mi>l</mi> <mi>n</mi> <mn>2</mn> </mrow>
S4. utility models are defined and are come to current upload code check with reference to the bandwidth cost of i-th of uploader and the QoE of viewing user Evaluated:
<mrow> <msubsup> <mi>U</mi> <mi>i</mi> <mi>o</mi> </msubsup> <mo>=</mo> <msubsup> <mi>Q</mi> <mi>i</mi> <mi>o</mi> </msubsup> <mo>-</mo> <mi>k</mi> <mo>*</mo> <msub> <mi>C</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mfrac> <msub> <mi>r</mi> <mi>i</mi> </msub> <msup> <mi>r</mi> <mi>min</mi> </msup> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mi>k</mi> <mo>*</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> <mo>*</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> </mrow>
Wherein, k represents the weight of bandwidth cost;
Define i-th of uploader using minimum uploading bandwidth upload when its utility models as:
<mrow> <msubsup> <mi>U</mi> <mi>i</mi> <mi>b</mi> </msubsup> <mo>=</mo> <msubsup> <mi>Q</mi> <mi>i</mi> <mi>b</mi> </msubsup> <mo>-</mo> <mi>k</mi> <mo>*</mo> <msub> <mi>C</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>a</mi> <mo>-</mo> <mi>k</mi> <mo>*</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> <mo>*</mo> <msup> <mi>r</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msup> <mo>;</mo> </mrow>
S5. with reference to the obtained utility models of S4 and the viewing number of users V of i-th of uploaderiDefine the effectiveness of i-th of uploader Function is:
<mrow> <msub> <mi>U</mi> <mi>i</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>U</mi> <mi>i</mi> <mi>o</mi> </msubsup> <mo>-</mo> <msubsup> <mi>U</mi> <mi>i</mi> <mi>b</mi> </msubsup> <mo>)</mo> </mrow> <msub> <mi>V</mi> <mi>i</mi> </msub> </msup> <mo>;</mo> </mrow>
S6. to setIn each uploader perform step S1~S5 operation and obtain each The utility function of uploader;
S7. the optimization problem of uploading bandwidth is defined as receiving assorted agreed-upon price problem, definition receives assorted agreed-upon price problem and is:
Wherein gatherThe upload code check of different uploader selections is represented, that is, needs the target of optimization;
S8. the corresponding P2 problems of P1 problem definitions are combined:
S9. Lagrangian conversion is carried out to P2 problems, the Lagrangian for obtaining P2 problems is:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>L</mi> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>l</mi> <mi>n</mi> <msup> <mrow> <mo>(</mo> <msubsup> <mi>U</mi> <mi>i</mi> <mi>o</mi> </msubsup> <mo>-</mo> <msubsup> <mi>U</mi> <mi>i</mi> <mi>b</mi> </msubsup> <mo>)</mo> </mrow> <msub> <mi>V</mi> <mi>i</mi> </msub> </msup> <mo>-</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>&amp;alpha;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mrow> <msup> <mi>r</mi> <mi>min</mi> </msup> <mo>-</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>-</mo> <msubsup> <mi>r</mi> <mi>i</mi> <mi>max</mi> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mi>&amp;gamma;</mi> <mrow> <mo>(</mo> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>b</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
Whereinγ is Lagrange multiplier;
S10. Lagrangian is decomposed, Lagrangian is rewritten as:
Wherein
S11. each is made on liThe inverse of Lagrangian be 0, obtain corresponding uploader and upload code check most preferably Select, i.e.,:
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;alpha;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mrow> <msup> <mi>r</mi> <mi>min</mi> </msup> <mo>-</mo> <msubsup> <mi>r</mi> <mi>i</mi> <mo>*</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>i</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>r</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msubsup> <mi>r</mi> <mi>i</mi> <mi>max</mi> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>i</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&amp;gamma;</mi> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> <msubsup> <mi>r</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mo>-</mo> <mi>b</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced>
WhereinRepresent to upload code check most preferably by receiving each uploader that assorted agreed-upon price decision-making obtains Select the set of composition.
2. the uploading bandwidth optimization method according to claim 1 applied to the live platform of cloud, it is characterised in that:
, it is necessary to multiply to Lagrange after the optimal selection of each uploader upload code check is obtained using uploading bandwidth optimization method Sonγ is updated iteration, and its specific process is as follows:
Many decomposition are carried out to P2 problems, P3 problems are converted to:
P3:Maxg (α, beta, gamma)
WhereinFor dual function, the strategy based on Sub-gradient can be obtained The more new strategy of Lagrange multiplier:
(1) Lagrange multiplierMore new strategy be:
<mrow> <msubsup> <mi>&amp;alpha;</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <msubsup> <mi>&amp;alpha;</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <mi>&amp;xi;</mi> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>g</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;alpha;</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>i</mi> <mo>,</mo> </mrow>
<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>g</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;alpha;</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>=</mo> <msup> <mi>r</mi> <mi>min</mi> </msup> <mo>-</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>i</mi> </mrow>
(2) Lagrange multiplierMore new strategy be:
<mrow> <msubsup> <mi>&amp;beta;</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <msubsup> <mi>&amp;beta;</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <mi>&amp;xi;</mi> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>g</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>i</mi> <mo>,</mo> </mrow> 2
<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>g</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>=</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>-</mo> <msubsup> <mi>r</mi> <mi>i</mi> <mi>max</mi> </msubsup> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>i</mi> </mrow>
(3) Lagrange multiplier γ more new strategy is:
<mrow> <msup> <mi>&amp;gamma;</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>=</mo> <mi>max</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <msup> <mi>&amp;gamma;</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </msup> <mo>+</mo> <mi>&amp;xi;</mi> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>g</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>&amp;gamma;</mi> </mrow> </mfrac> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>g</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>&amp;gamma;</mi> </mrow> </mfrac> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>b</mi> </mrow>
Wherein, s represents the order of iteration, and ξ represents the step-length of iteration each time;Work as satisfaction
| g (s+1)-g (s) | no longer to Lagrange multiplier during≤∈γ is updated, Wherein ∈ is the constant of setting.
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