CN101957760A - Method for measuring process execution time - Google Patents

Method for measuring process execution time Download PDF

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CN101957760A
CN101957760A CN2010105148115A CN201010514811A CN101957760A CN 101957760 A CN101957760 A CN 101957760A CN 2010105148115 A CN2010105148115 A CN 2010105148115A CN 201010514811 A CN201010514811 A CN 201010514811A CN 101957760 A CN101957760 A CN 101957760A
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execution time
model structure
basic model
basic
activity
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谢毅
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Zhejiang Gongshang University
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Zhejiang Gongshang University
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Abstract

The invention discloses a method for measuring process execution time, which comprises the following steps of: 1, establishing a process model formed by combining and nesting four basic model structures of sequence, cycle, parallel and selection; 2, establishing a queuing system at each resource, and calculating a waiting time density function and a mean value of a single activity instance at a corresponding resource; and 3, finding an innermost layer basic model structure which does not comprise the four basic model structures, judging that the innermost layer basic model structure belongs to one of the four basic model structures, calculating an execution time density function and a mean value thereof, replacing the innermost layer basic model structure by a novel equivalent activity of which the density function and the mean value are shown in the description to form a novel process model, and repeatedly iterating until the novel process model only comprises an activity, wherein the process execution time of an actual service process/workflow is mean execution time of the activity. The method for measuring the process execution time has the advantages of effectively supporting many-to-many relationship occasions of activities and resources and improving the calculation accuracy.

Description

The assay method of a kind of process execution time
Technical field
The present invention relates to computer technology, infotech and systems engineering field, the assay method of especially a kind of service-oriented process/workflow execution time.
Background technology
" process execution time " is defined as and receives customer service request/process instance to the time of finishing customer service request/process instance, as: the execution time of order processing process is generally defined as from receiving that client's order is to the duration of finishing the transmission of production of client's order or order product in manufacturing environment.Described " process " comprises business procedure or workflow, and time performance optimization (as: shortening the execution time) is one of main content of carrying out business procedure/Workflow optimization, and the computational analysis mensuration process execution time is to carry out the basis that time performance is optimized.
In the prior art, adopt based on several different methods such as graph theory and waiting line theories usually and measure the process execution time.As: Zhang Xiaoguang etc. have proposed to come analytical work to flow through the method for journey model time performance towards the etendue critical path of workflow process structure optimization, Duk-ho Chang, Jin Hyun Son, Haibo Li, Liu Sheng etc. have introduced the M/M/1 of waiting line theory and M/M/C model investigation the resource distribution quantity and the relation of business procedure/workflow execution time of each task in the workflow, improve the PERT/CPM method, proposed the workflow critical path identification and execution time computing method of task under different resource configuration quantity; Usually do not consider resource constraint based on graph theory method, and can only handle a certain class active instance/task based on the common resource of hypothesis of method (role or agency) of waiting line theory, or different resource is handled the stochastic distribution that similar active instance/task obedience is identical, do not consider the support relation of multi-to-multi between activity and the resource, these hypothesis may with hinder to actual complex business procedure/workflow execution time further, accurately describe, analyze and optimize.
Summary of the invention
Can't adaptive act and resource many-to-many relationship occasion, deficiency that precision is lower for what overcome existing process execution time assay method, the invention provides a kind of effective support activities and resource many-to-many relationship occasion, improve the assay method of a kind of process execution time of computational accuracy.
The technical solution adopted for the present invention to solve the technical problems is:
The assay method of a kind of process execution time, described assay method may further comprise the steps:
The first step, set up process model:
Practical business process/workflow is made up of a plurality of activities, forms following four kinds of basic model structures according to the control relation between each activity: order basic model structure, parallel basic model structure, selection basic model structure and the basic model structure that circulates;
Wherein, described control relation comprise order, with bifurcated, with converge or bifurcated or converge and circulate; Parallel basic model structure, selection basic model structure and the basic model structure that circulates are referred to as non-order basic model structure;
The process model of setting up satisfies following rule:
1: one of rule and bifurcated must have one to be complementary with converging, and form a parallel model structure;
Rule 2: one or bifurcated must have one or converge and be complementary, and form a selection or circulation model structure;
3: one non-sequential control modules of rule can be nested in another non-sequential control module, but two non-sequential control modules can not be overlapping;
Satisfying under the situation of above-mentioned rule, is by four kinds of nested process models that form of basic model textural association with practical business process/workflow modeling;
Described process model is defined as one 10 tuple
Figure 2010105148115100002DEST_PATH_IMAGE001
, wherein:
(1)
Figure 2010105148115100002DEST_PATH_IMAGE002
It is process instance/service object's arrival rate;
(2)
Figure 2010105148115100002DEST_PATH_IMAGE003
It is movable set; It is the set of tie point; Order
Figure 2010105148115100002DEST_PATH_IMAGE005
Be the set of process model node,
Figure 2010105148115100002DEST_PATH_IMAGE006
, then
Figure DEST_PATH_IMAGE007
The expression node
Figure 2010105148115100002DEST_PATH_IMAGE008
The number of preorder node,
Figure DEST_PATH_IMAGE009
The expression node
Figure 796278DEST_PATH_IMAGE008
The number of descendant node;
Figure 2010105148115100002DEST_PATH_IMAGE010
, if
Figure DEST_PATH_IMAGE011
, node so
Figure 455798DEST_PATH_IMAGE008
Be the fan-out tie point, if
Figure 2010105148115100002DEST_PATH_IMAGE012
, node so
Figure 867450DEST_PATH_IMAGE008
Be the fan-in tie point;
(3)
Figure DEST_PATH_IMAGE013
Be the set that connects arc,
Figure 2010105148115100002DEST_PATH_IMAGE014
,
Figure DEST_PATH_IMAGE015
Expression is from node
Figure 2010105148115100002DEST_PATH_IMAGE016
To node
Figure DEST_PATH_IMAGE017
The connection arc;
(4)
Figure 2010105148115100002DEST_PATH_IMAGE018
It is the set of resource;
(5)
Figure DEST_PATH_IMAGE019
It is set movable and resources relationship. The expression resource
Figure DEST_PATH_IMAGE021
Have the ability/qualification processing activity
Figure 2010105148115100002DEST_PATH_IMAGE022
Example;
(6)
Figure DEST_PATH_IMAGE023
: , be a mapping from tie point to the tie point type;
(7)
Figure DEST_PATH_IMAGE025
:
Figure 2010105148115100002DEST_PATH_IMAGE026
It is a mapping of carrying out probability from the connection arc to the connection arc;
Figure DEST_PATH_IMAGE027
, if
Figure 2010105148115100002DEST_PATH_IMAGE028
, then
Figure DEST_PATH_IMAGE029
, if , then
Figure DEST_PATH_IMAGE031
(8)
Figure 2010105148115100002DEST_PATH_IMAGE032
:
Figure DEST_PATH_IMAGE033
, be a mapping of handling active instance speed from movable and resources relationship to resource, if
Figure 2010105148115100002DEST_PATH_IMAGE034
,
Figure 534624DEST_PATH_IMAGE020
, resource then
Figure 821249DEST_PATH_IMAGE021
Can the processing activity in the unit interval
Figure 210642DEST_PATH_IMAGE022
The number of times of example be
Figure DEST_PATH_IMAGE035
, note by abridging and be
Figure 2010105148115100002DEST_PATH_IMAGE036
(9)
Figure DEST_PATH_IMAGE037
:
Figure 2010105148115100002DEST_PATH_IMAGE038
Be one from movable and the mapping of resources relationship to the task partition coefficient, described Task Distribution rate is to distribute to the probability of corresponding resource after active instance produces; If ,
Figure 284351DEST_PATH_IMAGE020
, then when movable
Figure 46770DEST_PATH_IMAGE022
Example distribute to resource after producing
Figure 290670DEST_PATH_IMAGE021
Probability be
Figure DEST_PATH_IMAGE039
, note by abridging and be
Figure 2010105148115100002DEST_PATH_IMAGE040
Because an active instance can only be carried out once by a resource, so have:
Figure DEST_PATH_IMAGE041
，
Figure 2010105148115100002DEST_PATH_IMAGE042
，
Figure DEST_PATH_IMAGE043
The expectation implementation rate of node the is defined as process node expectation is carried out when carrying out one time number of times;
If whole basic module expectation implementation rate is
Figure 2010105148115100002DEST_PATH_IMAGE044
, so order, parallel, select and the four kinds of basic model structures that circulate in being calculated as follows of expectation implementation rate of node:
By activity
Figure DEST_PATH_IMAGE045
In the order basic structure of forming, have:
Figure 196789DEST_PATH_IMAGE046
, wherein:
Figure DEST_PATH_IMAGE047
Be respectively movable
Figure 221245DEST_PATH_IMAGE045
The expectation implementation rate;
By activity
Figure 849673DEST_PATH_IMAGE048
With or the fan-in tie point
Figure DEST_PATH_IMAGE049
, or fan-out tie point
Figure 511861DEST_PATH_IMAGE050
In the circulation basic structure of forming, have:
Figure 200331DEST_PATH_IMAGE052
Wherein:
Figure DEST_PATH_IMAGE053
For withdrawing from the round-robin probability,
Figure 213548DEST_PATH_IMAGE054
Be respectively movable
Figure 380088DEST_PATH_IMAGE048
The expectation implementation rate,
Figure DEST_PATH_IMAGE055
Be respectively tie point
Figure 660896DEST_PATH_IMAGE056
The expectation implementation rate;
By activity
Figure 21733DEST_PATH_IMAGE045
With with the fan-out tie point
Figure 692885DEST_PATH_IMAGE049
, with the fan-in tie point
Figure 928695DEST_PATH_IMAGE050
In the parallel basic module structure of forming, have:
Figure DEST_PATH_IMAGE057
, wherein:
Figure 1693DEST_PATH_IMAGE058
Be respectively movable
Figure 533431DEST_PATH_IMAGE045
The expectation implementation rate,
Figure 691880DEST_PATH_IMAGE055
Be respectively tie point
Figure 200221DEST_PATH_IMAGE056
The expectation implementation rate;
By activity With or the fan-out tie point
Figure 95944DEST_PATH_IMAGE049
, or fan-in tie point
Figure 741689DEST_PATH_IMAGE050
In the selection basic module structure of forming, have:
Figure DEST_PATH_IMAGE059
，
Figure 53722DEST_PATH_IMAGE060
，
Figure DEST_PATH_IMAGE061
Wherein:
Figure 665094DEST_PATH_IMAGE062
Be the selection probability,
Figure DEST_PATH_IMAGE063
, Be respectively movable
Figure 232528DEST_PATH_IMAGE045
The expectation implementation rate,
Figure 849716DEST_PATH_IMAGE055
Be respectively tie point The expectation implementation rate;
The calculating of second step, single-unit activity execution time:
In practical business process/workflow, the arrival of assignment procedure example is Poisson flow, and resource is handled each obedience negative exponent distribution of movable time, then is modeled as one in each Energy Resources Service
Figure 294790DEST_PATH_IMAGE064
Queuing system calculates the Laplace-Stieltjes conversion that the single-unit activity example distributed in the stand-by period at respective resources place:
Figure DEST_PATH_IMAGE065
Wherein:
Figure 649548DEST_PATH_IMAGE066
The single-unit activity example in the average latency at respective resources place is:
Figure DEST_PATH_IMAGE067
Wherein:
Figure 121025DEST_PATH_IMAGE066
Movable
Figure 877629DEST_PATH_IMAGE022
The Laplace-Stieltjes that distributes of execution time be transformed to:
Figure 591507DEST_PATH_IMAGE068
Movable The density function of execution time be:
Figure DEST_PATH_IMAGE069
Movable
Figure 720448DEST_PATH_IMAGE022
The average execution time be:
Figure 331558DEST_PATH_IMAGE070
The execution time of the 3rd step, whole process model calculates:
3.1) find out an innermost layer basic model structure that does not comprise four kinds of basic model structures
Figure DEST_PATH_IMAGE071
, judge described innermost layer basic model structure
Figure 45698DEST_PATH_IMAGE071
Belong to a kind of in four kinds of basic model structures, calculate according to the computing method of four kinds of basic process model structure execution time
Figure 375048DEST_PATH_IMAGE072
With
3.2) with an execution time density function and average be
Figure 370686DEST_PATH_IMAGE072
With
Figure 665663DEST_PATH_IMAGE073
The movable innermost layer basic model structure of replacing of equivalence, form a new process model;
3.3) judge whether described new process model only comprises an activity? if not, turn back to 3.1), if, the average execution time of whole process model is the average execution time of a described activity, and the average execution time of described whole process model is the execution time of practical business process/workflow.
Further, described step 3.1) in, the computing method of four kinds of basic process model structure execution time are as follows:
Suppose
Figure 986923DEST_PATH_IMAGE074
With
Figure DEST_PATH_IMAGE075
Be movable Execution time density function and average;
(a) order basic model structure:
The Laplace-Stieltjes that the execution time of order basic model structure distributes is transformed to:
Figure DEST_PATH_IMAGE077
Wherein:
Figure 166680DEST_PATH_IMAGE078
The execution time density function of order basic model structure is:
Figure DEST_PATH_IMAGE079
The execution time average of order basic model structure is:
(b) the basic model structure that circulates:
The Laplace-Stieltjes that the execution time of the basic model structure that circulates distributes is transformed to:
Figure DEST_PATH_IMAGE081
Wherein: ,
Figure 909005DEST_PATH_IMAGE053
For withdrawing from the round-robin probability.
The execution time density function of the basic model structure that circulates is:
The execution time average of the basic model structure that circulates is:
Figure DEST_PATH_IMAGE083
Wherein:
Figure 453698DEST_PATH_IMAGE053
For withdrawing from the round-robin probability.
(c) parallel basic model structure:
The execution time density function of parallel basic model structure is:
Figure 116761DEST_PATH_IMAGE084
Wherein:
Figure DEST_PATH_IMAGE085
,
Figure 704737DEST_PATH_IMAGE086
The execution time average of parallel basic model structure is:
Figure DEST_PATH_IMAGE087
When the execution time of activity was similar to obeys index distribution, approximate treatment was as follows:
Figure 675229DEST_PATH_IMAGE088
(d) select the basic model structure:
Select the Laplace-Stieltjes of the execution time distribution of basic model structure to be transformed to:
Figure DEST_PATH_IMAGE089
Wherein:
Figure 235524DEST_PATH_IMAGE078
,
Figure 803908DEST_PATH_IMAGE062
Be the selection probability,
Figure 595626DEST_PATH_IMAGE063
Select the execution time density function of basic model structure to be:
Figure 540449DEST_PATH_IMAGE090
Select the execution time average of basic model structure to be:
Figure DEST_PATH_IMAGE091
Wherein:
Figure 17566DEST_PATH_IMAGE062
Be the selection probability,
Figure 258317DEST_PATH_IMAGE063
Beneficial effect of the present invention mainly shows: has adopted with respect to existing method based on M/M/1 and M/M/C waiting line system model (1)
Figure 758569DEST_PATH_IMAGE064
Waiting line system model, the effectively analysis optimization of the calculating of business procedure/workflow execution time and timeliness energy under support activities and the resource many-to-many relationship.
(2) with respect to existing graph theory method (as key methodology or improved critical path method etc.), consider resource constraint, can be used for the analysis of distributing rationally of resource; In addition, adopt the execution time of stochastic variable joint distribution Theoretical Calculation parallel model structure to distribute, improved process execution time computational accuracy.
Description of drawings
Fig. 1 is four kinds of basic model structural representations of process.
Fig. 2 is from the abstract process logic structural model synoptic diagram that comes out of manufacturing enterprise's business procedure.
Fig. 3 is the computation process synoptic diagram of process model execution time.
Embodiment
Below in conjunction with accompanying drawing the present invention is further described.
With reference to Fig. 1～Fig. 3, the assay method of a kind of process execution time may further comprise the steps:
The first step, set up process model
1) basic structure of process model
Practical business process/workflow is made up of a series of relevant activities, have between activity and the activity order (Sequence), with bifurcated (AND-Split), with converge (AND-Jion) or bifurcated (OR-Split) or converge (OR-Jion), circulation control relation such as (iteration), can form: in proper order, four kinds of basic model structures such as parallel, selection, circulation, as shown in Figure 1.Three kinds of basic model structures such as wherein, parallel, selection, circulation are called non-order basic model structure.
Order basic model structure: all activities order are successively carried out, except that first with last activity, each activity has only a preorder activity and follow-up activity, after each movable preorder activity was finished, it just can be carried out.
Parallel basic model structure: after an activity is finished, have the activity of a plurality of branches to carry out simultaneously thereafter, after all branch's activities all executed, the movable common follow-up activity of branch can be carried out.
Select the basic model structure: after an activity is finished, have the activity of a plurality of branches to carry out thereafter.But the activity of a plurality of branches is the condition mutual exclusion, has and have only branch's activity to carry out, and after the branch's activity in being elected to executed, the movable common follow-up activity of branch just can be carried out.
Basic model structure circulates: the one or more action needs in the process repeat repeatedly, satisfy up to certain condition.
In order to guarantee that process model has good logical organization, the process model of foundation need satisfy following rule:
1: one of rule and bifurcated must have one to be complementary with converging, and form a parallel model structure
Rule 2: one or bifurcated must have one or converge and be complementary, and form a selection or circulation model structure.
3: one non-sequential control modules of rule can be nested in another non-sequential control module, but two non-sequential control modules can not be overlapping;
Practical business process/the workflow of a corresponding complexity, its process model can be nested to form by these four kinds of basic model textural associations.Because these four kinds of basic model structures have the single export structure of single input, therefore are similar to structured programing design method, all has correct good logical organization by nested satisfied regular 1 ~ 3 any process model that forms of these four kinds of basic model textural associations.
2) formalization of process model
Process model may be defined as one 10 tuple
Figure 507082DEST_PATH_IMAGE001
, wherein:
(1)
Figure 714072DEST_PATH_IMAGE002
It is process instance/service object's arrival rate.
(2)
Figure 889839DEST_PATH_IMAGE003
It is movable set; It is the set of tie point; Order
Figure 665476DEST_PATH_IMAGE005
Be the set of workflow process model node,
Figure 54869DEST_PATH_IMAGE006
, then
Figure 401537DEST_PATH_IMAGE007
The expression node The number of preorder node, The expression node
Figure 446481DEST_PATH_IMAGE008
The number of descendant node; , if , node so
Figure 993765DEST_PATH_IMAGE008
Be the fan-out tie point, if
Figure 92171DEST_PATH_IMAGE012
, node so
Figure 780642DEST_PATH_IMAGE008
Be the fan-in tie point.
(3)
Figure 964498DEST_PATH_IMAGE013
It is the set that connects arc. ,
Figure 116573DEST_PATH_IMAGE015
Expression is from node
Figure 975945DEST_PATH_IMAGE016
To node The connection arc.
(4)
Figure 555011DEST_PATH_IMAGE018
It is the set of resource.
(5)
Figure 129474DEST_PATH_IMAGE019
It is set movable and resources relationship. The expression resource
Figure 318196DEST_PATH_IMAGE021
Have the ability/qualification processing activity
Figure 92117DEST_PATH_IMAGE022
Example.
(6)
Figure 786665DEST_PATH_IMAGE023
:
Figure 987840DEST_PATH_IMAGE024
, be a mapping from tie point to the tie point type.
(7)
Figure 368005DEST_PATH_IMAGE025
:
Figure 883300DEST_PATH_IMAGE026
It is a mapping of carrying out probability from the connection arc to the connection arc;
Figure 930891DEST_PATH_IMAGE027
, if
Figure 792712DEST_PATH_IMAGE028
, then
Figure 660174DEST_PATH_IMAGE029
, if
Figure 775898DEST_PATH_IMAGE030
, then
Figure 677995DEST_PATH_IMAGE031
(8)
Figure 722436DEST_PATH_IMAGE032
:
Figure 342773DEST_PATH_IMAGE033
, be a mapping of handling active instance speed from movable and resources relationship to resource, if
Figure 934292DEST_PATH_IMAGE034
,
Figure 956474DEST_PATH_IMAGE020
, resource then
Figure 670353DEST_PATH_IMAGE021
Can the processing activity in the unit interval
Figure 13871DEST_PATH_IMAGE022
The number of times of example be
Figure 471398DEST_PATH_IMAGE035
, note by abridging and be
(9)
Figure 232866DEST_PATH_IMAGE037
:
Figure 63681DEST_PATH_IMAGE038
Be one from movable and the mapping of resources relationship to the task partition coefficient, described Task Distribution rate is to be the probability of distributing to corresponding resource after active instance produces; If
Figure 324898DEST_PATH_IMAGE034
,
Figure 56094DEST_PATH_IMAGE020
, then when movable Example distribute to resource after producing Probability be
Figure 557111DEST_PATH_IMAGE039
, note by abridging and be
Figure 142813DEST_PATH_IMAGE040
Because an active instance can only be carried out once by a resource, so have:
，
Figure 174802DEST_PATH_IMAGE042
，
Figure 840138DEST_PATH_IMAGE043
3) definition and the calculating of expectation implementation rate
The expectation implementation rate of node the is defined as process node expectation is carried out when carrying out one time number of times.
If whole basic module expectation implementation rate is
Figure 781812DEST_PATH_IMAGE044
, so order, parallel, select and the four kinds of basic model structures that circulate in being calculated as follows of expectation implementation rate of node:
Shown in Fig. 1 (a) by activity
Figure 444874DEST_PATH_IMAGE045
In the order basic structure of forming, have:
， (1)
Wherein:
Figure 377244DEST_PATH_IMAGE047
Be respectively movable
Figure 173424DEST_PATH_IMAGE045
The expectation implementation rate;
Shown in Fig. 1 (b) by activity
Figure 7388DEST_PATH_IMAGE048
With or the fan-in tie point
Figure 20343DEST_PATH_IMAGE049
, or fan-out tie point
Figure 665300DEST_PATH_IMAGE050
In the circulation basic structure of forming, have:
(2)
Figure 586431DEST_PATH_IMAGE052
(3)
Wherein:
Figure 24365DEST_PATH_IMAGE053
For withdrawing from the round-robin probability,
Figure 835195DEST_PATH_IMAGE054
Be respectively movable
Figure 104503DEST_PATH_IMAGE048
The expectation implementation rate,
Figure 781734DEST_PATH_IMAGE055
Be respectively tie point
Figure 769281DEST_PATH_IMAGE056
The expectation implementation rate;
Shown in Fig. 1 (c) by activity
Figure 55906DEST_PATH_IMAGE045
With with the fan-out tie point
Figure 382982DEST_PATH_IMAGE049
, with the fan-in tie point
Figure 464071DEST_PATH_IMAGE050
In the parallel basic module structure of forming, have:
Figure 440379DEST_PATH_IMAGE057
， (4)
Wherein:
Figure 530695DEST_PATH_IMAGE058
Be respectively movable
Figure 774595DEST_PATH_IMAGE045
The expectation implementation rate,
Figure 292164DEST_PATH_IMAGE055
Be respectively tie point The expectation implementation rate;
Shown in Fig. 1 (d) by activity
Figure 118617DEST_PATH_IMAGE045
With or the fan-out tie point , or fan-in tie point
Figure 171072DEST_PATH_IMAGE050
In the selection basic module structure of forming, have:
Figure 856394DEST_PATH_IMAGE059
， ，
Figure 507004DEST_PATH_IMAGE061
(5)
Wherein:
Figure 366375DEST_PATH_IMAGE062
Be the selection probability,
Figure 975211DEST_PATH_IMAGE063
,
Figure 446906DEST_PATH_IMAGE058
Be respectively movable
Figure 519904DEST_PATH_IMAGE045
The expectation implementation rate, Be respectively tie point
Figure 708626DEST_PATH_IMAGE056
The expectation implementation rate;
Second step, single-unit activity execution time calculate
When the arrival of process example is a Poisson process, and the time that resource is handled each active instance in practical business process/workflow obeys negative exponent and distributes; Then arrival of each movable place example can be similar to and thinks a Poisson process in practical business process/workflow.Adopting under the separate queue situation, the active instance of obeying Poisson process arrives the back and gives corresponding service organization (resource) when handling by probability assignments, then the arrival of the total activity example that need handle of each Energy Resources Service is a synthetic Poisson flow, and resource is handled the time obedience hyperexponential distribution of total activity example, therefore, if set up a queuing system in each Energy Resources Service, this system is one
Figure 984012DEST_PATH_IMAGE064
Queuing system.Can calculate the Laplace-Stieltjes conversion that the single-unit activity example distributed in the stand-by period at respective resources place:
Figure 911517DEST_PATH_IMAGE065
(6)
Wherein:
Figure 112691DEST_PATH_IMAGE066
The single-unit activity example in the average latency at respective resources place is:
Figure 758436DEST_PATH_IMAGE067
(7)
Wherein:
Figure 273731DEST_PATH_IMAGE066
Movable
Figure 545488DEST_PATH_IMAGE022
The Laplace-Stieltjes that distributes of execution time be transformed to:
(8)
Movable
Figure 50605DEST_PATH_IMAGE022
The density function of execution time be:
Figure 166328DEST_PATH_IMAGE069
(9)
Movable
Figure 569890DEST_PATH_IMAGE022
The average execution time be:
Figure 112867DEST_PATH_IMAGE070
(10)
The calculating of the 3rd step, whole process model execution time
Practical business process/mensuration of workflow execution time can be converted into the calculating of its process model execution time, and the arthmetic statement of whole process model execution time is as follows:
Algorithm 1: the calculating of whole process model execution time
The step1:IF process model comprises a plurality of movable THEN
Find out an innermost layer basic model structure that does not comprise the basic model structure
Figure 670887DEST_PATH_IMAGE071
, forward step2 to
ELSE/* process model only comprise a movable */
The average execution time of process model
Figure 324722DEST_PATH_IMAGE092
Equal the average execution time of this activity, algorithm stops;
Step2: calculate
Figure 81326DEST_PATH_IMAGE072
With
Figure 562248DEST_PATH_IMAGE073
IF
Figure 404302DEST_PATH_IMAGE071
Be order basic model structure THEN
Computing method according to the order basic model structure execution time are calculated
Figure 861828DEST_PATH_IMAGE072
With
Figure DEST_PATH_IMAGE093
IF
Figure 302299DEST_PATH_IMAGE071
Be the basic model structure THEN of circulation
Computing method according to the circulation basic model structure execution time are calculated
Figure 187078DEST_PATH_IMAGE072
With
Figure 516429DEST_PATH_IMAGE093
IF
Figure 466061DEST_PATH_IMAGE071
Be parallel basic model structure THEN
Computing method according to the parallel basic model structure execution time are calculated
Figure 197257DEST_PATH_IMAGE072
With
Figure 754402DEST_PATH_IMAGE093
IF
Figure 571049DEST_PATH_IMAGE071
Be to select basic model structure THEN
Calculate according to the computing method of selecting the basic model structure execution time With
Figure 893763DEST_PATH_IMAGE093
Step3: be with an execution time density function and average
Figure 385924DEST_PATH_IMAGE072
With
Figure 253648DEST_PATH_IMAGE073
Movable this innermost layer basic model structure of replacing of equivalence, form a new process model.
Step4: forward step1 to.
Suppose
Figure 591088DEST_PATH_IMAGE074
With
Figure 234559DEST_PATH_IMAGE075
Be movable
Figure 632043DEST_PATH_IMAGE076
Execution time density function and average, the computing method of four kinds of basic process model structure execution time are:
(a) order basic model structure:
The Laplace-Stieltjes that the execution time of order basic model structure distributes is transformed to:
Figure 924746DEST_PATH_IMAGE077
(11)
Wherein:
The execution time density function of order basic model structure is:
Figure 626172DEST_PATH_IMAGE079
(12)
The execution time average of order basic model structure is:
(13)
(b) the basic model structure that circulates:
The Laplace-Stieltjes that the execution time of the basic model structure that circulates distributes is transformed to:
(14)
Wherein:
Figure 384542DEST_PATH_IMAGE078
,
Figure 923977DEST_PATH_IMAGE053
For withdrawing from the round-robin probability.
The execution time density function of the basic model structure that circulates is:
Figure 804208DEST_PATH_IMAGE082
(15)
The execution time average of the basic model structure that circulates is:
Figure 242142DEST_PATH_IMAGE083
(16)
Wherein:
Figure 351175DEST_PATH_IMAGE053
For withdrawing from the round-robin probability.
(c) parallel basic model structure:
The execution time density function of parallel basic model structure is:
Figure 761428DEST_PATH_IMAGE084
(17)
Wherein:
Figure 61828DEST_PATH_IMAGE085
,
Figure 924742DEST_PATH_IMAGE086
The execution time average of parallel basic model structure is:
Figure 899782DEST_PATH_IMAGE087
(18)
When the execution time of activity was similar to obeys index distribution, approximate treatment was as follows:
(19)
(d) select the basic model structure:
Select the Laplace-Stieltjes of the execution time distribution of basic model structure to be transformed to:
Figure 871729DEST_PATH_IMAGE089
(20)
Wherein:
Figure 284255DEST_PATH_IMAGE078
,
Figure 499205DEST_PATH_IMAGE062
Be the selection probability,
Figure 618471DEST_PATH_IMAGE063
Select the execution time density function of basic model structure to be:
Figure 496559DEST_PATH_IMAGE090
(21)
Select the execution time average of basic model structure to be:
Figure 84797DEST_PATH_IMAGE091
(22)
Wherein:
Figure 837859DEST_PATH_IMAGE062
Be the selection probability,
Figure 139527DEST_PATH_IMAGE063
Need to prove: in the process of concrete calculating whole process model execution time, by calculating the execution time density function of each activity/module, can accurately calculate the execution time density function and the average thereof of whole process model, if but only need measure average execution time of process model, and every of all parallel modules activity quantity few (as being less than 4) that branch comprises in the process model, and approximate obeys index distribution of the execution time that makes parallel every branch of module, the execution time density function of computational activity/module not in calculating the algorithm of whole process model execution time so, the average that only needs to calculate them gets final product, like this in the workload that guarantees can significantly reduce under the certain precision calculating.
Example: Fig. 2 is the abstract process model logical organization synoptic diagram that comes out of certain manufacturing enterprise's business procedure, and its formal process model may be defined as one 10 tuple
Figure 437784DEST_PATH_IMAGE001
, wherein:
The arrival rate of process instance is:
Figure 513319DEST_PATH_IMAGE094
Active set:
Figure DEST_PATH_IMAGE095
The tie point set:
Figure 7754DEST_PATH_IMAGE096
Connect arc set:
Figure DEST_PATH_IMAGE097
Resource collection:
Figure 524448DEST_PATH_IMAGE098
The set of activity and resources relationship:
Figure DEST_PATH_IMAGE099
The tie point type:
Figure 446137DEST_PATH_IMAGE100
,
Figure DEST_PATH_IMAGE101
Connect arc and carry out probability: ,
Figure DEST_PATH_IMAGE103
, ,
Figure DEST_PATH_IMAGE105
, it is 1 that all in addition connection arcs are carried out probability.
Resource is handled active instance speed:
Figure 541942DEST_PATH_IMAGE106
,
Figure DEST_PATH_IMAGE107
,
Figure 634532DEST_PATH_IMAGE108
,
Figure DEST_PATH_IMAGE109
,
Figure 356762DEST_PATH_IMAGE110
,
Figure DEST_PATH_IMAGE111
,
Figure 193000DEST_PATH_IMAGE112
,
Figure DEST_PATH_IMAGE113
, ,
Figure DEST_PATH_IMAGE115
,
Figure 636193DEST_PATH_IMAGE116
,
Figure DEST_PATH_IMAGE117
,
Figure 344255DEST_PATH_IMAGE118
, ,
Figure 220069DEST_PATH_IMAGE120
,
Figure DEST_PATH_IMAGE121
,
Figure 329977DEST_PATH_IMAGE122
,
Figure DEST_PATH_IMAGE123
,
Figure 265834DEST_PATH_IMAGE124
The Task Distribution rate of resource: ,
Figure 461192DEST_PATH_IMAGE126
,
Figure DEST_PATH_IMAGE127
,
Figure 452282DEST_PATH_IMAGE128
, ,
Figure 918160DEST_PATH_IMAGE130
,
Figure DEST_PATH_IMAGE131
,
Figure 523454DEST_PATH_IMAGE132
,
Figure DEST_PATH_IMAGE133
,
Figure 453713DEST_PATH_IMAGE134
,
Figure DEST_PATH_IMAGE135
,
Figure 435444DEST_PATH_IMAGE136
, ,
Figure 755829DEST_PATH_IMAGE138
, ,
Figure 594341DEST_PATH_IMAGE140
, ,
Figure 265756DEST_PATH_IMAGE142
,
Figure DEST_PATH_IMAGE143
Handle the time of comings and goings needs according to every kind of resource of historical statistics information and obey the negative exponent distribution.
Can calculate the expectation implementation rate of each activity according to formula (1)-(5), result of calculation is as follows:
Figure 785599DEST_PATH_IMAGE144
,
Figure DEST_PATH_IMAGE145
,
Figure 960491DEST_PATH_IMAGE146
,
Figure DEST_PATH_IMAGE147
,
Figure 173166DEST_PATH_IMAGE148
,
Figure DEST_PATH_IMAGE149
,
Figure 66298DEST_PATH_IMAGE150
Can calculate the average of each movable execution time according to formula (6)-(10), result of calculation is as shown in table 3:
? a1 a2 a3 a4 a5 a6 a7 a8
The execution time average 19.21 17.02 16.07 15.82 18.23 25.05 12.05 11.09
Table 3
According to algorithm 1, the execution time computation process of whole process model as shown in Figure 3, scanning process model (a) is at first selected by node
Figure DEST_PATH_IMAGE151
The innermost layer of forming is selected the basic model structure, calculates its execution time average according to formula (20)-(22) and is: 15.92, use the activity of an equivalence then
Figure 389832DEST_PATH_IMAGE152
Remove to replace a formation new process model (b), then scan the new process model (b) that forms, selection is by node
Figure DEST_PATH_IMAGE153
The innermost loop basic model structure of forming, calculate its average according to formula (14)-(16) and be: 15.06, use the activity of an equivalence then Remove to replace a formation new process model (c); Then the new process model (c) that forms of scanning is selected by node
Figure DEST_PATH_IMAGE155
The innermost layer of forming is the basic model structure in proper order, calculates its execution time average according to formula (11)-(13) and is: 58.00, use the activity of an equivalence then
Figure 615856DEST_PATH_IMAGE156
Remove to replace a formation new process model (d); Then the new process model (d) that forms of scanning is selected by node
Figure DEST_PATH_IMAGE157
The innermost layer of forming is the basic model structure in proper order, calculates its execution time average according to formula (11)-(13) and is: 33.29, use the activity of an equivalence then
Figure 494819DEST_PATH_IMAGE158
Remove to replace a formation new process model (e); Then the new process model (e) that forms of scanning is selected by node
Figure DEST_PATH_IMAGE159
The parallel basic model structure of the innermost layer of forming, calculate its execution time average according to formula (17)-(19) and be: 70.14, use the activity of an equivalence then
Figure 857930DEST_PATH_IMAGE160
Remove to replace a formation new process model (f); Then the new process model (f) that forms of scanning is selected by node
Figure DEST_PATH_IMAGE161
The innermost layer of forming is the basic model structure in proper order, calculates its execution time average according to formula (11)-(13) and is: 100.44, use the activity of an equivalence then
Figure 505949DEST_PATH_IMAGE162
Remove to replace a formation new process model (f); Then the new process model (f) that forms of scanning because it has only an activity, stops so calculate, and it is movable that the average that process model is carried out equals equivalence
Figure 935793DEST_PATH_IMAGE162
The execution time average, be: 100.44.
Adopt GPSSWorld to carry out emulation, this routine process execution time average is 98.02, and the result of calculation that proposes method with the present invention is very approaching, and the validity of the process execution time assay method that the present invention proposes has been described.

Claims (2)

1. the assay method of a process execution time, it is characterized in that: described assay method may further comprise the steps:
The first step, set up process model:
Practical business process/workflow is made up of a plurality of activities, forms following four kinds of basic model structures according to the control relation between each activity: order basic model structure, parallel basic model structure, selection basic model structure and the basic model structure that circulates;
Wherein, described control relation comprise order, with bifurcated, with converge or bifurcated or converge and circulate; Parallel basic model structure, selection basic model structure and the basic model structure that circulates are referred to as non-order basic model structure;
The process model of setting up satisfies following rule:
1: one of rule and bifurcated must have one to be complementary with converging, and form a parallel model structure;
Rule 2: one or bifurcated must have one or converge and be complementary, and form a selection or circulation model structure;
3: one non-sequential control modules of rule can be nested in another non-sequential control module, but two non-sequential control modules can not be overlapping;
Satisfying under the situation of above-mentioned rule, with practical business process/workflow modeling nested process model that forms of these four kinds of basic model textural associations of serving as reasons;
Described process model is defined as one 10 tuple , wherein:
(1)
Figure 2010105148115100001DEST_PATH_IMAGE002
It is process instance/service object's arrival rate;
(2)
Figure 927116DEST_PATH_IMAGE003
It is movable set;
Figure 2010105148115100001DEST_PATH_IMAGE004
It is the set of tie point; Order
Figure 332952DEST_PATH_IMAGE005
Be the set of process model node, , then
Figure 852795DEST_PATH_IMAGE007
The expression node
Figure 2010105148115100001DEST_PATH_IMAGE008
The number of preorder node,
Figure 293266DEST_PATH_IMAGE009
The expression node The number of descendant node;
Figure 2010105148115100001DEST_PATH_IMAGE010
, if
Figure 569712DEST_PATH_IMAGE011
, node so Be the fan-out tie point, if
Figure 2010105148115100001DEST_PATH_IMAGE012
, node so
Figure 125907DEST_PATH_IMAGE008
Be the fan-in tie point;
(3) Be the set that connects arc, ,
Figure 562015DEST_PATH_IMAGE015
Expression is from node
Figure 2010105148115100001DEST_PATH_IMAGE016
To node
Figure 423661DEST_PATH_IMAGE017
The connection arc;
(4)
Figure 2010105148115100001DEST_PATH_IMAGE018
It is the set of resource;
(5)
Figure 510828DEST_PATH_IMAGE019
Be set movable and resources relationship,
Figure 2010105148115100001DEST_PATH_IMAGE020
The expression resource
Figure 65306DEST_PATH_IMAGE021
Have the ability/qualification processing activity Example;
(6)
Figure 921311DEST_PATH_IMAGE023
:
Figure 2010105148115100001DEST_PATH_IMAGE024
, be a mapping from tie point to the tie point type;
(7) :
Figure 2010105148115100001DEST_PATH_IMAGE026
It is a mapping of carrying out probability from the connection arc to the connection arc; , if
Figure 2010105148115100001DEST_PATH_IMAGE028
, then
Figure 50439DEST_PATH_IMAGE029
, if
Figure 2010105148115100001DEST_PATH_IMAGE030
, then
Figure 405459DEST_PATH_IMAGE031
(8)
Figure 2010105148115100001DEST_PATH_IMAGE032
:
Figure 608907DEST_PATH_IMAGE033
, be a mapping of handling active instance speed from movable and resources relationship to resource, if
Figure 2010105148115100001DEST_PATH_IMAGE034
,
Figure 732983DEST_PATH_IMAGE020
, resource then
Figure 566947DEST_PATH_IMAGE021
Can the processing activity in the unit interval
Figure 579902DEST_PATH_IMAGE022
The number of times of example be
Figure 524724DEST_PATH_IMAGE035
, note by abridging and be
Figure 2010105148115100001DEST_PATH_IMAGE036
(9) :
Figure 2010105148115100001DEST_PATH_IMAGE038
Be one from movable and the mapping of resources relationship to the task partition coefficient, described Task Distribution rate is to distribute to the probability of corresponding resource after active instance produces; If
Figure 570489DEST_PATH_IMAGE034
, , then when movable
Figure 55139DEST_PATH_IMAGE022
Example distribute to resource after producing Probability be
Figure 765792DEST_PATH_IMAGE039
, note by abridging and be Because an active instance can only be carried out once by a resource, so have:
Figure 317122DEST_PATH_IMAGE041
，
Figure 2010105148115100001DEST_PATH_IMAGE042
，
Figure 666063DEST_PATH_IMAGE043
The expectation implementation rate of node the is defined as process node expectation is carried out when carrying out one time number of times;
If whole basic module expectation implementation rate is
Figure 2010105148115100001DEST_PATH_IMAGE044
, so order, parallel, select and the four kinds of basic model structures that circulate in being calculated as follows of expectation implementation rate of node:
By activity
Figure 291342DEST_PATH_IMAGE045
In the order basic structure of forming, have:
Figure 2010105148115100001DEST_PATH_IMAGE046
, wherein:
Figure 700327DEST_PATH_IMAGE047
Be respectively movable
Figure 175170DEST_PATH_IMAGE045
The expectation implementation rate;
By activity With or the fan-in tie point
Figure 840986DEST_PATH_IMAGE049
, or fan-out tie point In the circulation basic structure of forming, have:
Figure 147203DEST_PATH_IMAGE051
Figure 2010105148115100001DEST_PATH_IMAGE052
Wherein:
Figure 962974DEST_PATH_IMAGE053
For withdrawing from the round-robin probability, Be respectively movable
Figure 987431DEST_PATH_IMAGE048
The expectation implementation rate,
Figure 117323DEST_PATH_IMAGE055
Be respectively tie point
Figure 2010105148115100001DEST_PATH_IMAGE056
The expectation implementation rate;
By activity
Figure 543626DEST_PATH_IMAGE045
With with the fan-out tie point
Figure 904200DEST_PATH_IMAGE049
, with the fan-in tie point
Figure 353636DEST_PATH_IMAGE050
In the parallel basic module structure of forming, have:
Figure 287219DEST_PATH_IMAGE057
, wherein:
Figure 2010105148115100001DEST_PATH_IMAGE058
Be respectively movable
Figure 302448DEST_PATH_IMAGE045
The expectation implementation rate,
Figure 161820DEST_PATH_IMAGE055
Be respectively tie point
Figure 334437DEST_PATH_IMAGE056
The expectation implementation rate;
By activity
Figure 694880DEST_PATH_IMAGE045
With or the fan-out tie point
Figure 269344DEST_PATH_IMAGE049
, or fan-in tie point
Figure 299616DEST_PATH_IMAGE050
In the selection basic module structure of forming, have:
Figure 458065DEST_PATH_IMAGE059
，
Figure 2010105148115100001DEST_PATH_IMAGE060
，
Figure 231986DEST_PATH_IMAGE061
Wherein:
Figure 2010105148115100001DEST_PATH_IMAGE062
Be the selection probability, ,
Figure 924447DEST_PATH_IMAGE058
Be respectively movable
Figure 570192DEST_PATH_IMAGE045
The expectation implementation rate,
Figure 383689DEST_PATH_IMAGE055
Be respectively tie point
Figure 170294DEST_PATH_IMAGE056
The expectation implementation rate;
The calculating of second step, single-unit activity execution time:
In practical business process/workflow, the arrival of assignment procedure example is Poisson flow, and resource is handled each obedience negative exponent distribution of movable time, then is modeled as one in each Energy Resources Service
Figure 2010105148115100001DEST_PATH_IMAGE064
Queuing system calculates the Laplace-Stieltjes conversion that the single-unit activity example distributed in the stand-by period at respective resources place thus:
Figure 604686DEST_PATH_IMAGE065
, wherein:
Figure 2010105148115100001DEST_PATH_IMAGE066
The single-unit activity example in the average latency at respective resources place is:
Figure 301509DEST_PATH_IMAGE067
, wherein:
Figure 417232DEST_PATH_IMAGE066
Movable
Figure 319329DEST_PATH_IMAGE022
The Laplace-Stieltjes that distributes of execution time be transformed to:
Figure 2010105148115100001DEST_PATH_IMAGE068
, wherein:
Figure 363771DEST_PATH_IMAGE043
Movable
Figure 718529DEST_PATH_IMAGE022
The density function of execution time be:
Figure 637943DEST_PATH_IMAGE069
Movable The average execution time be:
Figure 2010105148115100001DEST_PATH_IMAGE070
Wherein:
Figure 672207DEST_PATH_IMAGE043
The calculating of the 3rd step, whole process model execution time:
3.1) find out an innermost layer basic model structure that does not comprise four kinds of basic model structures , judge described innermost layer basic model structure
Figure 237366DEST_PATH_IMAGE071
Belong to a kind of in four kinds of basic model structures, calculate according to the computing method of four kinds of basic process model structure execution time
Figure 2010105148115100001DEST_PATH_IMAGE072
With
Figure 412258DEST_PATH_IMAGE073
3.2) with an execution time density function and average be With The movable innermost layer basic model structure of replacing of equivalence, form a new process model;
3.3) judge whether described new process model only comprises an activity? if not, turn back to 3.1), if, the average execution time of whole process model is the average execution time of a described activity, and the average execution time of described whole process model is the execution time of practical business process/workflow.
2. the assay method of a kind of process execution time as claimed in claim 1 is characterized in that: described step 3.1), the computing method of four kinds of basic process model structure execution time are as follows:
Suppose
Figure 2010105148115100001DEST_PATH_IMAGE074
With
Figure 716965DEST_PATH_IMAGE075
Be movable
Figure 2010105148115100001DEST_PATH_IMAGE076
Execution time density function and average;
(a) order basic model structure:
The Laplace-Stieltjes that the execution time of order basic model structure distributes is transformed to:
Figure 244898DEST_PATH_IMAGE077
, wherein:
Figure 2010105148115100001DEST_PATH_IMAGE078
The execution time density function of order basic model structure is:
The execution time average of order basic model structure is:
Figure 2010105148115100001DEST_PATH_IMAGE080
(b) the basic model structure that circulates:
The Laplace-Stieltjes that the execution time of the basic model structure that circulates distributes is transformed to:
Figure 946586DEST_PATH_IMAGE081
Wherein:
Figure 745915DEST_PATH_IMAGE078
,
Figure 833082DEST_PATH_IMAGE053
For withdrawing from the round-robin probability;
The execution time density function of the basic model structure that circulates is:
Figure 2010105148115100001DEST_PATH_IMAGE082
The execution time average of the basic model structure that circulates is:
Figure 387560DEST_PATH_IMAGE083
Wherein:
Figure 425923DEST_PATH_IMAGE053
For withdrawing from the round-robin probability;
(c) parallel basic model structure:
The execution time density function of parallel basic model structure is:
Figure 2010105148115100001DEST_PATH_IMAGE084
，
Wherein:
Figure 604444DEST_PATH_IMAGE085
,
Figure 2010105148115100001DEST_PATH_IMAGE086
The execution time average of parallel basic model structure is:
Figure 372548DEST_PATH_IMAGE087
When the execution time of activity was similar to obeys index distribution, approximate treatment was as follows:
Figure 2010105148115100001DEST_PATH_IMAGE088
(d) select the basic model structure:
Select the Laplace-Stieltjes of the execution time distribution of basic model structure to be transformed to:
，
Wherein: ,
Figure 266183DEST_PATH_IMAGE062
Be the selection probability,
Figure 764161DEST_PATH_IMAGE063
Select the execution time density function of basic model structure to be:
Figure 2010105148115100001DEST_PATH_IMAGE090
Select the execution time average of basic model structure to be:
Figure 896327DEST_PATH_IMAGE091
Wherein:
Figure 174861DEST_PATH_IMAGE062
Be the selection probability,
Figure 119684DEST_PATH_IMAGE063
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