CN103678000A - Computational grid balance task scheduling method based on reliability and cooperative game - Google Patents

Abstract

A computational grid balance task scheduling method based on reliability and a cooperative game belong to the field of grid task scheduling. The method is characterized by being achieved in a computational grid system based on reliability and the cooperative game. In a stable state, the whole computational grid system is established according to computer capacity permitted and provided by grid computing nodes. A reliable optimized objective function is obtained by the following steps that an optimized value is set, a practical objective function value is calculated according to a parameter value in a stable state, if compared with the optimized value, an error of the practical objective function value is within a set range, then tasks are distributed in proportion, otherwise, a task distributing factors theta of the nodes themselves and a lower limiting value alpha of distributing tasks from a dispatcher to the nodes, when the theta is smaller than the alpha, the tasks are not distributed, and when the theta is larger than the alpha, the nodes with segmentation task average arriving velocity equaling zero are deleted, the objective function value, the steps are repeated to enable the remaining nodes to meet the requirements for the reliability and the cooperative game as far as possible. Along with addition of loads, compared with a non-cooperative game and a load-balancing algorithm, the nodes provide higher computer capacity.

Description

Computing grid equalization task dispatching method based on reliability and cooperative game

Technical field

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

Background technology

Task scheduling is the core research contents of grid computing.Computing grid is as a kind of special grid configuration, its resource is mainly grid computing node and the Internet resources with high-performance calculation ability, its task scheduling research be how the task of user's computation-intensive to be reasonably allocated on the grid computing node with high-performance calculation ability and to be carried out by Internet resources so that task obtains balanced distribution or make the Executing Cost of each task drop to minimum or make the performance of overall system obtain optimum.

In recent years, the computing grid Mission Scheduling of quality of service aware becomes a new research direction of computing grid task scheduling, grid user not only requires grid system to meet the functional demand of task, and the service quality of the task of concern, as first He etc. is embedded into quality of service information in Min-min dispatching algorithm, the gridding task scheduling problem of quality of service aware has been done to initiative work; Subrata etc. are usingd the task processing time as target, provided a kind of computing grid task balance scheduling model based on non-cooperative game, and computing grid operation assignment problem based on the task processing time is modeled as to a cooperative game, provided and received the structure of assorted bargaining solution.Above gridding task scheduling research work, adopted different thinkings, utilized different mathematical tools, obtained good achievement in research, but there is a common ground: task scheduling be take the processing time as foundation, processing time using task burst on grid computing node or the total processing time of task, as the target of Optimized Operation, are not all considered this key element of reliability role in gridding task scheduling.

Summary of the invention

Task scheduling different from the past be take the time as foundation, processing time using task on grid computing node or the total processing time of task are as the dispatching method of optimization aim, the object of the invention is reliability, it is the principal element that the stability that provides of computing power is considered as gridding task scheduling, each user's the providing capability of task steady state (SS) on grid computing node of take is target, the rate-allocation strategy of task on grid computing node of take is game strategies, determines the task scheduling scheme of grid system.

The invention is characterized in and contain following steps:

Step (1), construct a computing grid system based on reliability and cooperative game, comprising: a plurality of users, towards each scheduler i of each user, towards each grid computing node j of described each scheduler i, and a scheduling scheme counter, wherein:

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

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

Set: ignoring under scheduler i inter-process cost, the condition in task transmission time:

The mean speed λ of each scheduler i output burst task _iadd and be less than the average execution speed u of all grid nodes to whole burst tasks of receiving separately _jadd and, the unit of speed is the burst number of tasks in the unit interval, is expressed as:

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

The mean speed λ of the burst task that each scheduler i sends _ithe average arrival rate φ that adds and equal the burst task of all grid node j _jadd and, be expressed as:

0≤φ _j<u _jand $\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i=\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}{\mathrm{\&phi;}}_j---\left(2\right)$

To meet: each grid computing node j is in the maximum burst task arrival rate that keeps can accepting under service quality prerequisite simultaneously the burst task that is greater than grid computing node j on average reaches speed φ _j, be less than the average execution speed u of grid computing node j to whole burst tasks of receiving separately _j, be expressed as:

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

Step (2), described scheduling scheme counter is calculated as follows each grid computing node j the computing power A providing is provided when steady state (SS) _j, 0<A _j<1:

A _j＝1-φ _jβ _1j(1+u′ _jγ _j) (3)

Wherein, the burst task of arrival grid computing node j meets with burst task average arrival rate φ _jfor the Poisson distribution of average, β _1jfor the burst task average service time of grid computing node j, u ' _jfor the mean speed of grid computing node j busy failure, γ _jfor the average retry time of grid computing node j;

Step (3), described scheduling scheme counter allows according to each grid computing node j of input the computing power A providing by following formula _jcalculating target function optimal value D:

$D=\underset{j=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="DEST\_PATH\_HDA0000453798650000031.png,DEST\_PATH\_HDA0000453798650000032.png"\; state="\{\{state\}\}">J</figure-callout>}}{\mathrm{\&Sigma;}}}\frac{1}{1-{\mathrm{\&phi;}}_j{\mathrm{\&beta;}}_{1j}(1+u_j^{\&prime;}{\mathrm{\&gamma;}}_j)}---\left(4\right)$

Step (4), described scheduling scheme counter calculates the task scheduling scheme that sends to each scheduler i under the steady state (SS) of setting:

Step (4.1), systematic parameter initialization:

The mean speed that scheduler i sends burst task is λ _i(0), i=1,2 ..., i ..., I, " 0 " symbol represents steady state (SS), 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), after the data of described scheduling scheme counter in receive the step (4.1) of being sent by each scheduler i and each grid computing node j under described steady state (SS) (0), set:

initialization value be

for the maximum burst task arrival rate that grid computing node j can accept, the initialization value of the burst task average arrival rate of grid computing node j is

the error precision ε (0)≤10 of objective function optimization value D ^-6;

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

Step (4.4), if D (0)=latterD meets and is less than or equal to 10 with respect to the error ε (0) of the optimization target values of D ^-6, by following formula, obtain scheduling scheme, ask a _{i, j}if do not meet execution step (4.5);

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

Wherein, a _{i, j}for the burst task of scheduler i is assigned to the ratio of grid computing node j.

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

Step (4.6), is calculated as follows grid computing node j in the burst task arrival rate in maximum

time the burst task computation ability θ of unit that provides is provided _j, also claim task dividable to join regulatory factor;

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

And θ corresponding to each grid computing node j _jsequence 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:

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

Wherein, index (j) represents by the position of grid computing node j in index (J) after step (4.6) rearrangement, corresponding β ₁, u ', γ be expressed as β _{lindex (j)}, u ' _{index (j)}and γ _{index (j)}, b _{index (j)}=β _{lindex (j)}(1+u ' _{index (j)}γ _{index (j)}), α is that scheduler i judges whether to the lower limit of certain grid computing node j allocating task;

Step (4.8), judgement task dividable is joined regulatory factor θ _jcorresponding θ _{index (j)}be greater than α no, if θ _{index (j)}< α, each scheduler i is not to grid computing node i ndex (j) allocating task; If θ _{index (j)}> α, each scheduler i is to grid computing node i ndex (j) allocating task;

Step (4.9) is left out burst task average arrival rate φ from be likely assigned to the grid computing node of task from each scheduler _{index (j)}=0 node;

Step (4.10), in step (4.9), remaining grid computing node is calculated as follows burst task average arrival rate φ _{index (j)},

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

From resulting φ _{index (j)}in, leave out φ _{index (j)}the grid computing node of <0;

Step (4.11), the result that step (4.10) is obtained, by method step (4.3) Suo Shu, described target function value formerD and the new target function value latterD obtaining by the described method of step (3) are compared, ε=| latterD-formerD|, if ε≤10 ^-6, carry out step (4.4), by each scheduler, to grid computing node remaining in step (4.10), distribute burst task; If ε is >10 ^-6, repeated execution of steps (4.5)---step (4.11), until all burst task is assigned, finishes;

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 compared with prior art following advantage:

Principal element using task execution time as the dispatching method that sets the tasks different from the past, the present invention is from reliability angle, sets up to take the cooperative game model that grid computing node providing capability is objective function, obtains new grid task dispatching method.From experimental result, there is preferably effect.

Accompanying drawing explanation

In Fig. 1 the present invention, calculate the system model schematic drawing of gridding task scheduling.

Fig. 2 system user task requests and scheduler task distribution details drawing.

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 function value comparison diagram.

Cooperative game when grid computing node computing power is balanced in Fig. 5 system, non-cooperative game and equalization algorithm target function value comparison diagram.

Fig. 6 system load affect lab diagram.

The comparison diagram of Fig. 7 scheduler number of variations on the impact of system providing capability.

embodiment

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

Computer of the present invention is the above CPU of Pentium 2, and the above hard disk of 10G has the common Desktop Computer of general computing power.

First the present invention is on the basis of the reliability analysis model of computing grid system model and grid computing node, sets up the mathematical model of the providing capability of steady state (SS) on grid computing node; Secondly the providing capability of the steady state (SS) of gridding task on grid computing node of take is target, set up the cooperative game model of gridding task scheduling, obtain and receive assorted bargaining solution, obtain based on this task scheduling scheme, scheduler obtains just can task being assigned on grid computing node and being carried out according to this scheduling scheme after a new task.

Computing grid task scheduling system model schematic drawing of the present invention as shown in Figure 1.In Fig. 1, scheduling scheme counter calculates the task scheduling scheme of scheduler by the information of scheduler and the transmission of grid computing node according to the dispatching algorithm in this invention, and sent to corresponding scheduler, scheduler is distributed to corresponding grid computing node according to this task scheduling scheme by task and carries out, and forms thus whole grid system.Fig. 2 is that in Fig. 1, a plurality of users send task requests and scheduler according to the task scheduling scheme distributed tasks details drawing in this invention to certain scheduler.The grid computing node that has l user, an I scheduler, the individual burst of executing the task of J in the system model of assumed calculation gridding task scheduling, i scheduler is decomposed into J task burst by user's request.In the figure, each grid computing node is as the participant of game, independent of one another.Each grid computing node through consultation, forms alliance, thereby makes the providing capability of the steady state (SS) of gridding task on each grid computing node reach maximum, forms cooperative game.

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

1) current, e-Science is one of main application fields of grid, the cost that task is once moved is large (as longer in the execution time) conventionally, in addition the geographic range that grid covers may be larger, the transmission time of task burst on network is longer, so can ignore the inter-process cost of scheduler, suppose that the Executing Cost of task burst on grid computing node is the key point of tasks carrying cost.

2) scheduler obtains task burst after task is decomposed, and supposes that the node in grid all possesses the executive capability of task burst, because in the scope of a grid, the configuration of node is controlled.

Each user in the present invention: produce separately the request to scheduler, generation task independent of each other between each user, the mean speed that user k produces task is β _k, and obey Poisson distribution; The task that all users the produce device that is scheduled is decomposed into after task burst and sends on grid computing node and carry out.

Scheduler in the present invention: receive an assignment from each user, according to task scheduling scheme, task is distributed to the node in grid---grid computing node is carried out, the hypothesis 1 based on above), the time that task is decomposed 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 average execution speed of task burst on grid computing node j is u _j, the execution time can be obeyed any distribution, and each grid computing node can be counted as a M/G/1 queuing system with general retrial times and server failing.

In the present invention, establish λ _ifor scheduler i sends the mean speed of burst task, meet the restrictive condition of formula (1).The implication of formula (1) be adding of each scheduler mean speed of sending burst task and should be less than all grid computing nodes of described system to the average execution speed of burst task add and.Formula (1) is obvious.

In the present invention, establish φ _javerage burst task arrival rate for grid computing node j, for guaranteeing the stability of system, the average burst task arrival rate of grid computing node j should be less than its burst task and on average carry out speed, and in described system the mean speed of sending burst task of all schedulers add and should equal all grid computing nodes task average arrival rate add and, i.e. φ _jmeet following constraint condition:

0≤φ _j< u _jand $\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i=\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}{\mathrm{\&phi;}}_j$

In the present invention, establish

for grid computing node j is keeping under the prerequisite of service quality, the maximum burst task arrival rate that can accept, for guaranteeing the reliability of system,

should meet following constraint condition:

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

Scheduler i in the present invention (i=1,2 ..., i ..., actual burst task arrival rate λ I) _iby the relative burst task arrival rate of each scheduler try to achieve, specifically according to formula (8), calculate, wherein ρ is load factor.

The invention is characterized in the Method and Process that obtains the average burst task of each grid computing node arrival rate, its concrete steps are as follows:

1. select the model of problem to set up

Each grid computing node is independent of one another, always expects that the providing capability of the steady state (SS) of task on grid computing node is maximum, consults each other cooperation, forms cooperative game, and in cooperative game, each grid computing node is as the participant of game.For the grid computing node that can be regarded as the M/G/1 queuing system with general retrial times and server failing, the providing capability computing formula of its steady state (SS) is:

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

A wherein _jfor be grid computing node j (j=1 wherein, 2 ..., j ..., providing capability J), φ _jfor the average burst task arrival rate of grid computing node j, β _1jfor the grid computing node j burst task average of service time,

for the mean speed of grid computing node j busy failure, γ _javerage for retry time of grid computing node j.A _jmeet constraint 0 < A _j< 1.

Objective function using the sum reciprocal of the providing capability of the steady state (SS) on all grid computing nodes as game, that is:

$D=\underset{j=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="DEST\_PATH\_HDA0000453798650000031.png,DEST\_PATH\_HDA0000453798650000032.png"\; state="\{\{state\}\}">J</figure-callout>}}{\mathrm{\&Sigma;}}}\frac{1}{1-{\mathrm{\&phi;}}_j{\mathrm{\&beta;}}_{1j}(1+u_j^{\&prime;}{\mathrm{\&gamma;}}_j)}$

2. dispatching method solves

The concrete derivation algorithm of computing grid equalization task dispatching method based on reliability and cooperative game is as follows:

(1) systematic parameter initialization.The mean speed that scheduler i sends burst task is λ _i(0), i=1,2 ..., i ..., I, " 0 " symbol represents steady state (SS), lower same, the burst task average treatment speed u of grid computing node j _j(0), j=1,2 ..., j ..., J;

(2) after the data of described scheduling scheme counter in receive the step (4.1) of being sent by each scheduler i and each grid computing node j under described steady state (SS) (0), set: initialization value be

for the maximum burst task arrival rate that grid computing node j can accept, the burst task average arrival rate initialization value of grid computing node j is ${\mathrm{\&phi;}}_j\left(0\right)={\mathrm{\&phi;}}_j^{\max }\left(0\right),u_j^{\&prime;}\left(0\right)=\frac{u_j\left(0\right)}{10},{\mathrm{\&gamma;}}_j\left(0\right)=\frac{5}{u_j\left(0\right)},$ The error precision ε (0)≤10 of objective function optimization value D ^-6;

(3) utilize formula

calculating target function optimal value D (0)=latterD;

(4) if D (0)=latterD meets and is less than or equal to 10 with respect to the error ε (0) of the optimization target values of D ^-6, by formula

obtain scheduling scheme, ask a _{i, j}if do not meet execution step (4.1):

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

(4.2) by formula

computing grid computing node j is in the burst task arrival rate in maximum

time the burst task computation ability θ of unit that provides is provided _j, also claim task dividable to join regulatory factor, and θ corresponding to each grid computing node j _jsequence from small to large, the result of sequence is saved in variable i ndex (J);

(4.3) be calculated as follows and distribute critical factor α:

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

Wherein, index (j) represents by the position of grid computing node j in index (J) after step (4.2) rearrangement, corresponding β ₁, u ', γ be expressed as β _{lindex (j)}, u ' _{index (j)}and γ _{index (j)}, $b_{\mathrm{index}\left(j\right)}={\mathrm{\&beta;}}_{1\mathrm{index}\left(j\right)}(1+u_{\mathrm{index}\left(j\right)}^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{index}\left(j\right)}),$ α is that scheduler i judges whether to the lower limit of certain grid computing node j allocating task;

(4.4) judgement task dividable is joined regulatory factor θ _jcorresponding θ _{index (j)}be greater than α no, if θ _{index (j)}< α, each scheduler i is not to grid computing node i ndex (j) allocating task; If θ _{index (j)}> α, each scheduler i is to grid computing node i ndex (j) allocating task;

(4.5) from be likely assigned to the grid computing node of task from each scheduler, leave out burst task average arrival rate φ _{index (j)}=0 node;

(4.6) in step (4.5), remaining grid computing node is calculated as follows burst task average arrival rate φ _{index (j)},

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

From resulting φ _{index (j)}in, leave out φ _{index (j)}the grid computing node of < 0;

(4.7) result step (4.6) being obtained, by method step (3) Suo Shu described target function value formerD with press formula

the new target function value latterD obtaining compares, ε=| latterD-formerD|, if ε≤10 ^-6, carry out step (4), by each scheduler, to grid computing node remaining in step (4.6), distribute burst task; If ε > 10 ^-6, repeated execution of steps (4.1)---step (4.7), until all burst task is assigned, finishes;

Dispatching method in the present invention, cooperative game algorithm has preferably effect, can be by comparing explanation with non-cooperative game algorithm and equalized scheduling algorithm, specifically as experiment one, two, three shown in.

If the relative task arrival rate of the average treatment ability of each grid computing node and scheduler is known in grid, the actual task arrival rate of scheduler is calculated according to formula (8).

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

The computing power of grid computing node may be balanced, also may occur the situation that part of nodes computing power is stronger, for both of these case, carries out two groups of experiments.

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

First group is the stronger experiment of computing power that has part of nodes in grid computing node, and in the system of setting up departments, the computing power of grid computing node is as follows successively:

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 starting condition, by cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm, try to achieve respectively the average burst task arrival rate of each grid computing node in system, then the target function value that obtains reflecting providing capability under system stability state, experimental result is as shown in the table:

As can be seen from the table, under all grid computing node steady state (SS)s, allow in the sum reciprocal of the ability that provides, the minimum of cooperative game algorithm, cooperative game algorithm can make system that higher computing power is provided, thus explanation cooperative game algorithm is more excellent.

The comparison diagram reciprocal that accompanying drawing 4 is the ability that allows to provide under each grid computing node steady state (SS) of applying cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm in this experimentation and trying to achieve.

Second group is the experiment of the computing power equilibrium of grid computing node in system, supposes that the computing power of grid computing node in system is as follows successively:

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 starting condition, by cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm, try to achieve respectively the average burst task arrival rate of each grid computing node in system, then the target function value that obtains reflecting providing capability under system stability state, experimental result is as shown in the table:

As can be seen from the table, under all grid computing node steady state (SS)s, allow in the sum reciprocal of the ability that provides, the minimum of cooperative game algorithm, cooperative game algorithm can make system that higher computing power is provided, thus explanation cooperative game algorithm is more excellent.

The comparison diagram reciprocal that accompanying drawing 5 is the ability that allows to provide under each grid computing node steady state (SS) of applying the definite task scheduling scheme of cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm in this experimentation and trying to achieve.

In conjunction with above two groups of experiments, can draw a conclusion: in grid system, the computing power of grid computing node is balanced or when unbalanced, the algorithm in the present invention is all 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 call device increases, the comparison of cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm.In this experiment, make load factor ρ be increased to successively 0.9 from 0.1, increase by 0.1 at every turn, in system, the computing power of grid computing node is as follows successively:

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}

All the other parameters are identical with the parameter of first group of experiment in experiment one.

Under above starting condition, the task allocative decision of system while determining load variations by cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm respectively, then the target function value that obtains reflecting the providing capability under system stability state, experimental result is as shown in the table:

In upper table, from laterally, when no matter load is much, under the grid computing node steady state (SS) that always cooperative game algorithm is corresponding, allow the sum reciprocal of the ability that provides minimum, be that cooperative game algorithm can make system that higher computing power is provided, thereby explanation cooperative game algorithm is more excellent.

Accompanying drawing 6 is when system load increases in this experiment, to apply the aims of systems functional value comparison diagram that the definite task allocative decision of cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm is tried to achieve.As can be seen from the figure,, along with the increase of system load, the advantage of cooperative game algorithm increases gradually.

Experiment three: the impact experiment of system scale

The variation of system scale comprises the variation of scheduler number and the variation of grid computing interstitial content.Therefore experiment is divided into two groups.

First group of experiment, the impact of the variation of scheduler number on aims of systems functional value:

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

U={0.01, the relative task arrival rate of all schedulers of 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} is as follows:

Under above starting condition, the burst task arrival rate of each grid computing node in system while trying to achieve scheduler number of variations by cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm respectively, then the target function value that obtains reflecting the providing capability under system stability state, experimental result is as shown in the table:

In upper table, from longitudinally, when the increase of scheduler number causes the task of system to increase thereupon, the computing power that system can provide will reduce, and the target function value of corresponding system will increase; From laterally, the target function value of cooperative game algorithm is target function value minimum in three kinds of algorithms always, and cooperative game algorithm can make system that higher computing power is provided.

Accompanying drawing 7 is this experiment scheduler number while increasing, and utilizes the variation comparison diagram of the aims of systems functional value that the definite task allocative decision of cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm tries to achieve.As can be seen from the figure,, along with the increase of scheduler number, the advantage of cooperative game algorithm also strengthens gradually.

Second group of experiment, the impact of the variation of grid computing interstitial content on system providing capability:

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

The computing power that all grid computing nodes of described system are 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 starting condition, the burst task arrival rate of each computing node in system while trying to achieve described grid computing node number of variations by cooperative game algorithm, non-cooperative game algorithm and equalized scheduling algorithm respectively, then the target function value that obtains reflecting the providing capability under system stability state, experimental result is as shown in the table:

In upper table, from laterally, the target function value that cooperative game algorithm is corresponding is minimum in three algorithms, and cooperative game algorithm can make system that higher computing power is provided, and cooperative game algorithm is optimum in three algorithms.Along with increasing of computing node, the advantage of cooperative game algorithm strengthens gradually.

Comprehensive these two groups experiments can be found out, when system scale increases, the present invention is more and more obvious compared with the advantage of non-cooperative game algorithm and equalized scheduling algorithm, further illustrating the present invention can allow system that higher computing power is provided, thereby accelerate the execution of gridding task, improve the efficiency of system works.

Claims (1)

1. the computing grid equalization task dispatching method based on reliability and cooperative game, is characterized in that, is in a computing grid system based on reliability and cooperative game, hereinafter to be referred as system, realizes according to the following steps successively:

Step (1), construct a computing grid system based on reliability and cooperative game, comprising: a plurality of users, towards each scheduler i of each user, towards each grid computing node j of described each scheduler i, and a scheduling scheme counter, wherein:

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

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

Set: ignoring under scheduler i inter-process cost, the condition in task transmission time:

The mean speed λ of each scheduler i output burst task _iadd and be less than the average execution speed u of all grid nodes to whole burst tasks of receiving separately _jadd and, the unit of speed is the burst number of tasks in the unit interval, is expressed as:

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

The mean speed λ of the burst task that each scheduler i sends _ithe average arrival rate φ that adds and equal the burst task of all grid node j _jadd and, be expressed as:

0≤φ _j<u _jand $\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i=\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}{\mathrm{\&phi;}}_j---\left(2\right)$

To meet: each grid computing node j is in the maximum burst task arrival rate that keeps can accepting under service quality prerequisite simultaneously

the burst task that is greater than grid computing node j on average reaches speed φ _j, be less than the average execution speed u of grid computing node j to whole burst tasks of receiving separately _j, be expressed as:

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

Step (2), described scheduling scheme counter is calculated as follows each grid computing node j the computing power A providing is provided when steady state (SS) _j, 0<A _j<1:

A _j=1-φ _jβ _1j(1+u′ _jγ _j) (3)

Wherein, the burst task of arrival grid computing node j meets with burst task average arrival rate φ _jfor the Poisson distribution of average, β _1jfor the burst task average service time of grid computing node j, u ' _jfor the mean speed of grid computing node j busy failure, γ _jfor the average retry time of grid computing node j;

Step (3), described scheduling scheme counter allows according to each grid computing node j of input the computing power A providing by following formula _jcalculating target function optimal value D:

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

Step (4), described scheduling scheme counter calculates the task scheduling scheme that sends to each scheduler i under the steady state (SS) of setting:

Step (4.1), systematic parameter initialization:

The mean speed that scheduler i sends burst task is λ _i(0), i=1,2 ..., i ..., I, " 0 " symbol represents steady state (SS), 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), after the data of described scheduling scheme counter in receive the step (4.1) of being sent by each scheduler i and each grid computing node j under described steady state (SS) (0), set:

initialization value be

for the maximum burst task arrival rate that grid computing node j can accept, the initialization value of the burst task average arrival rate of grid computing node j is

the error precision ε (0)≤10 of objective function optimization value D ^-6;

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

Step (4.4), if D (0)=latterD meets and is less than or equal to 10 with respect to the error ε (0) of the optimization target values of D ^-6,

By following formula, obtain scheduling scheme, ask a _{i, j}if do not meet execution step (4.5);

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

Wherein, a _{i, j}for the burst task of scheduler i is assigned to the ratio of grid computing node j;

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

Step (4.6), is calculated as follows grid computing node j in the burst task arrival rate in maximum

time the burst task computation ability θ of unit that provides is provided _j, also claim task dividable to join regulatory factor;

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

And θ corresponding to each grid computing node j _jsequence 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:

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

Wherein, index (j) represents by the position of grid computing node j in index (J) after step (4.6) rearrangement, corresponding β ₁, u ', γ be expressed as β _{lindex (j)}, u ' _{index (j)}and γ _{index (j)},

B _{index (j)}=β _{lindex (j)}(1+u ' _{index (j)}γ _{index (j)}), α is that scheduler i judges whether to the lower limit of certain grid computing node j allocating task;

Step (4.8), judgement task dividable is joined regulatory factor θ _jcorresponding θ _{index (j)}be greater than α no, if θ _{index (j)}< α, each scheduler i is not to grid computing node i ndex (j) allocating task; If θ _{index (j)}> α, each scheduler i is to grid computing node i ndex (j) allocating task;

Step (4.9) is left out burst task average arrival rate φ from be likely assigned to the grid computing node j of task from each scheduler i _{index (j)}=0 node;

Step (4.10), in step (4.9), remaining grid computing node is calculated as follows burst task average arrival rate φ _{index (j)},

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

From resulting φ _{index (j)}in, leave out φ _{index (j)}the grid computing node of <0;

Step (4.11), the result that step (4.10) is obtained, by method step (4.3) Suo Shu, described target function value formerD and the new target function value latterD obtaining by the described method of step (3) are compared, ε=| latterD-formerD|, if ε≤10 ^-6, carry out step (4.4), by each scheduler, to grid computing node remaining in step (4.10), distribute burst task; If ε is >10 ^-6, repeated execution of steps (4.5)---step (4.11), until all burst task is assigned, finishes;

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

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