CN103678000B - Calculating grid schedule equalization tasks method based on reliability and cooperative game - Google Patents

Abstract

Calculating grid schedule equalization tasks method based on reliability and cooperative game belongs to gridding task scheduling field, it is characterized in that realization in computing grid system based on reliability and cooperative game: at steady state, the computing capability provided is allowed to set up whole computing grid system according to each grid computing node, reliability optimization object function is to set optimal value, according to the parameter value calculation realistic objective functional value under stable state, if with the error of optimal value in the range of setting, then pro rata distribute task, otherwise, the task dividable of decision node self is joined factor θ and is distributed task lower limit α with from scheduler to node: during as θ ＜ α, do not distribute task；As θ ＞ α, leave out the burst null node of task average arrival rate, recalculate target function value, repeat above step, make remaining node do one's best, reach the requirement of reliability and cooperative game.When increasing with load, with non-cooperative game and equalization algorithm ratio, node is made to provide higher computing capability.

Description

Calculating grid schedule equalization tasks method based on reliability and cooperative game

Technical field

The present invention relates to a kind of dispatching method in grid computing field, particularly gridding task scheduling field.

Background technology

Task scheduling is the core research contents of grid computing.Calculate grid as a kind of special grid configuration, it Resource mainly has grid computing node and the Internet resources of high-performance calculation ability, its task scheduling research be how The task of the computation-intensive of user is reasonably allocated to the grid computing node with high-performance calculation ability by Internet resources Upper execution so that task be equalized distribution or make the Executing Cost of each task be preferably minimized or make system overall Performance obtain optimum.

In recent years, the gridding task scheduling problem that calculates of quality of service aware becomes one of calculating gridding task scheduling newly Research direction, grid user does not require nothing more than grid system and meets the functional requirements of task, and pays close attention to the Service Quality of task Amount, is first embedded into quality of service information in Min-min dispatching algorithm such as He etc., adjusts the gridding task of quality of service aware Degree problem has done initiative work；Subrata etc., using the task process time as target, give a kind of based on non-cooperative game Calculating gridding task balance dispatching model, and task based access control process the time calculating grid work assignment problem be modeled as one Individual cooperative game, gives Nash Bargaining formal similarity.Above gridding task scheduling research work, have employed different think ofs Road, make use of different mathematical tools, achieves preferable achievement in research, but there is a common ground: task scheduling is to process Time is foundation, using the task burst total processing time processing time or task on grid computing node as Optimized Operation Target, all do not account for the effect played in gridding task scheduling of this key element of reliability.

Summary of the invention

Task scheduling different from the past is with the time as foundation, task process time on grid computing node or task Total processing time as the dispatching method of optimization aim, it is an object of the invention to provide reliability, i.e. computing capability is steady The qualitative principal element considered as gridding task scheduling, with the task of each user the carrying of stable state on grid computing node It is target for ability, with task rate-allocation strategy on grid computing node as game strategies, determines appointing of grid system Business scheduling scheme.

It is a feature of the present invention that containing following steps:

Step (1), construct one based on reliability and the computing grid system of cooperative game, including: multiple users, Each scheduler i towards each user, each grid computing node j towards described each scheduler i, and a scheduling scheme meter Calculate device, wherein:

I=1,2 ..., i ..., I, I are the sum of scheduler i；

J=1,2 ..., j ..., J, J are the sum of grid computing node；

Set: ignoring scheduler i inter-process cost, under conditions of the multiplexed transport time:

Mean Speed λ of each scheduler i output burst task_iAdd and less than all grid nodes to each being received All the average of burst task performs speed u_jAdd and, the unit of speed is the burst number of tasks in the unit time, is expressed as:

$\underset{i=1}{\overset{I}{\&Sigma;}}{\mathrm{\&lambda;}}_i<\underset{j=1}{\overset{J}{\&Sigma;}}{u}_j---\left(1\right)$

Mean Speed λ of the burst task that each scheduler i sends_iAdd and equal to the burst task of all grid node j Average arrival rate φ_jAdd and, be expressed as:

0≤φ_j＜ u_jAnd

To meet: the maximum burst task that each grid computing node j can accept under keeping service quality premise simultaneously Arrival rateBurst task more than grid computing node j averagely reaches speed φ_j, less than grid computing node j to each The average of the whole burst tasks received performs speed u_j, it is expressed as:

${\mathrm{\&phi;}}_j<{\mathrm{\&phi;}}_j^{\max }<u_j$

Step (2), described scheduling scheme calculator is calculated as follows each grid computing node j and allows to carry when stable state Computing capability A of confession_j, 0 ＜ A_j＜ 1:

A_j=1-φ_jβ_1j(1+u'_jγ_j) (3)

Wherein, the burst task arriving grid computing node j meets with burst task average arrival rate φ_jFor average Poisson distribution, β_1jFor the burst task average service time of grid computing node j, u '_jFor the failure of grid computing node j busy Mean Speed, γ_jThe time that averagely retries for grid computing node j；

Step (3), described scheduling scheme calculator allows the meter provided as the following formula according to each grid computing node j of input Calculation ability A_jCalculating target function optimal value D:

$D=\underset{j=1}{\overset{J}{\&Sigma;}}\frac{1}{1-{\mathrm{\&phi;}}_j{\mathrm{\&beta;}}_{1j}(1+u_j^{\&prime;}{\mathrm{\&gamma;}}_j)}---\left(4\right)$

Step (4), described scheduling scheme calculator calculates the task of being sent to each scheduler i under the stable state set Scheduling scheme:

Step (4.1), systematic parameter initializes:

It is λ that scheduler i sends the Mean Speed of burst task_i(0), i=1,2 ..., i ..., I, " 0 " symbol represents stable State, lower same, the burst task average treatment speed of grid computing node j is u_j(0), j=1,2 ..., j ..., J；

Step (4.2), described scheduling scheme calculator is receiving under described stable state (0) by each scheduler i and each After data in the step (4.1) that grid computing node j sends, set:Initialization value be The maximum burst task arrival rate that can accept for grid computing node j, the burst task of grid computing node j averagely arrives The initialization value of speed is The error of objective function optimization value D Precision ε (0)≤10^-6；

Step (4.3), utilizes formula calculating target function optimal value D (the 0)=latterD of step (3)；

Step (4.4), if the error ε (0) of D (0)=latterD optimization target values relative to D meets less than or equal to 10^-6, obtain scheduling scheme the most as the following formula, seek a_i,jIf being unsatisfactory for, perform step (4.5)；

$a_{i,j}={\mathrm{\&lambda;}}_i\&CenterDot;\frac{{\mathrm{\&phi;}}_j}{\underset{i=1}{\overset{I}{\&Sigma;}}{\mathrm{\&lambda;}}_i}---\left(5\right)$

Wherein, a_i,jBurst task for scheduler i is assigned to the ratio of grid computing node j.

Step (4.5), makes formerD=latterD, the formerD target letter under temporary last scheduling scheme Numerical value latterD；

Step (4.6), is calculated as follows grid computing node j in the burst task arrival rate being in maximumShi Yun Unit burst task computation ability θ provided is provided_j, also referred to as task dividable joins regulatory factor；

${\mathrm{\&theta;}}_j=\frac{1}{{\mathrm{\&phi;}}_j^{\max }}-{\mathrm{\&beta;}}_{1j}(1+u_j^{\&prime;}{\mathrm{\&gamma;}}_j)$

And each θ corresponding for grid computing node j_jSorting from small to large, the result of sequence is saved in variable i ndex (J) In；

Step (4.7), is calculated as follows and distributes critical factor α:

$\underset{j=1}{\overset{m}{\&Sigma;}}\frac{1}{b_{index\left(j\right)}}+\underset{j=1}{\overset{m}{\&Sigma;}}{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }-\underset{j=1}{\overset{m}{\&Sigma;}}\frac{\sqrt{(1-{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }{b}_{index\left(j\right)})\left(\right(1-{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }{b}_{index\left(j\right)})+\frac{4b_{index\left(j\right)}}{\mathrm{\&alpha;}})}}{b_{index\left(j\right)}}-2\underset{i=1}{\overset{I}{\&Sigma;}}{\mathrm{\&lambda;}}_i=0$

Wherein, index (j) represents by grid computing node j position in index (J) after step (4.6) rearrangement Put, corresponding β₁, u', γ be expressed as β_1index(j)、u′_index(j)And γ_index(j), b_index(j)=β_1index(j)(1+ u′_index(j)γ_index(j)), α is the lower limit that scheduler i judges whether to certain grid computing node j distribution task；

Step (4.8), it is judged that task dividable auxiliary tone joint factor θ_jCorresponding θ_index(j)No more than α, if θ_index(j)＜ α, The most each scheduler i does not distributes task to grid computing node i ndex (j)；If θ_index(j)＞ α, the most each scheduler i is to grid computing Node i ndex (j) distribution task；

Step (4.9), from being likely assigned in the grid computing node of task leave out burst task from each scheduler Average arrival rate φ_index(j)The node of=0；

Step (4.10), is calculated as follows burst task in the middle remaining grid computing node of step (4.9) and averagely arrives Reach speed φ_index(j),

${\mathrm{\&phi;}}_{index\left(j\right)}=\frac{1}{2b_{index\left(j\right)}}+\frac{{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }}{2}-\frac{\sqrt{(1-{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }{b}_{index\left(j\right)})\left(\right(1-{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }{b}_{index\left(j\right)})+\frac{4b_{index\left(j\right)}}{\mathrm{\&alpha;}})}}{2b_{index\left(j\right)}}$

From obtained φ_index(j)In, leave out φ_index(j)The grid computing node of ＜ 0；

Step (4.11), the result obtaining step (4.10), the method as described in step (4.3) is described object function Value formerD compares with the new target function value latterD obtained by step (3) described method, and ε=| latterD- FormerD |, if ε≤10^-6, then step (4.4) is carried out, by each scheduler remaining grid computing node in step (4.10) Distribution burst task；If ε ＞ 10^-6, then repeated execution of steps (4.5) step (4.11), until whole burst tasks are distributed Complete, terminate；

Step (4.12), enters next new stable operation cycle.

The present invention is grid task dispatching method in a kind of computing grid system, has following excellent compared with prior art Gesture:

Different from the past using task execution time as the principal element determining method for scheduling task, the present invention is from reliability Angle is set out, and sets up and provides the ability Cooperative reference as object function with grid computing node, obtains new gridding task Dispatching method.From the point of view of experimental result, there is preferably effect.

Accompanying drawing explanation

Fig. 1 present invention calculates the system model schematic drawing of gridding task scheduling.

Fig. 2 system user task requests and scheduler tasks distribution figure in detail.

Fig. 3 obtains the program flow chart of dispatching method.

Cooperative game when grid computing node has stronger node in Fig. 4 system, non-cooperative game and equalization algorithm target letter Numerical value comparison diagram

The cooperative game during equilibrium of grid computing node computing capability, non-cooperative game and equalization algorithm target in Fig. 5 system Functional value comparison diagram

Fig. 6 system load affect lab diagram

Fig. 7 scheduler number of variations provides the comparison diagram of capacity to system

Detailed description of the invention

Below in conjunction with instantiation, the invention will be further described.

Computer of the present invention is Pentium more than 2 CPU, more than 10G hard disk, and the common table with general computing capability declines Machine.

First the present invention is on the basis of the reliability analysis model of computing grid system model and grid computing node, The Mathematical Modeling of the offer ability of stable state on grid computing node is provided；Secondly with gridding task on grid computing node The offer ability of stable state be target, set up the Cooperative reference of gridding task scheduling, obtain Nash Bargaining solution, Obtaining task scheduling approach based on this, scheduler just can be according to this scheduling scheme by task after obtaining a new task It is assigned on grid computing node perform.

The calculating gridding task scheduling system model schematic drawing of the present invention is as shown in Figure 1.Scheduling scheme calculator in Fig. 1 The task that the information transmitted by scheduler and grid computing node calculates scheduler according to the dispatching algorithm in this invention is adjusted Degree scheme, and be transferred to corresponding scheduler, task is distributed to corresponding net according to this task scheduling approach by scheduler Lattice calculate node and perform, and thus constitute whole grid system.Fig. 2 is that in Fig. 1, multiple users please to certain scheduler dispatches task Ask and scheduler is schemed in detail according to the task scheduling approach distributed tasks in this invention.Assuming that calculate the system of gridding task scheduling Model has l user, I scheduler, the grid computing node of J execution task burst, i-th scheduler asking user Ask and be decomposed into J task burst.In the figure, each grid computing node is as the participant of game, independently of one another.Each net Lattice calculate node through consultation, constitute alliance, so that the carrying of the stable state that gridding task is on each grid computing node Reach maximum for ability, constitute cooperative game.

The present invention based on following 2 it is assumed that according to the feature of grid system, these 2 hypothesis are rational:

1) current, e-Science is one of main application fields of grid, and the cost that task is once run is the biggest (as longer in performed the time), the geographic range that grid covers in addition may be relatively big, and the task burst transmission time on network is relatively Long, so the inter-process cost of negligible scheduler, it is assumed that task burst Executing Cost on grid computing node is to appoint The key point of business Executing Cost.

2) scheduler obtains task burst after carrying out task decomposing, it is assumed that the node in grid all possesses task burst Executive capability because in the range of a grid, the configuration of node is controlled.

Each user in the present invention: each producing the request to scheduler, between each user, generation independent of each other is appointed Business, it is β that user k produces the Mean Speed of task_k, and obey Poisson distribution；All users produce task be scheduled device decompose For being sent to after task burst on grid computing node perform.

Scheduler in the present invention: receive an assignment from each user, according to task scheduling approach, distributes to task in grid Node grid calculate node perform, the hypothesis 1 based on above), the time decomposing task ignores.

Grid computing node in the present invention: the executor of task burst, the hypothesis 2 based on above), grid computing node Possesses the executive capability to general task burst；The task burst average speed that performs on grid computing node j is u_j, hold The row time can obey Arbitrary distribution, and each grid computing node can be counted as one and have general retrial times and service The M/G/1 queuing system of device collapse.

The present invention sets λ_iSend the Mean Speed of burst task for scheduler i, meet the restrictive condition of formula (1).Formula (1) It is meant that each scheduler sends adding and should saving less than all grid computings of described system of the Mean Speed of burst task Point burst task average is performed speed add and.Formula (1) is obvious.

The present invention sets φ_jFor the average burst task arrival rate of grid computing node j, for ensureing stablizing of system Property, the average burst task arrival rate of grid computing node j should averagely perform speed less than its burst task, and described The task of adding and should be equal to all grid computing nodes of the Mean Speed sending burst task of all schedulers in system Average arrival rate add and, i.e. φ_jMeet following constraints:

0≤φ_j＜ u_jAnd

The present invention setsFor grid computing node j on the premise of keeping service quality, it is possible to maximum the dividing of acceptance Sheet task arrival rate, for ensureing the reliability of system,Should meet following constraints:

${\mathrm{\&phi;}}_j<{\mathrm{\&phi;}}_j^{max}<u_j$

Scheduler i in the present invention (i=1,2 ..., i ..., I) actual burst task arrival rate λ_iDispatched by each The relative burst task arrival rate of device(i=1,2 ..., i ..., I) try to achieve, specifically calculate according to formula (8), wherein ρ is negative Carry coefficient.

It is a feature of the present invention that method and the process obtaining each grid computing node average burst task arrival rate, its Specifically comprise the following steps that

1. the model of select permeability is set up

Each grid computing node is independent of one another, always expects the offer of task stable state on grid computing node Ability is maximum, and negotiate with one another cooperation, constitutes cooperative game, and in cooperative game, each grid computing node is as the participation of game Person.For the grid computing node with the M/G/1 queuing system of general retrial times and server crash can be seen as, its The offer capacity calculation formula of stable state is:

A_j=1-φ_jβ_1j(1+u'_jγ_j)

Wherein A_jBe directed to grid computing node j (wherein j=1,2 ..., j ..., J) offer ability, φ_jFor grid meter The average burst task arrival rate of operator node j, β_1jFor the average of grid computing node j burst task service time, u '_jFor net Lattice calculate the Mean Speed that node j busy is failed, γ_jAverage for the time that retries of grid computing node j.A_jMeet constraint 0 ＜ A_j＜ 1.

Using the sum reciprocal of the offer ability of the stable state on all grid computing nodes as the object function of game, That is:

$D=\underset{j=1}{\overset{J}{\&Sigma;}}\frac{1}{1-{\mathrm{\&phi;}}_j{\mathrm{\&beta;}}_{1j}(1+u_j^{\&prime;}{\mathrm{\&gamma;}}_j)}$

2. dispatching method solves

The calculating grid concrete derivation algorithm of schedule equalization tasks method based on reliability and cooperative game is as follows:

(1) systematic parameter initializes.It is λ that scheduler i sends the Mean Speed of burst task_i(0), i=1,2 ..., I ..., I, " 0 " symbol represents stable state, lower same, burst task average treatment speed u of grid computing node j_j(0), j= 1,2,…,j…,J；

(2) described scheduling scheme calculator is receiving under described stable state (0) by each scheduler i and each grid computing After data in the step (4.1) that node j sends, set:Initialization value be For grid meter The maximum burst task arrival rate that operator node j can accept, the burst task average arrival rate of grid computing node j is initial Change value isThe error precision ε (0) of objective function optimization value D≤ 10^-6；

(3) formula is utilizedCalculating target function optimal value D (0)=latterD；

(4) if the error ε (0) of D (0)=latterD optimization target values relative to D meets less than or equal to 10^-6, then by formulaObtain scheduling scheme, seek a_i,jIf being unsatisfactory for, execution step (4.1):

(4.1) formerD=latterD is made, formerD target function value under temporary last scheduling scheme latterD；

(4.2) by formulaCalculate grid computing node j to arrive in the burst task being in maximum Reach speedTime allow provide unit burst task computation ability θ_j, also referred to as task dividable joins regulatory factor, and each grid Calculate θ corresponding to node j_jSorting from small to large, the result of sequence is saved in variable i ndex (J)；

(4.3) be calculated as follows distribution critical factor α:

$\underset{j=1}{\overset{m}{\&Sigma;}}\frac{1}{b_{index\left(j\right)}}+\underset{j=1}{\overset{m}{\&Sigma;}}{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }-\underset{j=1}{\overset{m}{\&Sigma;}}\frac{\sqrt{(1-{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }{b}_{index\left(j\right)})\left(\right(1-{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }{b}_{index\left(j\right)})+\frac{4b_{index\left(j\right)}}{\mathrm{\&alpha;}})}}{b_{index\left(j\right)}}-2\underset{i=1}{\overset{I}{\&Sigma;}}{\mathrm{\&lambda;}}_i=0$

Wherein, index (j) represents by grid computing node j position in index (J) after step (4.2) rearrangement Put, corresponding β₁, u', γ be expressed as β_1index(j)、u′_index(j)And γ_index(j), b_index(j)=β_1index(j)(1+ u′_index(j)γ_index(j)), α is the lower limit that scheduler i judges whether to certain grid computing node j distribution task；

(4.4) judge that task dividable auxiliary tone saves factor θ_jCorresponding θ_index(j)No more than α, if θ_index(j)＜ α, respectively adjusts Degree device i do not distribute task to grid computing node i ndex (j)；If θ_index(j)＞ α, the most each scheduler i is to grid computing node Index (j) distributes task；

(4.5) from be likely assigned in the grid computing node of task to leave out from each scheduler burst task averagely to Reach speed φ_index(j)The node of=0；

(4.6) in step (4.5), remaining grid computing node is calculated as follows burst task average arrival rate φ_index(j),

${\mathrm{\&phi;}}_{index\left(j\right)}=\frac{1}{2b_{index\left(j\right)}}+\frac{{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }}{2}-\frac{\sqrt{(1-{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }{b}_{index\left(j\right)})\left(\right(1-{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }{b}_{index\left(j\right)})+\frac{4b_{index\left(j\right)}}{\mathrm{\&alpha;}})}}{2b_{index\left(j\right)}}$

From obtained φ_index(j)In, leave out φ_index(j)The grid computing node of ＜ 0；

(4.7) result obtaining step (4.6), the method as described in step (3) is described target function value formerD With by formulaThe new target function value latterD obtained compares, and ε=| latterD- FormerD |, if ε≤10^-6, then step (4) is carried out, by the remaining grid computing node distribution in step (4.6) of each scheduler Burst task；If ε ＞ 10^-6, then repeated execution of steps (4.1) step (4.7), until whole burst tasks are assigned, Terminate；

Dispatching method in the present invention, i.e. cooperative game algorithm have preferably effect, can by with non-cooperative game Algorithm and equalized scheduling algorithm compare explanation, concrete as tested one, two, shown in three.

If the average processing power of each grid computing node task arrival rate relative with scheduler is in grid Knowing, the actual task arrival rate of scheduler calculates according to formula (8).

Experiment one: the experiment of target function value under equilibrium state

The computing capability of grid computing node may equalize, it is also possible to the situation that part of nodes computing capability is stronger occurs, For both of these case, carry out two groups of experiments.

In experiment one, the load factor ρ making grid system is 0.6, and scheduler number is 10, the number of grid computing node Mesh is that the relative task arrival rate of 15,10 schedulers is followed successively by:

First group is the experiment having the computing capability of part of nodes stronger in grid computing node, if grid computing in system The computing capability of node is as follows:

U={0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.033,0.033,0.033,0.0231, 0.02511,0.0153,0.023,0.025}

Under above primary condition, try to achieve with cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm respectively The average burst task arrival rate of each grid computing node in system, then obtains reflecting the ability that provides under system stability state Target function value, experimental result is as shown in the table:

As can be seen from the table, the sum reciprocal of the ability provided is provided under all grid computing node stable states In, the minimum of cooperative game algorithm, i.e. cooperative game algorithm can make system provide higher computing capability, thus cooperation is described Game playing algorithm is more excellent.

Accompanying drawing 4 is asked for applying cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm in this experimentation The comparison diagram reciprocal of the ability provided is provided under each grid computing node stable state obtained.

Second group be grid computing node in system computing capability equilibrium experiment, it is assumed that grid computing node in system Computing capability as follows:

U={0.031,0.03,0.029,0.0312,0.03,0.03,0.032,0.033,0.032,0 .033,0.029, 0.029,0.03,0.030,0.031}

Under above primary condition, try to achieve with cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm respectively The average burst task arrival rate of each grid computing node in system, then obtains reflecting the ability that provides under system stability state Target function value, experimental result is as shown in the table:

As can be seen from the table, the sum reciprocal of the ability provided is provided under all grid computing node stable states In, the minimum of cooperative game algorithm, i.e. cooperative game algorithm can make system provide higher computing capability, thus cooperation is described Game playing algorithm is more excellent.

Accompanying drawing 5 is to apply cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm true in this experimentation The comparison diagram reciprocal of the ability provided is provided under each grid computing node stable state that fixed task scheduling approach is tried to achieve.

In conjunction with above two groups of experiments, it can be deduced that a conclusion: in grid system, the computing capability of grid computing node is equal When weighing or be unbalanced, the algorithm in the present invention is better than non-cooperative game algorithm and equalized scheduling algorithm.

Experiment two: the impact experiment of system load

This experiment is when the actual task of System Scheduler increases, cooperative game algorithm, non-cooperative game algorithm and The comparison of equalized scheduling algorithm.In this experiment, make load factor ρ increase to 0.9 successively from 0.1, increase by 0.1, system every time The computing capability of middle grid computing node is as follows:

U={0.01,0.01,0.01,0.02,0.02,0.02,0.02,0.033,0.033,0.033,0.028,0.03, 0.028,0.024,0.03}

Remaining parameter is identical with the parameter of first group of experiment in experiment one.

Under above primary condition, determine with cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm respectively The task allocative decision of system during load change, then obtains the object function of the offer ability under system stability state that reflects Value, experimental result is as shown in the table:

In upper table, from the point of view of laterally, when no matter load is much, the grid computing joint that always cooperative game algorithm is corresponding Allow the sum reciprocal minimum of the ability provided, i.e. cooperative game algorithm that system can be made to provide higher meter under some stable state Calculation ability, thus illustrate that cooperative game algorithm is more excellent.

Application cooperative game algorithm, non-cooperative game algorithm and equilibrium when accompanying drawing 6 is that in this experiment, system load increases The system goal function value comparison diagram that the task allocative decision that dispatching algorithm determines is tried to achieve.It can be seen that along with system The increase of load, the advantage of cooperative game algorithm is gradually increased.

Experiment three: the impact experiment of system scale

The change of system scale includes change and the change of grid computing interstitial content of scheduler number.Therefore experiment point It it is two groups.

First group of experiment, the change of the scheduler number impact on system goal function value:

In this group experiment, scheduler number of variations, in the range of n=5～20, increases a scheduler successively；System is born Carrying is ρ=0.6, and the number of grid computing node is 15, and the computing capability of each node is as follows:

U={0.01,0.01,0.01,0.02,0.02,0.02,0.02,0.033,0.033,0.033,0.028,0.03, 0.028,0.024,0.03}

The relative task arrival rate of all schedulers is as follows:

Under above primary condition, try to achieve with cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm respectively The burst task arrival rate of each grid computing node in system during scheduler number of variations, then obtains reflecting system stability shape The target function value of the offer ability under state, experimental result is as shown in the table:

In upper table, from the point of view of longitudinally, when scheduler number increase causes the task of system to increase therewith, system can The computing capability provided will reduce, and the target function value of corresponding system will increase；From the point of view of laterally, cooperative game algorithm Target function value to be always target function value in three kinds of algorithms minimum, i.e. cooperative game algorithm can make system provide higher Computing capability.

When accompanying drawing 7 is this experiment scheduler number increase, utilize cooperative game algorithm, non-cooperative game algorithm and equilibrium The change comparison diagram of the system goal function value that the task allocative decision that dispatching algorithm determines is tried to achieve.It can be seen that with The increase of scheduler number, the advantage of cooperative game algorithm is also gradually increased.

Second group of experiment, the change of the grid computing interstitial content impact on system offer ability:

In this group experiment, the number n=15 of scheduler, system load factor ρ=0.6, grid computing interstitial content becomes The scope changed is m=10～20, and the relative task arrival rate of scheduler is as follows:

The computing capability that described system all grid computings node is corresponding is as follows:

U={0.01,0.01,0.01,0.02,0.02,0.02,0.02,0.033,0.033,0.033,0.028,0.03, 0.028,0.024,0.03,0.028,0.033,0.025,0.019,0.021}

Under above primary condition, try to achieve with cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm respectively When described grid calculates interstitial content change, each burst task arrival rate calculating node in system, is then reflected The target function value of the offer ability under system stability state, experimental result is as shown in the table:

In upper table, from the point of view of laterally, the target function value that cooperative game algorithm is corresponding is minimum, i.e. in three algorithms Cooperative game algorithm can make the computing capability that system offer is higher, optimum during i.e. cooperative game algorithm is three algorithms.Along with Calculating increasing of node, the advantage of cooperative game algorithm is gradually increased.

Comprehensive these two groups experiments it can be seen that when system scale increases, the present invention relatively non-cooperative game algorithm and equilibrium The advantage of dispatching algorithm is more and more obvious, further illustrates the present invention and system can be allowed to provide higher computing capability, thus add The execution of fast gridding task, improves the efficiency of system work.

Claims (1)

1. calculating grid schedule equalization tasks method based on reliability and cooperative game, it is characterised in that be one based on In the computing grid system of reliability and cooperative game, hereinafter referred to as system, realize the most according to the following steps:

Step (1), construct one based on reliability and the computing grid system of cooperative game, including: multiple users, towards Each scheduler i of each user, each grid computing node j towards described each scheduler i, and a scheduling scheme calculates Device, wherein:

I=1,2 ..., i ..., I, I are the sum of scheduler i；

J=1,2 ..., j ..., J, J are the sum of grid computing node；

Set: ignoring scheduler i inter-process cost, under conditions of the multiplexed transport time:

Mean Speed λ of each scheduler i output burst task_iAdd and less than all grid nodes whole to each received The average of burst task performs speed u_jAdd and, the unit of speed is the burst number of tasks in the unit time, is expressed as:

$\underset{i=1}{\overset{I}{\&Sigma;}}{\mathrm{\&lambda;}}_i<\underset{j=1}{\overset{J}{\&Sigma;}}{u}_j---\left(1\right)$

Mean Speed λ of the burst task that each scheduler i sends_iAdd and burst task average equal to all grid node j Arrival rate φ_jAdd and, be expressed as:

0≤φ_j＜ u_jAnd

To meet: the maximum burst task that each grid computing node j can accept under keeping service quality premise arrives simultaneously SpeedBurst task more than grid computing node j averagely reaches speed φ_j, less than grid computing node j to each being received The average of the whole burst tasks arrived performs speed u_j, it is expressed as:

${\mathrm{\&phi;}}_j<{\mathrm{\&phi;}}_j^{max}<u_j$

Step (2), described scheduling scheme calculator is calculated as follows each grid computing node j and allows offer when stable state Computing capability A_j, 0 ＜ A_j＜ 1:

A_j=1-φ_jβ_1j(1+u'_jγ_j) (3)

Wherein, the burst task arriving grid computing node j meets with burst task average arrival rate φ_jPoisson for average Distribution, β_1jFor the burst task average service time of grid computing node j, u '_jFor grid computing node j busy failure average Speed, γ_jThe time that averagely retries for grid computing node j；

Step (3), described scheduling scheme calculator allows the calculating energy provided as the following formula according to each grid computing node j of input Power A_jCalculating target function optimal value D:

$D=\underset{j=1}{\overset{J}{\&Sigma;}}\frac{1}{1-{\mathrm{\&phi;}}_j{\mathrm{\&beta;}}_{1j}(1+u_j^{\&prime;}{\mathrm{\&gamma;}}_j)}---\left(4\right)$

Step (4), described scheduling scheme calculator calculates the task scheduling being sent to each scheduler i under the stable state set Scheme:

Step (4.1), systematic parameter initializes:

It is λ that scheduler i sends the Mean Speed of burst task_i(0), i=1,2 ..., i ..., I, " 0 " symbol represents stable state, Lower same, the burst task average treatment speed of grid computing node j is u_j(0), j=1,2 ..., j ..., J；

Step (4.2), described scheduling scheme calculator is receiving under described stable state (0) by each scheduler i and each grid After calculating the data in the step (4.1) that node j sends, set:Initialization value be For net Lattice calculate the maximum burst task arrival rate that node j can accept, the burst task average arrival rate of grid computing node j Initialization value be The error precision of objective function optimization value D ε(0)≤10^-6；

Step (4.3), utilizes formula calculating target function optimal value D (the 0)=latterD of step (3)；

Step (4.4), if the error ε (0) of D (0)=latterD optimization target values relative to D meets less than or equal to 10^-6, then Obtain scheduling scheme as the following formula, seek a_i,jIf being unsatisfactory for, perform step (4.5)；

$a_{i,j}={\mathrm{\&lambda;}}_i\&CenterDot;\frac{{\mathrm{\&phi;}}_j}{\underset{i=1}{\overset{I}{\&Sigma;}}{\mathrm{\&lambda;}}_i}---\left(5\right)$

Wherein, a_i,jBurst task for scheduler i is assigned to the ratio of grid computing node j；

Step (4.5), makes formerD=latterD, the formerD target function value under temporary last scheduling scheme latterD；

Step (4.6), is calculated as follows grid computing node j in the burst task arrival rate being in maximumTime allow to carry Unit burst task computation ability θ of confession_j, also referred to as task dividable joins regulatory factor；

${\mathrm{\&theta;}}_j=\frac{1}{{\mathrm{\&phi;}}_j^{\max }}-{\mathrm{\&beta;}}_{1j}(1+u_j^{\&prime;}{\mathrm{\&gamma;}}_j)$

And each θ corresponding for grid computing node j_jSorting from small to large, the result of sequence is saved in variable i ndex (J)；

Step (4.7), is calculated as follows and distributes critical factor α:

$\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{1}{b_{index\left(j\right)}}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\sqrt{\left(1-{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }{b}_{index\left(j\right)}\right)\left(\left(1-{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }{b}_{index\left(j\right)}\right)+\frac{4b_{index\left(j\right)}}{\mathrm{\&alpha;}}\right)}}{b_{index\left(j\right)}}-2\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i=0$

Wherein, index (j) represents by grid computing node j position in index (J), phase after step (4.6) rearrangement Corresponding β₁, u', γ be expressed as β_1index(j)、u′_index(j)And γ_index(j),

b_index(j)=β_1index(j)(1+u′_index(j)γ_index(j)), α is that scheduler i judges whether to certain grid computing node j The lower limit of distribution task；

Step (4.8), it is judged that task dividable auxiliary tone joint factor θ_jCorresponding θ_index(j)No more than α, if θ_indx(j)＜ α, respectively adjusts Degree device i do not distribute task to grid computing node i ndex (j)；If θ_index(j)＞ α, the most each scheduler i is to grid computing node Index (j) distributes task；

Step (4.9), puts down from being likely assigned in the grid computing node j of task to leave out burst task from each scheduler i All arrival rates φ_index(j)The node of=0；

Step (4.10), in step (4.9), remaining grid computing node is calculated as follows burst task and averagely arrives speed Rate φ_index(j),

${\mathrm{\&phi;}}_{index\left(j\right)}=\frac{1}{2b_{index\left(j\right)}}+\frac{{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }}{2}-\frac{\sqrt{\left(1-{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }{b}_{index\left(j\right)}\right)\left(\left(1-{\mathrm{\&phi;}}_{index\left(j\right)}^{\max }{b}_{index\left(j\right)}\right)+\frac{4b_{index\left(j\right)}}{\mathrm{\&alpha;}}\right)}}{2b_{index\left(j\right)}}$

From obtained φ_index(j)In, leave out φ_index(j)The grid computing node of ＜ 0；

Step (4.11), the result obtaining step (4.10), the method as described in step (4.3) is described target function value FormerD compares with the new target function value latterD obtained by step (3) described method, and ε=| latterD- FormerD |, if ε≤10^-6, then step (4.4) is carried out, by each scheduler remaining grid computing node in step (4.10) Distribution burst task；If ε ＞ 10^-6, then repeated execution of steps (4.5) step (4.11), until whole burst tasks are distributed Complete, terminate；

Step (4.12), enters next new stable operation cycle.