CN110221907B - Real-time task scheduling method based on EDF algorithm and fuzzy set - Google Patents

Real-time task scheduling method based on EDF algorithm and fuzzy set Download PDF

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CN110221907B
CN110221907B CN201910438335.4A CN201910438335A CN110221907B CN 110221907 B CN110221907 B CN 110221907B CN 201910438335 A CN201910438335 A CN 201910438335A CN 110221907 B CN110221907 B CN 110221907B
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task
time
random
execution
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CN110221907A (en
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张晶
陈诚
范明炀
黄天泽
龙忠琳
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Yunnan Xiaorun Technology Service Co ltd
Kunming University of Science and Technology
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Kunming University of Science and Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00—Arrangements for program control, e.g. control units
    • G06F9/06—Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/46—Multiprogramming arrangements
    • G06F9/48—Program initiating; Program switching, e.g. by interrupt
    • G06F9/4806—Task transfer initiation or dispatching
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00—Arrangements for program control, e.g. control units
    • G06F9/06—Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/46—Multiprogramming arrangements
    • G06F9/48—Program initiating; Program switching, e.g. by interrupt
    • G06F9/4806—Task transfer initiation or dispatching
    • G06F9/4843—Task transfer initiation or dispatching by program, e.g. task dispatcher, supervisor, operating system
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Abstract

The invention relates to a real-time task scheduling method based on an EDF algorithm and a fuzzy set, and belongs to the field of system task scheduling. The method can ensure that the random tasks with highest importance at the head of the queue in the priority queue and the periodic tasks participate in the scheduling process together, and can effectively ensure the submission rate of the important random tasks by considering the importance difference between the random tasks, so that the random tasks with high priority are preferentially executed, and the probability of serious errors of a system caused by missing the deadline of the important random tasks is reduced.

Description

Real-time task scheduling method based on EDF algorithm and fuzzy set
Technical Field
The invention relates to a real-time task scheduling method based on an EDF algorithm and a fuzzy set, and belongs to the field of system task scheduling.
Background
There are real-time periodic tasks and random tasks in the system, the random task arrival time is unpredictable, and the execution time and deadline are unknown. And the arrival time, execution time and deadline of the periodic task may be determined by its periodicity. Thus, mixed scheduling of periodic and random tasks has been studied by a great deal of scholars. But none take into account the importance differences between the random tasks, which may result in priority scheduling of important tasks. While important random tasks miss deadlines, can cause significant problems for the system.
Disclosure of Invention
The invention provides a real-time task scheduling method based on an EDF algorithm and a fuzzy set, which is used for adding random tasks into a priority queue and participating in task scheduling together with periodic tasks.
The technical scheme of the invention is as follows: a real-time task scheduling method based on an EDF algorithm and fuzzy sets comprises the following steps:
step1, recording the periodic task set as pi= { T 1 ,T 2 ,...,T i ,..}, remembering the random task set as Γ= { a 1 ,A 2 ,...,A a ,..}, building a priority queue; wherein T is i The j-th schedule representing the i-th periodic task is denoted as T ij ，A a Represents the a-th random task, and gathers task A for the random task a Setting the arrival time to G a ；
Step2, a scheduling process of the periodic task is obtained according to an EDF algorithm, an inverse scheduling process is obtained according to the scheduling process and the overcycle, and a latest execution time set, a predicted ending time set and a maximum movable time set of the periodic task are obtained according to the scheduling process and the inverse scheduling process;
the forward executing process of the periodic task set is obtained according to the EDF algorithm and is marked as a scheduling process xi, and each scheduling of each period of each task in the scheduling process xi of the periodic task set is marked as xi ij ＝(p ij ,q ij ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein xi ij Representing periodic task T in forward execution i P ij Representing xi ij Start execution time, q ij Representing xi ij End time of (2);
the reverse execution process of the periodic task set is recorded as a reverse scheduling process xi -1 Reverse scheduling process ζ of periodic task set -1 Each execution of each cycle of each task in (a) is noted as
Figure BDA0002071259860000011
Wherein->
Figure BDA0002071259860000012
Representing a reverse execution time period task T i Is (are) j-th scheduling of->
Figure BDA0002071259860000021
Representation->
Figure BDA0002071259860000022
Is the latest execution moment of->
Figure BDA0002071259860000023
Representation->
Figure BDA0002071259860000024
Is a predicted end time of (2);
Figure BDA0002071259860000025
the sum of j and k-1 is the periodic task T i The times of co-scheduling in an overcycle H, H is the overcycle, namely the least common multiple of all periodic tasks in a periodic task set;
the latest execution time set of the periodic task set is recorded as
Figure BDA0002071259860000026
The set of expected ending moments is +.>
Figure BDA0002071259860000027
The maximum movable time set is marked as f'; f' represents a time period remaining by removing the execution period of the inverse scheduling process in the super period;
step3, when the current task arrives, judging the type of the currently arrived task: if the multiple tasks which arrive at the same time comprise both periodic tasks and random tasks, executing a Step4 on all the periodic tasks, and waiting for all the random tasks; if only random tasks exist, executing Step7;
step4, if periodic task scheduling T exists at the current moment ij Reaching its latest execution time
Figure BDA0002071259860000028
Go to Step5;
if the periodic task schedule T does not exist at the current moment ij Reaching its maximumLate execution time
Figure BDA0002071259860000029
And if random tasks exist in the priority queue, the process goes to Step8;
if the periodic task schedule T does not exist at the current moment ij Reaching the latest execution time
Figure BDA00020712598600000210
And if no random task exists in the priority queue, the periodic task schedule which does not reach the latest execution time waits for the latest execution time to reach, and the process goes to Step3;
in the executing process of Step4, if the task arrives at the current moment and before the current moment, the Step3 needs to be synchronously executed;
step5, if the arrival time of a schedule of a task with one cycle is equal to the latest execution time, executing the schedule T ij And go to Step6;
if the arrival time of a certain schedule with a plurality of periodic tasks is equal to the corresponding latest execution time, randomly selecting one schedule T ij Executing, terminating other periodic task scheduling, and turning to Step6;
step6, if periodic task scheduling T ij Is the actual end time r of (2) ij Equal to its estimated end time
Figure BDA00020712598600000211
Turning to Step4;
if periodic task schedule T ij Is the actual end time r of (2) ij Not reaching its expected end time
Figure BDA00020712598600000212
Recording the current execution ending time as the actual ending time r ij And update the phase difference time +.>
Figure BDA00020712598600000213
And an idle time f=f' +f ", then go to Step4;
if periodic task schedule T ij At its expected end time
Figure BDA00020712598600000214
If not, terminating the scheduling task and making the actual end time r ij Equal to its expected end time->
Figure BDA0002071259860000031
Then go to Step4;
wherein, the jth scheduling T of the ith periodic task executed in Step5 ij The actual end time is denoted as r ij Jth schedule T of ith periodic task ij Is (are) the expected end time of (a)
Figure BDA0002071259860000032
And the actual end time r ij The time between them is recorded as phase difference time +.>
Figure BDA0002071259860000033
The sum of the maximum movable time and the phase difference time is denoted as the idle time, i.e. f=f' +f ";
step7, if the random task is one and no task exists in the current priority queue, directly arranging the random task into the head of the priority queue; otherwise, calculating the priorities of all the random tasks according to the fuzzy sets of the available time, the fuzzy sets of the key degree and the fuzzy sets of the execution time of the random tasks, and inserting priority queues according to the priorities; go to Step8;
step8, waiting if a task is being executed at the current moment;
if no task is executing at the current moment and random tasks exist in the priority queue, selecting the random task at the head of the queue to execute, and switching to Step9;
if no task is executing at the current moment and no random task exists in the priority queue, the process goes to Step3;
step9, if random task A a The execution end time equals the latest execution time set
Figure BDA0002071259860000034
At some point in the process, terminating the random task A a And go to Step4;
if it is random task A a Execution end time of not reaching latest execution time set
Figure BDA0002071259860000035
At a certain time, go to Step8;
if it is random task A a The latest execution time set is reached in the execution process
Figure BDA0002071259860000036
At some point in time, the random task A is aborted a Placing the first priority queue, and turning to Step4;
in the execution process of Step9, if the task arrives at and before the execution end time, step3 needs to be executed synchronously.
Step7 specifically comprises the following steps:
step7.1: computing fuzzy sets of available time for random tasks
Will random task A a Is G a Scheduling T to the latest one cycle task ij Latest execution time of (a)
Figure BDA0002071259860000037
The time of (a) is recorded as random task A a Is available for time S a I.e. +.>
Figure BDA0002071259860000038
Definition of available time in ambiguous language is recorded +.>
Figure BDA0002071259860000039
Wherein v is more than or equal to 1 and less than or equal to m, and the discourse domain is recorded as
Figure BDA0002071259860000041
Then the available time S a Is of the fuzzy set of (a)(1)：
Figure BDA0002071259860000042
Wherein "+" denotes the availability time S a In the field of discussion
Figure BDA0002071259860000043
The whole body is arranged on the upper part;
Figure BDA0002071259860000044
Representation->
Figure BDA0002071259860000045
And (3) with
Figure BDA0002071259860000046
Corresponding relation of (3);
Figure BDA0002071259860000047
Is the availability time S a Is a membership function of S a Belonging to->
Figure BDA0002071259860000048
The extent of (3);
time of availability S a The normal distribution is met, so the membership function is expressed as formula (2):
Figure BDA0002071259860000049
wherein c (v) is a function of determining the central position of the membership function, i.e
Figure BDA00020712598600000410
Sigma is a constant determining the width of the curve, determined by the superseriod H and m together, i.e. +.>
Figure BDA00020712598600000411
Step7.2: fuzzy set for calculating criticality of random task
Will random task A a The criticality of (C) a Definition in ambiguous language is noted as
Figure BDA00020712598600000412
Designating the discourse as +.>
Figure BDA00020712598600000413
Then random task a a Criticality C of (2) a The fuzzy set of (2) is the formula (3):
Figure BDA00020712598600000414
wherein "+" represents criticality C a In the field of discussion
Figure BDA00020712598600000415
The whole body is arranged on the upper part;
Figure BDA00020712598600000416
Representation->
Figure BDA00020712598600000417
And->
Figure BDA00020712598600000418
Corresponding relation of (3);
Figure BDA00020712598600000419
Is criticality C a Is a membership function of (C) a Belonging to->
Figure BDA00020712598600000420
The extent of (3);
criticality C a The membership function of (2) is expressed as formula (4):
Figure BDA0002071259860000051
wherein,,
Figure BDA0002071259860000052
Figure BDA0002071259860000053
as the center point, C z Representing random task A z W represents the total number of random tasks participated in when Step7 is executed this time; sigma is a constant determining the width of the curve, determined by the superseriod H and m together, i.e. +.>
Figure BDA0002071259860000054
Step7.3: computing fuzzy sets of execution times for random tasks
Random task A a Execution time E of (2) a Definition in ambiguous language is noted as
Figure BDA0002071259860000055
Wherein v is more than or equal to 1 and less than or equal to m, and the discourse domain is marked as +.>
Figure BDA0002071259860000056
Then random task a a Execution time E of (2) a The fuzzy set of (2) is the formula (5):
Figure BDA0002071259860000057
wherein "+" denotes execution time E a In the field of discussion
Figure BDA0002071259860000058
The whole body is arranged on the upper part;
Figure BDA0002071259860000059
Representation->
Figure BDA00020712598600000510
And->
Figure BDA00020712598600000511
Corresponding relation of (3);
Figure BDA00020712598600000512
Is execution time E a Is a membership function of (E) a Belonging to->
Figure BDA00020712598600000513
The extent of (3);
record execution time E a Is P (E) a ) Random task A a E of execution time of (2) a The membership of (2) is:
Figure BDA0002071259860000061
wherein,,
Figure BDA0002071259860000062
Figure BDA0002071259860000063
as the center point E z Representing random task A z Execution time of P (E) z ) Representing execution time E z Probability of (2);
step7.4: computing priority of random tasks
Random task A a Importance of (1) is determined by priority P a Determining the priority P a The comment set is defined and recorded as m fuzzy languages
Figure BDA0002071259860000064
Wherein->
Figure BDA0002071259860000065
And priority P a By random task A a Is determined together with the fuzzy set of the available time, the fuzzy set of the criticality and the fuzzy set of the execution time; thus random task A a The priority factor set of (c) is x= { "availability time", "criticality", "execution time" }, which isThe fuzzy relation matrix is expressed as formula (7):
Figure BDA0002071259860000066
because the influence of the fuzzy set of available time, the fuzzy set of key degree and the fuzzy set of execution time on the priority is different, the fuzzy sets are given different weights, and the fuzzy set is recorded as a weighted fuzzy set R= (R) 1 ,R 2 ,R 3 ) Wherein R is 1 +R 2 +R 3 ＝1；
By synthesizing a decision set from a and R, the decision set is represented by formula (8):
Figure BDA0002071259860000071
wherein,,
Figure BDA0002071259860000072
the fuzzy synthesis max-min is represented, the fuzzy operator 'Λ' adopts small-taking operation, and the 'V' adopts large-taking operation;
priority P in decision set B a The maximum value in the decision set B corresponds to the subset of the comment set as the priority of the random task.
The beneficial effects of the invention are as follows: the method can ensure that the random tasks with highest importance at the head of the queue in the priority queue and the periodic tasks participate in the scheduling process together, and can effectively ensure the submission rate of the important random tasks by considering the importance difference between the random tasks, so that the random tasks with high priority are preferentially executed, and the probability of serious errors of a system caused by missing the deadline of the important random tasks is reduced.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
Example 1: as shown in fig. 1, a real-time task scheduling method based on an EDF algorithm and fuzzy sets comprises the following steps:
step1, recording the periodic task set as pi= { T 1 ,T 2 ,...,T i ,..}, remembering the random task set as Γ= { a 1 ,A 2 ,...,A a ,..}, building a priority queue; wherein T is i The j-th schedule representing the i-th periodic task is denoted as T ij ，A a Represents the a-th random task, and gathers task A for the random task a Setting the arrival time to G a ；
Step2, a scheduling process of the periodic task is obtained according to an EDF algorithm, an inverse scheduling process is obtained according to the scheduling process and the overcycle, and a latest execution time set, a predicted ending time set and a maximum movable time set of the periodic task are obtained according to the scheduling process and the inverse scheduling process;
the forward executing process of the periodic task set is obtained according to the EDF algorithm and is marked as a scheduling process xi, and each scheduling of each period of each task in the scheduling process xi of the periodic task set is marked as xi ij ＝(p ij ,q ij ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein xi ij Representing periodic task T in forward execution i P ij Representing xi ij Start execution time, q ij Representing xi ij End time of (2);
the reverse execution process of the periodic task set is recorded as a reverse scheduling process xi -1 Reverse scheduling process ζ of periodic task set -1 Each execution of each cycle of each task in (a) is noted as
Figure BDA0002071259860000073
Wherein->
Figure BDA0002071259860000074
Representing a reverse execution time period task T i Is (are) j-th scheduling of->
Figure BDA0002071259860000081
Representation->
Figure BDA0002071259860000082
Is the most significant of (3)Late execution time, ->
Figure BDA0002071259860000083
Representation->
Figure BDA0002071259860000084
Is a predicted end time of (2);
Figure BDA0002071259860000085
The sum of j and k-1 is the periodic task T i The times of co-scheduling in an overcycle H, H is the overcycle, namely the least common multiple of all periodic tasks in a periodic task set;
the latest execution time set of the periodic task set is recorded as
Figure BDA0002071259860000086
The set of expected ending moments is +.>
Figure BDA0002071259860000087
The maximum movable time set is marked as f'; f' represents a time period remaining by removing the execution period of the inverse scheduling process in the super period;
step3, when the current task arrives, judging the type of the currently arrived task: if the multiple tasks which arrive at the same time comprise both periodic tasks and random tasks, executing a Step4 on all the periodic tasks, and waiting for all the random tasks; if only random tasks exist, executing Step7;
step4, if periodic task scheduling T exists at the current moment ij Reaching its latest execution time
Figure BDA0002071259860000088
Go to Step5;
if the periodic task schedule T does not exist at the current moment ij Reaching its latest execution time
Figure BDA0002071259860000089
And if random tasks exist in the priority queue, the process goes to Step8;
if the current time isAbsence of periodic task schedule T ij Reaching the latest execution time
Figure BDA00020712598600000810
And if no random task exists in the priority queue, the periodic task schedule which does not reach the latest execution time waits for the latest execution time to reach, and the process goes to Step3;
in the executing process of Step4, if the task arrives at the current moment and before the current moment, the Step3 needs to be synchronously executed;
step5, if the arrival time of a schedule of a task with one cycle is equal to the latest execution time, executing the schedule T ij And go to Step6;
if the arrival time of a certain schedule with a plurality of periodic tasks is equal to the corresponding latest execution time, randomly selecting one schedule T ij Executing, terminating other periodic task scheduling, and turning to Step6;
step6, if periodic task scheduling T ij Is the actual end time r of (2) ij Equal to its estimated end time
Figure BDA00020712598600000811
Turning to Step4;
if periodic task schedule T ij Is the actual end time r of (2) ij Not reaching its expected end time
Figure BDA00020712598600000812
Recording the current execution ending time as the actual ending time r ij And update the phase difference time +.>
Figure BDA00020712598600000813
And an idle time f=f' +f ", then go to Step4;
if periodic task schedule T ij At its expected end time
Figure BDA00020712598600000814
If not, terminating the scheduling task and making it actually bindTime of beam r ij Equal to its expected end time->
Figure BDA0002071259860000091
Then go to Step4;
wherein, the jth scheduling T of the ith periodic task executed in Step5 ij The actual end time is denoted as r ij Jth schedule T of ith periodic task ij Is (are) the expected end time of (a)
Figure BDA0002071259860000092
And the actual end time r ij The time between them is recorded as phase difference time +.>
Figure BDA0002071259860000093
The sum of the maximum movable time and the phase difference time is denoted as the idle time, i.e. f=f' +f ";
step7, if the random task is one and no task exists in the current priority queue, directly arranging the random task into the head of the priority queue; otherwise, calculating the priorities of all the random tasks according to the fuzzy sets of the available time, the fuzzy sets of the key degree and the fuzzy sets of the execution time of the random tasks, and inserting priority queues according to the priorities; go to Step8;
step8, waiting if a task is being executed at the current moment;
if no task is executing at the current moment and random tasks exist in the priority queue, selecting the random task at the head of the queue to execute, and switching to Step9;
if no task is executing at the current moment and no random task exists in the priority queue, the process goes to Step3;
step9, if random task A a The execution end time equals the latest execution time set
Figure BDA0002071259860000094
At some point in the process, terminating the random task A a And go to Step4;
if it is random task A a The execution end time is not reachedBy the latest execution time set
Figure BDA0002071259860000095
At a certain time, go to Step8;
if it is random task A a The latest execution time set is reached in the execution process
Figure BDA0002071259860000096
At some point in time, the random task A is aborted a Placing the first priority queue, and turning to Step4;
in the execution process of Step9, if the task arrives at and before the execution end time, step3 needs to be executed synchronously.
Further, step7 may be set, specifically:
step7.1: computing fuzzy sets of available time for random tasks
Will random task A a Is G a Scheduling T to the latest one cycle task ij Latest execution time of (a)
Figure BDA0002071259860000097
The time of (a) is recorded as random task A a Is available for time S a I.e. +.>
Figure BDA0002071259860000098
Definition of available time in ambiguous language is recorded +.>
Figure BDA0002071259860000099
Wherein v is more than or equal to 1 and less than or equal to m, and the discourse domain is recorded as
Figure BDA0002071259860000101
Then the available time S a The fuzzy set of (2) is the formula (1):
Figure BDA0002071259860000102
wherein "+" denotes the availability time S a In the field of discussion
Figure BDA0002071259860000103
The whole body is arranged on the upper part;
Figure BDA0002071259860000104
Representation->
Figure BDA0002071259860000105
And->
Figure BDA0002071259860000106
Corresponding relation of (3);
Figure BDA0002071259860000107
Is the availability time S a Is a membership function of S a Belonging to->
Figure BDA0002071259860000108
The extent of (3);
time of availability S a The normal distribution is met, so the membership function is expressed as formula (2):
Figure BDA0002071259860000109
wherein c (v) is a function of determining the central position of the membership function, i.e
Figure BDA00020712598600001010
Sigma is a constant determining the width of the curve, determined by the superseriod H and m together, i.e. +.>
Figure BDA00020712598600001011
Step7.2: fuzzy set for calculating criticality of random task
Will random task A a The criticality of (C) a Definition in ambiguous language is noted as
Figure BDA00020712598600001012
Designating the discourse as +.>
Figure BDA00020712598600001013
Then random task a a Criticality C of (2) a The fuzzy set of (2) is the formula (3):
Figure BDA00020712598600001014
wherein "+" represents criticality C a In the field of discussion
Figure BDA00020712598600001015
The whole body is arranged on the upper part;
Figure BDA00020712598600001016
Representation->
Figure BDA00020712598600001017
And->
Figure BDA00020712598600001018
Corresponding relation of (3);
Figure BDA00020712598600001019
Is criticality C a Is a membership function of (C) a Belonging to->
Figure BDA00020712598600001020
The extent of (3);
criticality C a The membership function of (2) is expressed as formula (4):
Figure BDA0002071259860000111
wherein,,
Figure BDA0002071259860000112
Figure BDA0002071259860000113
as the center point, C z Representing random task A z W represents the total number of random tasks participated in when Step7 is executed this time; sigma is a constant determining the width of the curve, determined by the superseriod H and m together, i.e. +.>
Figure BDA0002071259860000114
Step7.3: computing fuzzy sets of execution times for random tasks
Random task A a Execution time E of (2) a Definition in ambiguous language is noted as
Figure BDA0002071259860000115
Wherein v is more than or equal to 1 and less than or equal to m, and the discourse domain is marked as +.>
Figure BDA0002071259860000116
Then random task a a Execution time E of (2) a The fuzzy set of (2) is the formula (5):
Figure BDA0002071259860000117
wherein "+" denotes execution time E a In the field of discussion
Figure BDA0002071259860000118
The whole body is arranged on the upper part;
Figure BDA0002071259860000119
Representation->
Figure BDA00020712598600001110
And->
Figure BDA00020712598600001111
Corresponding relation of (3);
Figure BDA00020712598600001112
Is the execution timeE a Is a membership function of (E) a Belonging to->
Figure BDA00020712598600001113
The extent of (3);
record execution time E a Is P (E) a ) Random task A a E of execution time of (2) a The membership of (2) is:
Figure BDA0002071259860000121
wherein,,
Figure BDA0002071259860000122
Figure BDA0002071259860000123
as the center point E z Representing random task A z Execution time of P (E) z ) Representing execution time E z Probability of (2);
step7.4: computing priority of random tasks
Random task A a Importance of (1) is determined by priority P a Determining the priority P a The comment set is defined and recorded as m fuzzy languages
Figure BDA0002071259860000124
Wherein->
Figure BDA0002071259860000125
And priority P a By random task A a Is determined together with the fuzzy set of the available time, the fuzzy set of the criticality and the fuzzy set of the execution time; thus random task A a The priority factor set of (c) is x= { "availability time", "criticality", "execution time" }, and its fuzzy relation matrix is expressed as formula (7):
Figure BDA0002071259860000126
because the influence of the fuzzy set of available time, the fuzzy set of key degree and the fuzzy set of execution time on the priority is different, the fuzzy sets are given different weights, and the fuzzy set is recorded as a weighted fuzzy set R= (R) 1 ,R 2 ,R 3 ) Wherein R is 1 +R 2 +R 3 ＝1；
By synthesizing a decision set from a and R, the decision set is represented by formula (8):
Figure BDA0002071259860000131
wherein,,
Figure BDA0002071259860000132
the fuzzy synthesis max-min is represented, the fuzzy operator 'Λ' adopts small-taking operation, and the 'V' adopts large-taking operation;
priority P in decision set B a The maximum value in the decision set B corresponds to the subset of the comment set as the priority of the random task.
Further, the following example is made for the steps in the present application:
cycle taking task T 1 And T 2 Periodic task T 1 The execution time of (2), the period and the relative deadline are both 8; periodic task T 2 The execution time of (2) is 3, and the period and the relative deadline are 10. Periodic task T 1 And T 2 And simultaneously arrives, the overcycle H is 40.
Suppose that at time 0 random task a 1 Arrival at time 1 random task A 2 、A 3 Arrival at time 8 random task A 4 Arrival, random task A at time 10 5 Arrival, the arrival time of the random task set is G 1 ＝0，G 2 ＝1，G 3 ＝1，G 4 ＝8，G 5 ＝10。
Random task A a Time of availability S a Description in ambiguous language "short", "medium", "long" corresponding to
Figure BDA0002071259860000133
Criticality C a The terms "low", "medium", "high" and "low" are used in a fuzzy language, corresponding to->
Figure BDA0002071259860000134
Execution time E a The description of "long", "medium", "short" in ambiguous language corresponds to +.>
Figure BDA0002071259860000135
Priority P a The terms "low", "medium", "high" and "low" are used in a fuzzy language, corresponding to->
Figure BDA0002071259860000136
The weighted fuzzy set takes r= (0.2.0.6.0.2).
The partial scheduling process is as follows, assuming that the time spent in the judgment and step jump is not counted:
step1, the periodic task set is pi= { T 1 ,T 2 The random task set is Γ= { a } 1 ,A 2 ,A 3 ,A 4 ,A 5 Arrival time of random task G 1 ＝0，G 2 ＝1，G 3 ＝1，G 4 ＝8，G 5 ＝10。
Step2, obtaining a periodic task T according to an EDF algorithm 1 And T 2 The schedule xi is specifically: zeta type toy 11 ＝(p 11 ,q 11 )＝(0,2)，ξ 12 ＝(p 12 ,q 12 )＝(8,10)，ξ 13 ＝(p 13 ,q 13 )＝(16,18)，ξ 14 ＝(p 14 ,q 14 )＝(24,26)，ξ 15 ＝(p 15 ,q 15 )＝(33,35)，ξ 21 ＝(p 21 ,q 21 )＝(2,5)，ξ 22 ＝(p 22 ,q 22 )＝(10,13)，ξ 23 ＝(p 23 ,q 23 )＝(20,23)，ξ 24 ＝(p 24 ,q 24 )＝(30,33)。
While periodic task T 1 And T 2 Is to reverse schedule xi -1 In particular to
Figure BDA0002071259860000137
Figure BDA0002071259860000141
Figure BDA0002071259860000142
Figure BDA0002071259860000143
Periodic task T 1 And T 2 The latest execution time set of (1) is recorded as
Figure BDA0002071259860000144
The set of expected end times is
Figure BDA0002071259860000145
The maximum usable time set is f' = ((0, 5), (10, 14), (16, 17), (20, 22), (24, 27), (32, 35)) (i.e., in the time of 0-40, (5, 7), (14, 16), (22, 24), (30, 32), (38, 40), (7, 10), (17, 20), (27, 30), (35, 38)) is removed.
Step3, at time 0, the task currently arriving has a periodic task schedule T 11 And T 21 Random task A 1 For periodic task T 11 And T 21 Step4 is executed; random task A 1 Waiting;
step4, at time 0 (since Step3 is a judgment Step, no time is consumed, and thus the system time is still 0 when this Step is executed), and the periodic task schedule T 11 And T 21 None reach T 11 And T 21 Latest execution time of (a)
Figure BDA0002071259860000146
And->
Figure BDA0002071259860000147
And no random task exists in the priority queue, the periodic task schedule T of the latest execution time is not reached 11 And T 21 Waiting for the latest execution time to arrive, and turning to Step3;
step3, at time 0, T 11 And T 21 The latest execution time is not reached, and the current time has random task A 1 Waiting, executing Step7;
step7, at time 0, no task is in the current priority queue, and the random task A is directly processed 1 Enqueue, go to Step8;
step8, at time 0, no task is currently executing, and selecting the first task A of the priority queue 1 Execution and transition to Step9, execution Step9 is divided into two cases:
step9 first case is performed: step9, at time 3, random task A 1 Ending the execution, wherein before the execution ending time, at the time 1, the currently arrived task has a random task A 2 ，A 3 Turning to Step3; step3, for random task A 2 ，A 3 Step7 is executed; step7, random task A a Time of availability S a Is that
Figure BDA0002071259860000148
Criticality C a Is that
Figure BDA0002071259860000149
Execution time E a Is->
Figure BDA00020712598600001410
Priority P a Is that
Figure BDA00020712598600001411
The weighted fuzzy set takes r= (0.2.0.6.0.2). A is that 2 Is->
Figure BDA00020712598600001412
Critical->
Figure BDA00020712598600001413
Execution time->
Figure BDA0002071259860000151
A 3 Is->
Figure BDA0002071259860000152
Critical->
Figure BDA0002071259860000153
Execution time
Figure BDA0002071259860000154
A 2 Decision set->
Figure BDA0002071259860000155
Then A 2 Priority P of (2) 2 Is->
Figure BDA0002071259860000156
A 3 Decision set->
Figure BDA0002071259860000157
Then A 3 Priority P2 of (2) is
Figure BDA0002071259860000158
No task is in the priority queue at this time, so task a will be random 3 Enqueue first priority queue, random task A 2 After the random task, go to step8; step8, at time 1, there is a random task A 1 Executing and waiting.
Step9 second case is performed: step9, at time 3, random task A 1 Execution ends, and the latest execution time set is not reached
Figure BDA0002071259860000159
Turning to step8; at time 3, no task is currently executing, and priority queue head task A is selected 3 Executing and turning to step9;
after the two cases are performed, the following is performed:
step9, at time 4, followingMission A 3 Execution ends, and the latest execution time set is not reached
Figure BDA00020712598600001510
At a certain time, go to Step8;
step8, at time 4, no task is currently executing, and the first task A of the priority queue is selected 2 Executing and turning to step9;
step9, random task A at time 5 2 The latest execution time set is reached in the execution process
Figure BDA00020712598600001511
At time 5, the random task a is suspended 2 And to take the random task A 2 Placing the first queue into the queue, and turning to step4;
step4, at time 5, periodic task T 11 Reaching its latest execution time
Figure BDA00020712598600001512
Turning to step5;
step5, at time 5, there is a periodic task T 11 Reaching its latest execution time
Figure BDA00020712598600001513
Executing periodic task T 11 And go to step6;
step6, at time 7, periodic task T 11 Is equal to its expected end time
Figure BDA00020712598600001514
And go to step4;
step4, at time 7, there is a periodic task T 21 Reaching its latest execution time
Figure BDA00020712598600001515
Turning to step5;
step5, at time 7, there is a periodic task T 21 Reaching its latest execution time
Figure BDA00020712598600001516
Executing periodic task T 21 And go to step6;
step6, at time 9, periodic task T 21 Execution ends without reaching its expected end time
Figure BDA0002071259860000161
Recording the actual end time, i.e. r 21 =9, phase difference time +.>
Figure BDA0002071259860000169
Idle time f=f' +f "= ((0, 5), (9, 14), (16, 17), (20, 22), (24, 27), (32, 35)), and go to Step4; the execution Step4 is divided into two cases:
the first case of Step4 is performed: at time 8, random task A 4 Reaching, turning to step3; step3, at time 8, the current task has a random task A 2 、A 4 Turning to step7; step7, at time 8, the priority queue has task A 2 Its priority P 2 Is that
Figure BDA0002071259860000162
Random task A 4 Is->
Figure BDA0002071259860000163
Critical->
Figure BDA0002071259860000164
Execution time->
Figure BDA0002071259860000165
Random task A 4 Decision set->
Figure BDA0002071259860000166
Then random task a 4 Priority P2 of +.>
Figure BDA0002071259860000167
So will random task A 4 Put on random task A 2 Then, turning to step8; step8, at time 8, there is currently a task T 21 Executing, random task A 2 Waiting;
the second case of Step4 is performed: step4, at time 9, the non-periodic task reaches its latest execution time, and there is a random task A in the priority queue 2 Turning to step8; step8, at time 9, no task is currently executing, and the first random task A of the priority queue is selected 2 Executing and turning to step9;
after the two cases are executed, the following procedure is then executed, and the following procedure is divided into two cases:
the first case of step9 is performed: at time 10, random task A 2 Execution ends, and at this execution end time 10, task a is randomized 5 Reaching, turning to step3; step3, at time 10, there is currently only random task A 5 Step7 is executed; step7, at time 10, no task is in the priority queue, and the random task A is directly processed 5 Enqueue head, go to step8; step8, at time 10, a task is currently executing, random task A 5 Waiting;
the second case of Step9 is performed: step9, at time 10, random task A 2 Execution ends, and the latest execution time set is not reached
Figure BDA0002071259860000168
At a certain time, go to step8; step8, at time 10, no task is currently executing, select priority queue head random task A 4 Executing and turning to step9; step9, at time 11, random task A 4 Execution ends, and the latest execution time set is not reached
Figure BDA0002071259860000171
At a certain time, go to step8; step8, at time 11, no task is currently executing, select priority queue head random task A 5 Executing and turning to step9;
after the two cases are performed, the following is performed:
step9, random task A at time 12 5 Execution ends, and the latest execution time set is not reached
Figure BDA0002071259860000172
Turning to step8;
step8, currently no task is executed, and no task exists in the priority queue, and then Step3 is performed;
(follow-up execution procedure is the same as above)
The working principle of the invention is as follows: firstly, a scheduling process and an inverse scheduling process of a periodic task are obtained according to an EDF algorithm, so that the maximum usable time is obtained; meanwhile, the time difference between the actual execution ending time and the estimated execution ending time of the periodic task is recorded as phase difference time; then, the available time, the criticality and the execution time of the random task are processed by the fuzzy set, and the priority of the random task is calculated; and finally, selecting the high-priority random task to execute by using the maximum available time and the phase difference time. The method can improve the submission rate of important random tasks, can ensure that the random tasks with high priority are executed preferentially, and reduces the probability of serious errors of a system caused by missing the deadline of the tasks.
While the present invention has been described in detail with reference to the drawings, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.

Claims (2)

1. A real-time task scheduling method based on an EDF algorithm and fuzzy sets is characterized in that: the method comprises the following steps:
step1, recording the periodic task set as pi= { T 1 ,T 2 ,...,T i ,..}, remembering the random task set as Γ= { a 1 ,A 2 ,...,A a ,..}, building a priority queue; wherein T is i The j-th schedule representing the i-th periodic task is denoted as T ij ，A a Represents the a-th random task, for random arbitraryTask A for task concentration a Setting the arrival time to G a ；
Step2, a scheduling process of the periodic task is obtained according to an EDF algorithm, an inverse scheduling process is obtained according to the scheduling process and the overcycle, and a latest execution time set, a predicted ending time set and a maximum movable time set of the periodic task are obtained according to the scheduling process and the inverse scheduling process;
the forward executing process of the periodic task set is obtained according to the EDF algorithm and is marked as a scheduling process xi, and each scheduling of each period of each task in the scheduling process xi of the periodic task set is marked as xi ij ＝(p ij ,q ij ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein xi ij Representing periodic task T in forward execution i P ij Representing xi ij Start execution time, q ij Representing xi ij End time of (2);
the reverse execution process of the periodic task set is recorded as a reverse scheduling process xi -1 Reverse scheduling process ζ of periodic task set -1 Each execution of each cycle of each task in (a) is noted as
Figure FDA0004179564690000011
Wherein->
Figure FDA0004179564690000012
Representing a reverse execution time period task T i Is (are) j-th scheduling of->
Figure FDA0004179564690000013
Representation->
Figure FDA0004179564690000014
Is the latest execution moment of->
Figure FDA0004179564690000015
Representation->
Figure FDA0004179564690000016
Is a predicted end time of (2);
Figure FDA0004179564690000017
The sum of j and k-1 is the periodic task T i The times of co-scheduling in an overcycle H, H is the overcycle, namely the least common multiple of all periodic tasks in a periodic task set;
the latest execution time set of the periodic task set is recorded as
Figure FDA0004179564690000018
The set of expected end times is noted as
Figure FDA0004179564690000019
The maximum movable time set is marked as f'; f' represents a time period remaining by removing the execution period of the inverse scheduling process in the super period;
step3, when the current task arrives, judging the type of the currently arrived task: if the multiple tasks which arrive at the same time comprise both periodic tasks and random tasks, executing a Step4 on all the periodic tasks, and waiting for all the random tasks; if only random tasks exist, executing Step7;
step4, if periodic task scheduling T exists at the current moment ij Reaching its latest execution time
Figure FDA00041795646900000110
Go to Step5;
if the periodic task schedule T does not exist at the current moment ij Reaching its latest execution time
Figure FDA00041795646900000111
And if random tasks exist in the priority queue, the process goes to Step8;
if the periodic task schedule T does not exist at the current moment ij Reaching the latest execution time
Figure FDA0004179564690000021
And no random task exists in the priority queue, the latest execution time is not reachedThe scheduled task waits for the latest execution time to arrive, and the process goes to Step3;
in the executing process of Step4, if the task arrives at the current moment and before the current moment, the Step3 needs to be synchronously executed;
step5, if the arrival time of a schedule of a task with one cycle is equal to the latest execution time, executing the schedule T ij And go to Step6;
if the arrival time of a certain schedule with a plurality of periodic tasks is equal to the corresponding latest execution time, randomly selecting one schedule T ij Executing, terminating other periodic task scheduling, and turning to Step6;
step6, if periodic task scheduling T ij Is the actual end time r of (2) ij Equal to its estimated end time
Figure FDA0004179564690000022
Turning to Step4;
if periodic task schedule T ij Is the actual end time r of (2) ij Not reaching its expected end time
Figure FDA0004179564690000023
Recording the current execution ending time as the actual ending time r ij And update the phase difference time +.>
Figure FDA0004179564690000024
And an idle time f=f' +f ", then go to Step4;
if periodic task schedule T ij At its expected end time
Figure FDA0004179564690000025
If not, the scheduling task is terminated and the actual end time r is made ij Equal to its expected end time->
Figure FDA0004179564690000026
Then go to Step4;
wherein, the jth scheduling T of the ith periodic task executed in Step5 ij The actual end time is denoted as r ij Jth schedule T of ith periodic task ij Is (are) the expected end time of (a)
Figure FDA0004179564690000027
And the actual end time r ij The time between them is recorded as the phase difference time
Figure FDA0004179564690000028
The sum of the maximum movable time and the phase difference time is denoted as the idle time, i.e. f=f' +f ";
step7, if the random task is one and no task exists in the current priority queue, directly arranging the random task into the head of the priority queue; otherwise, calculating the priorities of all the random tasks according to the fuzzy sets of the available time, the fuzzy sets of the key degree and the fuzzy sets of the execution time of the random tasks, and inserting priority queues according to the priorities; go to Step8;
step8, waiting if a task is being executed at the current moment;
if no task is executing at the current moment and random tasks exist in the priority queue, selecting the random task at the head of the queue to execute, and switching to Step9;
if no task is executing at the current moment and no random task exists in the priority queue, the process goes to Step3;
step9, if random task A a The execution end time equals the latest execution time set
Figure FDA0004179564690000031
At some point in the process, terminating the random task A a And go to Step4;
if it is random task A a Execution end time of not reaching latest execution time set
Figure FDA0004179564690000032
At a certain time, go to Step8;
if it is random task A a The latest execution time set is reached in the execution process
Figure FDA0004179564690000033
At some point in time, the random task A is aborted a Placing the first priority queue, and turning to Step4;
in the execution process of Step9, if the task arrives at and before the execution end time, step3 needs to be executed synchronously.
2. The EDF algorithm and fuzzy set based real-time task scheduling method of claim 1, wherein: step7 specifically comprises the following steps:
step7.1: computing fuzzy sets of available time for random tasks
Will random task A a Is G a Scheduling T to the latest one cycle task ij Latest execution time of (a)
Figure FDA00041795646900000317
The time of (a) is recorded as random task A a Is available for time S a I.e. +.>
Figure FDA0004179564690000034
Definition of available time in ambiguous language is recorded +.>
Figure FDA0004179564690000035
Wherein v is more than or equal to 1 and less than or equal to m, and the argument is +.>
Figure FDA0004179564690000036
Then the available time S a The fuzzy set of (2) is the formula (1):
Figure FDA0004179564690000037
wherein "+" denotes the availability time S a In the field of discussion
Figure FDA0004179564690000038
The whole body is arranged on the upper part;
Figure FDA0004179564690000039
Representation->
Figure FDA00041795646900000310
And->
Figure FDA00041795646900000311
Corresponding relation of (3);
Figure FDA00041795646900000312
Is the availability time S a Is a membership function of S a Belonging to->
Figure FDA00041795646900000313
The extent of (3);
time of availability S a The normal distribution is met, so the membership function is expressed as formula (2):
Figure FDA00041795646900000314
wherein c (v) is a function of determining the central position of the membership function, i.e
Figure FDA00041795646900000315
Sigma is a constant determining the width of the curve, determined by the superseriod H and m together, i.e. +.>
Figure FDA00041795646900000316
Step7.2: fuzzy set for calculating criticality of random task
Will random task A a The criticality of (C) a Definition in ambiguous language is noted as
Figure FDA0004179564690000041
Designating the discourse as +.>
Figure FDA0004179564690000042
Then random task a a Criticality C of (2) a The fuzzy set of (2) is the formula (3):
Figure FDA0004179564690000043
wherein "+" represents criticality C a In the field of discussion
Figure FDA0004179564690000044
The whole body is arranged on the upper part;
Figure FDA0004179564690000045
Representation->
Figure FDA0004179564690000046
And->
Figure FDA0004179564690000047
Corresponding relation of (3);
Figure FDA0004179564690000048
Is criticality C a Is a membership function of (C) a Belonging to->
Figure FDA0004179564690000049
The extent of (3);
criticality C a The membership function of (2) is expressed as formula (4):
Figure FDA00041795646900000410
wherein,,
Figure FDA00041795646900000411
Figure FDA00041795646900000412
as the center point, C z Representing random task A z W represents the total number of random tasks participated in when Step7 is executed this time; sigma is a constant determining the width of the curve, determined by the superseriod H and m together, i.e. +.>
Figure FDA00041795646900000413
Step7.3: computing fuzzy sets of execution times for random tasks
Random task A a Execution time E of (2) a Definition in ambiguous language is noted as
Figure FDA0004179564690000051
Wherein v is more than or equal to 1 and less than or equal to m, and the discourse domain is marked as +.>
Figure FDA0004179564690000052
Then random task a a Execution time E of (2) a The fuzzy set of (2) is the formula (5):
Figure FDA0004179564690000053
wherein "+" denotes execution time E a In the field of discussion
Figure FDA0004179564690000054
The whole body is arranged on the upper part;
Figure FDA0004179564690000055
Representation->
Figure FDA0004179564690000056
And->
Figure FDA0004179564690000057
Corresponding relation of (3);
Figure FDA0004179564690000058
Is execution time E a Is a membership function of (E) a Belonging to->
Figure FDA0004179564690000059
The extent of (3);
record execution time E a Is P (E) a ) Random task A a E of execution time of (2) a The membership of (2) is:
Figure FDA00041795646900000510
wherein,,
Figure FDA00041795646900000511
Figure FDA00041795646900000512
as the center point E z Representing random task A z Execution time of P (E) z ) Representing execution time E z Probability of (2);
step7.4: computing priority of random tasks
Random task A a Importance of (1) is determined by priority P a Determining the priority P a The comment set is defined and recorded as m fuzzy languages
Figure FDA0004179564690000061
Wherein->
Figure FDA0004179564690000062
And priority P a From randomTask A a Is determined together with the fuzzy set of the available time, the fuzzy set of the criticality and the fuzzy set of the execution time; thus random task A a The priority factor set of (c) is x= { "availability time", "criticality", "execution time" }, and its fuzzy relation matrix is expressed as formula (7):
Figure FDA0004179564690000063
because the influence of the fuzzy set of available time, the fuzzy set of key degree and the fuzzy set of execution time on the priority is different, the fuzzy sets are given different weights, and the fuzzy set is recorded as a weighted fuzzy set R= (R) 1 ,R 2 ,R 3 ) Wherein R is 1 +R 2 +R 3 ＝1；
By synthesizing a decision set from a and R, the decision set is represented by formula (8):
Figure FDA0004179564690000064
wherein,,
Figure FDA0004179564690000065
the fuzzy synthesis max-min is represented, the fuzzy operator 'Λ' adopts small-taking operation, and the 'V' adopts large-taking operation;
priority P in decision set B a The maximum value in the decision set B corresponds to the subset of the comment set as the priority of the random task.
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