CN106934539A - It is a kind of with limited and expense restriction workflow schedule method - Google Patents

Abstract

The invention belongs to workflow schedule field under Distributed Calculation, it is related to a kind of with limited and expense restriction workflow schedule method.The present invention gives new model and proposes a kind of new dispatching method to the workflow schedule problem in band time limit and expense, the method define the actual average budget erc of each task, the complexity of algorithm is reduced as decision function using it, more reasonably to consider the constraint in time limit, algorithm determines the priority of task with SDL.Experiment shows that the success rate of this method DAG scheduling under two constraints of expense and time limit is higher.Goal of the invention：To solve the scheduling problem of the workflow when there are two constraints of expense and time limit, expect to complete DAG scheduling under given expense and the constraint in time limit, that is, obtain DAG scheduling success ratios higher.

Description

It is a kind of with limited and expense restriction workflow schedule method

Technical field

The invention belongs to workflow schedule field under Distributed Calculation, it is related to a kind of with limited and expense restriction work Stream scheduling method.

Background technology

In recent years, the large-scale scientific algorithm application that develops into of grid and cloud computing provides good platform, Hen Duo great Scale Scientific computational problem can abstract be workflow (DAG) model.Workflow schedule problem, refers to appointing for given workflow Business as object, some processor as the task of completion resource, be in the case where certain constraints is met, to task and place Reason device is allocated and arranges precedence, and required resource is carried out into optimum allocation and optimal scheduling.Scheduling problem logistics, Each field such as Aero-Space, medical treatment, biology is all widely used.

Under grid or cloud platform, user generally needs to complete workflow schedule in certain hour and expense, resource Manager provides different prices according to the different performance of resource, and user wants that renting resource completes complicated application program, therefore They need to pay the certain expense of Resource Manager and wish to complete task within the limited time, and the manager of resource Need reasonable distribution resource so that resource is not wasted, this be accomplished by designer provide rational dispatching method so that user and Resource Manager all receives [1].Therefore, user, Resource Manager, designer are that the workflow constrained with expense and time limit is adjusted The entity of degree problem, Fig. 1 illustrates the relation of user, Resource Manager, designer three.

For workflow (DAG) scheduling problem constrained with expense and time limit under cloud environment, the expense fixed for user Under constraint B and time limit constraint D, general only with expense and time limit, the two constrain the work to describe to be constrained with expense and time limit Stream scheduling problem, Mathematical Modeling is expressed as：∑ cost≤B, makespan≤D.Wherein ∑ cost represents completion task scheduling institute The total cost for needing, makespan represents the earliest finish time for completing export task.Rational optimization is given for designer Scheduling scheme is critically important.For band time limit and the workflow schedule Study on Problems of expense, the pertinent literature of nearly 2 years gives one A little main algorithms are mainly shown in document [1,2,3].

, the BHEFT algorithms that Zhang and Sakellariou is proposed in 2013^[1]It is to be examined in the case where resource has load Consider the optimized algorithm of time limit and expense, but can not find the situation of resource completely in the absence of decision function, but actually exist this The situation of kind, so do not existed using the in the case of of scheduling on earliest finish time in the case of for expense very little.2014, Arabnejad and Barbosa propose HBCS algorithms^[2], it is proposed that the definition of minimum residual RCB, according to time limit and expense Defined parameters carry out the selection of resource.But the success rate of HBCS algorithms DAG scheduling under the constraint of time limit and expense is not high. 2016, Arabnejad and Barbosa gave DBCS algorithms again^[3], sub- time limit SDL is added in the time parameter factor, To carry out the selection of resource, this causes that what the Equilibrium constraints in expense and time limit in the scheduling of task played plays a role clearly, but Be DBCS algorithms DAG scheduling success rate still not as this method DAG scheduling success ratios it is high.

The content of the invention

For the problem that existing model and method are present, the present invention is given to the workflow schedule problem of band time limit and expense New model simultaneously proposes a kind of new dispatching method.The actual average budget erc of each task is the method define, with it The complexity of algorithm is reduced as decision function.More reasonably to consider the constraint in time limit, algorithm determines task with SDL Priority.Experiment shows that the success rate of this method DAG scheduling under two constraints of expense and time limit is higher.

Goal of the invention：To solve the scheduling problem of the workflow when there are two constraints of expense and time limit, expect in given expense Dispatched with DAG is completed under the constraint with the time limit, that is, obtain DAG scheduling success ratios higher.

Workflow (DAG) scheduling problem for being constrained with expense and time limit under cloud environment is described as follows：Remember the figure of DAG It is G={ V, E } that wherein set of tasks is V={ n₁, n₂... n_n, | V |=n represents the number of all task nodes in workflow It is n；E is the front and rear dependence between the set of directed edge, expression task, to arbitrary side (n_i, n_q) ∈ E, task n_iAfter execution Just perform task n_q, task n_iTo task n_qThere is passing time A_iq, do not have in DAG before after task referred to as entrance task n_entry, there is no follow-up task referred to as export task n_exit.What Fig. 2 was represented be one contains 10 DAG tasks of task node Figure.Resource collection is designated as P={ p₁, p₂... p_m, | P |=m indicates m resource, each task n_iWill be in resource p_jOn Perform and exist execution time w_ij, task n_iIn resource p_jOn have execution cost c_ij, in given expense restriction B and time limit constraint Under D, expect to obtain the deadline (makespan) of last task and total cost (cost) is minimum.By problem analysis and change Relation between amount, to this The present invention gives this problem linear programming model (IP)：,

(IP)

(ST_ij+w_ij)x_ij≤ d, i=1 ... n, j=1 ... m, (1.4)

x_ij∈ { 0,1 } (1.5)

Here x_ijIt is a Boolean variable, as task n_iSelection resource p_jWhen, x_ijIt is 1 to be worth, as task n_iResource p is not selected_j When, x_ijBe worth is 0；(1.1) represent that each task will be arranged into resource；(1.2) deadline of last task is represented not More than d, the wherein time limit of the optimal scheduling of d problem of representation,Represent the deadline of last task；(1.3) represent and appoint It is engaged in being no more than given expense B in the expense sum of resource；(1.4) the deadline not super d of each arranging for task is represented, its Middle ST_ijExpression task n_iIn resource p_jOn arrival time.

It is a kind of with limited and expense restriction workflow schedule method, comprise the following steps：

Step 1：The determination of each task priority in DAG, specific method is as follows：

The sub- time limit SDL values of each task in DAG are calculated, formula is as follows：

Wherein succ (n_i) it is task n_iSubsequent tasks set, A_{I, p}Expression task n_iTo task n_pPassing time, ET_min(n_p) represent task n_pThe minimum execution time in all resources, because export task n_exitThere is no descendant node, so By SDL (n_exit) as the initial value for calculating, make SDL (n_exit)=D, wherein D are the given time limit.From export task n_exit's SDL values are derived forward, you can calculate the sub- duration value of all tasks.With sub- time limit SDL values as task node dispatch it is excellent First level, SDL values are smaller, and priority is higher, and task is according to priority ranked up successively from high to low, obtain one group of sequence to be dispatched Row L.

Step 2：The selection of resource, specific method is as follows：

Step (2.1) takes the task n for treating highest priority in schedule sequences L_k, it is calculated as follows current task n_k's Residual sab：

Wherein B is given budget, c_fExpression task n_fExpense on resource has been arranged,Represent that priority comes to appoint Business n_kBelow do not arrange task n_hAverage cost in all resources.

Step (2.2) calculating task n_kActual average budget erc

Wherein f_kIt is regulation parameter, is defined as follows：

Expression task n_kAverage cost in all resources,Represent that priority comes task n_kNot not arranging below Task n_hAverage cost in all resources, if sab (n_k) value be more than or equal to 0, f_kValue be task n_kIn all resources On average cost with residue do not arrange the ratio between the average cost sum of task in all resources, if sab (n_k) value be less than 0, f_kValue be 0.Rb is expressed as task n_kRemaining cost, update remaining cost when calculating next task every time, l is not for The number of scheduler task.

Step (2.3) is for task n_k, according to equation below, find current scheduling task n_kExpense in resource is less than Equal to a n_kActual average budget erc_kResource set w_k：

Wherein c_koExpression task n_kIn resource p_oOn execution cost, erc_kExpression task n_kActual average budget, w_koTable Show task n_kSelected resource p_o, the wherein value of o is unique, w_kSet act as finding and meets condition c_ko≤erc_k's Resource p_o。

Step (2.4) calculating task n_kIn set w_kIn resource p_jOn EFT (n on earliest finish time_k, p_j), first calculate Task n_kIn resource p_jOn earliest start time EST (n_k, p_j), it is defined as follows：

EFT(n_k, p_j)=EST (n_k, p_j)+w_{K, j} (6)

Wherein pred (n_k) represent task n_kBefore take over sb.'s job the set of business, T_avail[j]Expression task is in resource p_jOn can be with The earliest time of beginning, AFT (n_g) represent task n_kBefore take over sb.'s job business n_gActual finish time, A_gkExpression task n_gTo task n_kBetween passing time, internal layer max represents task n_kIt is all of before take over sb.'s job business n_gReach resource p_jTime, w_{K, j}Represent and appoint Business n_kIn resource p_jOn run time；For entrance task n_entry, EST (n_entry, p_j)=0.

Step (2.5) is if sab (n_k) it is more than or equal to 0, for task n_kEFT on earliest finish time in selection step (2.4) It is worth minimum resource, if sab (n_k) 0 is less than, for task n_kSelection ω_kThe minimum resource of middle execution cost；Record is as predecessor Business n_kThe expense of selected resource

Step 3：L is the number of unscheduled task, so task n_kWhen scheduling is completed, the value of l subtracts 1；Now residue is taken Removing task n is should be with rb_kIn resource p_jOn execution cost c_kjExpense afterwards；Current priority is deleted from schedule sequences L Highest task n_kIf L non-NULLs go to step 2；Otherwise, 4 are gone to step.

Step 4：Scheduling schemes of the output services stream DAG under expense B and time limit D constraints, completes workflow schedule.

Compared with prior art, this method has the advantage that：

The present invention gives new plan model for the DAG scheduling problems of band time limit and expense, by the sub- time limit of DAG Value determine the priority of task, this causes more reasonably to consider the constraint in time limit in scheduling process.Secondly it is of the invention The actual average budget erc of each task is defined, the complexity of algorithm is reduced as decision function using it, and BHEFT, HBCS scheduling algorithms are compared, and under two constraints of given time limit and expense, what DAG was dispatched has higher success rate this method.

Brief description of the drawings

Fig. 1 is user, Resource Manager, the relation of designer three；

Fig. 2 is 10 DAG task images of task node；

Fig. 3 is execution cost of each task in each resource；

Fig. 4 is 100 success rates of DAG scheduling in 4 kinds of methods.

Specific embodiment

The present invention is described further with reference to the accompanying drawings and examples.

The present invention realizes a kind of workflow schedule under time limit and expense restriction in conjunction with the embodiments, according to shown in Fig. 2 DAG tasks between relation be scheduled, give expense B=95, the constraints expense that time limit D=200, i.e. user give No more than 95, the time limit is no more than 200, and user wants to carry out DAG scheduling under this constraints, it is assumed that Resource Manager has three moneys Source is respectively p₁, p₂, p₃, execution cost c of each task in each resource_ijAs shown in figure 3, designer is according to user and money Each situation provides rational management scheme to source control person, has both met the requirement of user, and the situation of Resource Manager, this hair are met again It is bright to be the rational scheme of designer, the scheduling scheme of DAG is finally exported, step is as follows：

The determination of each task priority in 1.DAG, the sub- time limit of each task of DAG in Fig. 2 is calculated according to formula (1) SDL(n_i), then it is ranked up by SDL values are ascending for each task, as shown in table 1：

Former sequence	1	2	3	4	5	6	7	8	9	10
											SDL values	107.51	133.37	136.84	137.99	142.02	158.55	162.73	181.79	182.95	200
New sequence	1	4	6	2	5	3	8	7	9	10

2. the selection of resource, the new sequence of being obtained according to table 1 for task, chooses task successively, then according to Fig. 2 and Fig. 3 Data and formula (2), (3) (4), (5), (6), the residual sab of calculating task, actual average budget erc successively, for Current each task meets the set w of the resource of condition_i, earliest start time EST of the task in resource, earliest finish time EFT, then records each task and is choosing the expense in resource, as indicated in the chart 2：

F represents regulation parameter in table, and select represents the resource of each task finally selection, such as w_1,2Expression task n₁The resource of selection is p₂, cost represent each task selection resource on execution cost.By table 2, it can be seen that each task Selected resource, is shown in Table 3：

Task

n1

n4

n6

n2

n5

n3

n8

n7

n9

n10

Resource

p2

p2

p2

p3

p2

p2

p3

p1

p3

p2

Total cost required for finally completing scheduling is 71.90 ＜ 95, export task n₁₀Earliest finish time be 145, The final time dispatched is 145 ＜ 200, meets condition.

3 last output scheduling schemes, as table 3, complete scheduling required for expense be 71.9, complete scheduling needed for when Between be 145.

The present invention is scheduled to 100 DAG containing 50 task nodes randomly generating, in given expense and Time limit constraint is lower to complete scheduling, and as DAG scheduling is successful, compared for BHEFT, and HBCS, DBCS algorithm find this method The success rate of DAG is higher, and as a result as shown in figure 4, representing the success rate of DAG scheduling in wherein Fig. 4, M is represented in the present invention Method.

Leading reference：

[1]W.Zhang and R.Sakellariou,Budget-Deadline Constrained Workflow Planning for Admission Control,J Grid Computing,11,633-651,2013.

[2]H.Arabnejad,J.Barbosa,A Budget Constrained scheduling Algorithm for Workflow Applications,J Grid Computing,12,665-679,2014.

[3]H.Arabnejad,J.Barbosa,R.Prodan,Low-time Complexity Budget-deadline Constrained Workflow Scheduling on Heterogeneous Resources,Future Generation Computer Systems,55,29-40,2016.

Claims (1)

1. it is a kind of with limited and expense restriction workflow schedule method, it is characterised in that to comprise the following steps：

Step 1：The determination of each task priority in DAG, specific method is as follows：

The sub- time limit SDL values of each task in DAG are calculated, formula is as follows：

$\mathrm{SDL}\left(n_i\right)={\min }_{n_p\∈\mathrm{succ}\left(n_i\right)}[\mathrm{SDL}\left(n_p\right)-A_{i,p}-{\mathrm{ET}}_{\min }\left(n_p\right)]---\left(1\right)$

Wherein succ (n_i) it is task n_iSubsequent tasks set, A_{I, p}Expression task n_iTo task n_pPassing time, ET_min(n_p) Expression task n_pThe minimum execution time in all resources, because export task n_exitThere is no descendant node, so by SDL (n_exit) as the initial value for calculating, make SDL (n_exit)=D, wherein D are the given time limit；From export task n_exitSDL values Derive forward, you can calculate the sub- duration value of all tasks；The priority dispatched as task node with sub- time limit SDL values, SDL values are smaller, and priority is higher, and task is according to priority ranked up successively from high to low, obtain one group and treat schedule sequences L；

Step 2：The selection of resource, specific method is as follows：

Step (2.1) takes the task n for treating highest priority in schedule sequences L_k, it is calculated as follows current task n_kResidue Budget sab：

$sab\left(n_k\right)=B-\underset{f=1}{\overset{k}{\mathrm{\Σ}}}{c}_f-\underset{h=k+1}{\overset{n}{\Σ}}{\stackrel{\‾}{c}}_h---\left(2\right)$

Wherein B is given budget, c_fExpression task n_fExpense on resource has been arranged, c_hRepresent that priority comes task n_kAfterwards Face does not arrange task n_hAverage cost in all resources；

Step (2.2) calculating task n_kActual average budget erc

$erc\left(n_k\right)=\frac{rb}{l}+sab\left(n_k\right)\×f_k---\left(3\right)$

Wherein f_kIt is regulation parameter, is defined as follows：

$f_k=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{c}}_k}{\underset{h=k+1}{\overset{n}{\&Sigma;}}{\stackrel{\&OverBar;}{c}}_h}& ifsab\left(n_k\right)\&GreaterEqual;0,\\ 0& ifsab\left(n_k\right)<0.\end{array}\right.$

Expression task n_kAverage cost in all resources,Represent that priority comes task n_kBelow do not arrange task n_h Average cost in all resources, if sab (n_k) value be more than or equal to 0, f_kValue be task n_kIt is flat in all resources Equal expense does not arrange the ratio between the average cost sum of task in all resources with residue, if sab (n_k) value be less than 0, f_kTake Be worth is 0；r_bIt is expressed as task n_kRemaining cost, update remaining cost when calculating next task every time, l is unscheduled task Number；

Step (2.3) is for task n_k, according to equation below, find current scheduling task n_kExpense in resource is less than or equal to Appoint n_kActual average budget erc_kResource set ω_k：

Wherein c_koExpression task n_kIn resource p_oOn execution cost, erc_kExpression task n_kActual average budget, w_koRepresent and appoint Business n_kSelected resource p_o, the wherein value of o is unique, ω_kSet act as finding and meets condition c_ko≤erc_kResource p_o；

Step (2.4) calculating task n_kIn set ω_kIn resource p_jOn EFT (n on earliest finish time_k, p_j), first calculating task n_kIn resource p_jOn earliest start time EST (n_k, p_j), it is defined as follows：

$EST(n_k,p_j)=max\{T_{avail\&lsqb;j\&rsqb;},{\max }_{n_g\&Element;pred\left(n_k\right)}\left(AFT\right(n_g)+A_{g,k})\}---\left(5\right)$

EFT(n_k, p_j)=EST (n_k, p_j)+w_{K, j}

(6)

Wherein pred (n_k) represent task n_kBefore take over sb.'s job the set of business, T_avail[j]Expression task is in resource p_jOn can start Earliest time, AFT (n_g) represent task n_kBefore take over sb.'s job business n_gActual finish time, A_gkExpression task n_gTo task n_kIt Between passing time, internal layer max represents task n_kIt is all of before take over sb.'s job business n_gReach resource p_jTime, w_{K, j}Expression task n_k In resource p_jOn run time；For entrance task n_entry, EST (n_entry, p_j)=0；

Step (2.5) is if sab (n_k) it is more than or equal to 0, for task n_kIn selection step (2.4) earliest finish time EFT values most Small resource, if sab (n_k) 0 is less than, for task n_kSelection ω_kThe minimum resource of middle execution cost；Record current task n_k The expense of selected resource

Step 3：L is the number of unscheduled task, so task n_kWhen scheduling is completed, the value of l subtracts 1；Now remaining cost rb should To remove task n_kIn resource p_jOn execution cost c_kjExpense afterwards；Current priority highest is deleted from schedule sequences L Task n_kIf L non-NULLs go to step 2；Otherwise, 4 are gone to step；

Step 4：Scheduling schemes of the output services stream DAG under expense B and time limit D constraints, completes workflow schedule.