CN109918181A - Mixing critical system task Schedulability Analysis method based on the worst response time - Google Patents
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Abstract
The mixing critical system task Schedulability Analysis method based on the worst response time that the present invention provides a kind of, the present invention provides double safety-critical (DM) task models of mixing first, and redefines to system action；The variation of duty cycle, priority when in conjunction with the conversion of system safety-critical grade, provides the worst response time derivation process of mixing key task and task-set schedulability theorem.Finally, examples comparative is analysis shows effectiveness of the invention.When safety-critical grade is promoted, worst response time analysis method proposed by the present invention can provide better service under the premise of guaranteeing HC task schedulability for LC task；Analytic process of the invention more simplifies, and shorter task average response time, higher CUP resource utilization are able to maintain higher, more stable throughput of system.
Description
Technical field
The present invention relates to computer field, especially a kind of safety-critical task dispatch analysis method.
Background technique
With the complication of embedded system demand and the development of multi-core technology, the mixing key system based on multi-core platform
System (MCS) comes into being.In order to guarantee the safety of system, need to complete unified tune of the different safety-critical grade tasks between multicore
Degree.Schedulability Analysis plays a crucial role in mixing key task scheduling.And it is existing most popular based on response
The Schedulability Analysis method of time is set forth in paper " Response-time analysis of mixed criticality
Systems with pessimistic frequency specification ", it is published in IEEE International
Conference on Embedded and Real-Time Computing Systems and Applications 2014:
237-246.Fixed-priority Scheduling Strategy analysis method is described in paper, this method analyzes fixed preferential by given task
Grade realizes safety-critical task scheduling and runtime in the iterative task that scheduling is triggered by the external event of unknown definite frequency
Between balance between high resource utilization, system needs can completed to call in the system based on lower security key task
Task schedule effect, while the utilization rate of CPU also very sufficiently.But after the promotion of safety-critical grade, high safety key task
Quantity increases, and is handled by the high safety key task that this method CPU always selects priority high, at lower security key task
Reason is excessively passive, is easy to cause cpu resource waste, reduces lower security key task scheduling success ratio.
Summary of the invention
For overcome the deficiencies in the prior art, the present invention provides a kind of mixing critical system based on the worst response time times
Business Schedulability Analysis method.
Steps are as follows for the realization that the technical solution adopted by the present invention to solve the technical problems is:
Step 1: by safety-critical task wiIt is expressed as five-tupleForm；
Wherein, wi: indicate i-th of key task, i is natural number, LiExpression task wiSafety-critical rank, Li∈
{ LO, HI }, LO indicate minimum safe key rank, and HI indicates highest safety-critical rank, SiIt is task wiRelease time, i.e.,
Arrival time,Expression task wiThe worst execution time in different modes, wherein * ∈ { LO, HI }, represents current system
Safety-critical rank,Expression task wiPeriod under different safety-critical modes,Indicate different safety-critical modes
Lower wiPriority,Expression task wiPriority be higher than task wj, key task refers to very heavy during system operation
Wanting for task；
Step 2: with W={ w1,w2,...wnIndicate that there are the double safety-critical task collection of the mixing of n DM task, wherein
DM is to mix double key tasks；
Step 3: the operating system that scheduling mixes double safety-critical tasks is executed since LO-cri mode, LO-cri is
Lower security critical level mode；
Step 4: under LO-cri mode, each task wiAccording to the period under LO-cri modeOperation is discharged,
WithExpression task wiJ-th of operation of release, task wiRelease time be denoted asIt is denoted as between absolutely extremely prescribing a time limitProcessor resource, the operation of processor highest priority per treatment are fought in all operations；
Step 5: iterating to calculate the worst response time by formula (1) under LO-cri mode:
Wherein,Expression task wiWorst response time under LO-cri mode, hp*(i) indicate excellent under * mode
First grade is higher than wiSet of tasks, the hp of same taskHI(i) and hpLO(i) might not be identical, i.e., if current all tasks
Safety-critical rank when all meet high safety critical mode requirement two set be identical, remaining situation not phase
Together.
Step 6: under LO-cri mode, if the actual run time of LC task and HC task is no more than current mould
Under formula it is absolute it is dead in limited time between, into step 7 is executed, LC task and HC task are all with p at this timeLOPeriod discharges operation；If HC
Task actual execution time be more than its under LO-cri mode it is absolute it is dead in limited time between, jump to step 9 execution；
Step 7: DM task-set is judged, if all tasks in task-set all meetI.e. all tasks
The worst response time be no more than period of the current task under LO-cri mode, then the task-set is schedulable；
Step 8: being directed to the schedulable task-set of step 7, judge whether crucial (LC) task of lower security is overtime, if LC
The executions time of task release operation have exceeded current LC task it is absolute it is dead in limited time between, will terminate immediately execute it is LC current
Business；
Step 9: when high safety key HC task actual execution time be more than its under LO-cri mode it is absolute it is dead in limited time
Between, system is high safety critical level by two lifting process by lower security critical level, and the lifting process is to be first switch to
HC/LC cross-operation state, secondly each task is according to the η under HI-cri modeHIPriority is adjusted, after lifting process
The conversion moment be denoted as t*, the HC/LC cross-operation state, which is respectively as follows: HC cross-operation, indicates being discharged by HC for task,
It is equivalent in the state waited, is restored to HC task status when being called again；LC cross-operation expression is discharged by LC
Task, be equivalent in wait state, again be called when be restored to LC task status；
The detailed step of the response time of two kinds of cross-operation under high safety critical mode are as follows:
1) the LC cross-operation response time of high safety critical level mode is analyzed；
If there isAndTask wjThe operation of release can be to task wiThe cross-operation of release
The worst execution time have an impact, the influence show as safety-critical mode conversion moment t*And it is divided into before and later two
Point, t*Before and t*W laterjIn number of jobs be limited to respectivelyWithThen wjTo wiFriendship
Pitch the worst response time of operationInfluence constraint condition it is as follows:
If there isAndwiCross-operation the worst response time only in t*Before by
To LC task wjInfluence, the constraint condition of the influence is formula (3):
IfAndLC task wjOnly in t*W is influenced lateriThe worst sound of cross-operation
Between seasonable, the constraint condition of the influence is formula (4):
2) the HC cross-operation response time of high safety critical level mode is analyzed；
IfAndWhen, no matter it is in LO-cri mode or HI-cri mode, Gao You
The HC task w of first gradejT can be converted in mode*Front-to-back effect wiCross-operation worst-case response time calculate, the pact of the influence
Beam condition is formula (5):
IfAndWhen, wiThe cross-operation of release is only in t*Before by HC task wj
Influence constraint condition are as follows:
IfAndWhen, HC task wjOnly in mode switch instant t*W is influenced lateriIt hands over
The response time for pitching operation calculates, the constraint condition of influence are as follows:
Step 10: calculating task wiCross-operation the worst response time are as follows:
Step 11: t*The state after operation later is known as routine work state, and system is promoted by LO-cri mode
After HI-cri mode, if be not present in system there is no the operation for crossing HI-cri mode from LO-cri mode
Cross-operation, title system enter stable HI-cri operational mode, only exist the routine work of DM task in system at this time, use N
Represent routine work state；
Task wiThe worst response time for discharging operation is only influenced by high-priority task, usesIt indicates, calculates
Formula is as follows:
Step 12: adding the routine work response time to obtain high safety critical mode by the cross-operation worst response time
Lower task wiThe worst response time:
Step 13: being respectively comparedWithAndWithIfAndSo should
Task-set be it is schedulable, otherwise terminate immediately and execute current HI task.
When being promoted the beneficial effects of the present invention are safety-critical grade, worst response time analysis method proposed by the present invention
Better service can be provided for LC task under the premise of guaranteeing HC task schedulability；Analytic process of the invention is more
Simplify, shorter task average response time, higher CUP resource utilization are able to maintain higher, more stable system throughput
Amount.
Specific embodiment
With embodiment, the present invention is further described below.
After mixing critical system safety-critical grade is promoted, due to handling lower security key task passiveness, lead to task
The problems such as worst response time analysis is insufficient, inaccurate, and the CPU null cycle is long, the present invention is mixed as point of penetration
The research of key task dispatching method.It is proposed a kind of mixing critical system task schedule analysis method based on the worst response time
(ERTA).Double safety-critical (DM) task models of mixing are provided first, and system action is redefined；It is closed safely in conjunction with system
The variation of duty cycle, priority when bond order is converted provides the worst response time derivation process of mixing key task and task-set
Schedulability theorem.Finally, examples comparative is analysis shows effectiveness of the invention.
Step 1: by safety-critical task wiIt is expressed as five-tupleForm；
Wherein, wi: indicate i-th of key task, i is natural number, LiExpression task wiSafety-critical rank, Li∈
{ LO, HI }, LO indicate minimum safe key rank, and HI indicates highest safety-critical rank, SiIt is task wiRelease time, i.e.,
Arrival time,Expression task wiThe worst execution time in different modes, wherein * ∈ { LO, HI }, represents current system
Safety-critical rank,Expression task wiPeriod under different safety-critical modes,Indicate different safety-critical modes
Lower wiPriority,Expression task wiPriority be higher than task wj, key task refers to very heavy during system operation
Wanting for task；
Step 2: with W={ w1,w2,...wnIndicate that there are the double safety-critical task collection of the mixing of n DM task, wherein
DM is to mix double key tasks；
Step 3: the operating system that scheduling mixes double safety-critical tasks is executed since LO-cri mode, LO-cri is
Lower security critical level mode；
Step 4: under LO-cri mode, each task wiAccording to the period under LO-cri modeOperation is discharged,
WithExpression task wiJ-th of operation of release, task wiRelease time be denoted asIt is denoted as between absolutely extremely prescribing a time limitProcessor resource, the operation of processor highest priority per treatment are fought in all operations；
Step 5: iterating to calculate the worst response time by formula (1) under LO-cri mode:
Wherein,Expression task wiWorst response time under LO-cri mode, hp*(i) indicate excellent under * mode
First grade is higher than wiSet of tasks, the hp of same taskHI(i) and hpLO(i) might not be identical, i.e., if current all tasks
Safety-critical rank when all meet high safety critical mode requirement two set be identical, remaining situation not phase
Together.
Step 6: under LO-cri mode, if the actual run time of LC task and HC task is no more than current mould
Under formula it is absolute it is dead in limited time between, into step 7 is executed, LC task and HC task are all with p at this timeLOPeriod discharges operation；If HC
Task actual execution time be more than its under LO-cri mode it is absolute it is dead in limited time between, jump to step 9 execution；
Note: HC: high safety key task.
LC: lower security key task.
HI-cri: high safety critical level mode.
LO-cri: lower security critical level mode.
Step 7: DM task-set is judged, if all tasks in task-set all meetI.e. all tasks
The worst response time be no more than period of the current task under LO-cri mode, then the task-set is schedulable；
Step 8: being directed to the schedulable task-set of step 7, judge whether crucial (LC) task of lower security is overtime, if LC
The executions time of task release operation have exceeded current LC task it is absolute it is dead in limited time between, will terminate immediately execute it is LC current
Business；
Step 9: when high safety key HC task actual execution time be more than its under LO-cri mode it is absolute it is dead in limited time
Between, system is high safety critical level by two lifting process by lower security critical level, and the lifting process is to be first switch to
HC/LC cross-operation state, secondly each task is according to the η under HI-cri modeHIPriority is adjusted, after lifting process
The conversion moment be denoted as t*, the HC/LC cross-operation state, which is respectively as follows: HC cross-operation, indicates being discharged by HC for task,
It is equivalent in the state waited, is restored to HC task status when being called again；LC cross-operation expression is discharged by LC
Task, be equivalent in wait state, again be called when be restored to LC task status；
The detailed step of the response time of two kinds of cross-operation under high safety critical mode are as follows:
1) the LC cross-operation response time of high safety critical level mode is analyzed；
If there isAndTask wjThe operation of release can be to task wiThe cross-operation of release
The worst execution time have an impact, the influence show as safety-critical mode conversion moment t*And it is divided into before and later two
Point, t*Before and t*W laterjIn number of jobs be limited to respectivelyWithThen wjTo wiFriendship
Pitch the worst response time of operationInfluence constraint condition it is as follows:
If there isAndwiCross-operation the worst response time only in t*Before by
To LC task wjInfluence, the constraint condition of the influence is formula (3):
IfAndLC task wjOnly in t*W is influenced lateriThe worst sound of cross-operation
Between seasonable, the constraint condition of the influence is formula (4):
2) the HC cross-operation response time of high safety critical level mode is analyzed；
IfAndWhen, no matter it is in LO-cri mode or HI-cri mode, Gao You
The HC task w of first gradejT can be converted in mode*Front-to-back effect wiCross-operation worst-case response time calculate, the pact of the influence
Beam condition is formula (5):
IfAndWhen, wiThe cross-operation of release is only in t*Before by HC task wj
Influence constraint condition are as follows:
IfAndWhen, HC task wjOnly in mode switch instant t*W is influenced lateriIt hands over
The response time for pitching operation calculates, the constraint condition of influence are as follows:
Step 10: calculating task wiCross-operation the worst response time are as follows:
Step 11: t*The state after operation later is known as routine work state, and system is promoted by LO-cri mode
After HI-cri mode, if be not present in system there is no the operation for crossing HI-cri mode from LO-cri mode
Cross-operation, title system enter stable HI-cri operational mode, only exist the routine work of DM task in system at this time, use N
Represent routine work state；
Task wiThe worst response time for discharging operation is only influenced by high-priority task, usesIt indicates, calculates
Formula is as follows:
Step 12: adding the routine work response time to obtain high safety critical mode by the cross-operation worst response time
Lower task wiThe worst response time:
Step 13: being respectively comparedWithAndWithIfAndSo should
Task-set be it is schedulable, otherwise terminate immediately and execute current HI task.
The invention reside in analytic processes more to simplify, shorter task average response time, the higher CUP utilization of resources
Rate is able to maintain higher, more stable throughput of system.
In order to illustrate the present invention propose worst response time can guarantee HC task meet it is schedulable under the premise of, improve LC
The schedulability of task, the present invention is by way of instance analysis, by ERTA analysis method and the " A being widely used at present
Wait-Free Multi-Word Compare-and-Swap Operation " in the AMC-rtb method mentioned compare.
Firstly, providing following mixing key task collection W={ w1,w2,w3, wherein task w1For LC task, task w2And w3Appoint for HC
Business.The time response of each task is as shown in the table:
Task-set time parameter
Worst-case response time under different models
Worst response time calculation formula of the AMC-rtb under HI-cri mode and LO-cri mode by formula (11) and
Formula (12) provides:
Under LO-cri mode, ERTA method of the invention is identical as AMC-rtb method calculation formula, in HI-cri mould
Calculation formula is formula (13) under formula:
According to above formula, worst response time calculating is carried out to three tasks respectively, calculated result see the table below.
Worst-case response time under different models
As seen from the above table, under LO-cri mode, AMC-rtb analysis method and ERTA analysis method of the invention are utilized
It can guarantee the schedulability of three tasks, and the worst response time of each task is identical, priority is identicalAfter system safety-critical grade is promoted, AMC-rtb analysis method, in order to guarantee HC task execution time,
The LC task of highest priority is taken into passive strategy, is directly abandoned, it is believed that its non-scheduling.On the contrary, being proposed using the present invention
ERTA method is analyzed, and allows LC task w at this time1It is executed under HI-cri mode, and calculates each task most
Poor response time, wherein task w1And w2The worst response time it is identical, but task w2Period is 9, w1Period is 28, so logical
Priority orders readjustment is crossed, guarantees that three tasks all meet schedulability condition, at this time the priority orders of three tasks
Become
In summary, when safety-critical grade is promoted, worst response time analysis method proposed by the present invention can protected
Under the premise of demonstrate,proving HC task schedulability, better service is provided for LC task.
Compared with the prior art, the invention has the following advantages: analytic process more simplifies, shorter task average response
Time, higher CUP resource utilization, it is able to maintain higher, more stable throughput of system.
Claims (1)
1. a kind of mixing critical system task Schedulability Analysis method based on the worst response time, it is characterised in that including under
State step:
Step 1: by safety-critical task wiIt is expressed as five-tupleForm；
Wherein, wi: indicate i-th of key task, i is natural number, LiExpression task wiSafety-critical rank, Li∈ { LO, HI },
LO indicates minimum safe key rank, and HI indicates highest safety-critical rank, SiIt is task wiRelease time, i.e. arrival time,Expression task wiThe worst execution time in different modes, wherein * ∈ { LO, HI }, represents the safety-critical of current system
Rank,Expression task wiPeriod under different safety-critical modes,Indicate w under different safety-critical modesiIt is preferential
Grade,Expression task wiPriority be higher than task wj, key task refer to system operation during very important task；
Step 2: with W={ w1,w2,...wnIndicating the mixing pair safety-critical task collection with n DM task, wherein DM is
Mix double key tasks；
Step 3: the operating system that scheduling mixes double safety-critical tasks is executed since LO-cri mode, LO-cri is low peace
Full critical level mode；
Step 4: under LO-cri mode, each task wiAccording to the period under LO-cri modeOperation is discharged, is used
Expression task wiJ-th of operation of release, task wiRelease time be denoted asIt is denoted as between absolutely extremely prescribing a time limitIt is all
Processor resource, the operation of processor highest priority per treatment are fought in operation；
Step 5: iterating to calculate the worst response time by formula (1) under LO-cri mode:
Wherein,Expression task wiWorst response time under LO-cri mode, hp*(i) indicate that priority is high under * mode
In wiSet of tasks, the hp of same taskHI(i) and hpLO(i) might not be identical, i.e., if the safety of current all tasks
Two set are identical when crucial rank all meets high safety critical mode requirement, remaining situation is all different；
Step 6: under LO-cri mode, if the actual run time of LC task and HC task is no more than under present mode
It is absolute it is dead in limited time between, into step 7 is executed, LC task and HC task are all with p at this timeLOPeriod discharges operation；If HC task
Actual execution time be more than its under LO-cri mode it is absolute it is dead in limited time between, jump to step 9 execution；
Step 7: DM task-set is judged, if all tasks in task-set all meetI.e. all tasks it is worst
Response time is no more than period of the current task under LO-cri mode, then the task-set is schedulable；
Step 8: being directed to the schedulable task-set of step 7, judge whether crucial (LC) task of lower security is overtime, if LC task
The executions time of release operation have exceeded current LC task it is absolute it is dead in limited time between, the current LC task of execution will be terminated immediately；
Step 9: when high safety key HC task actual execution time be more than its under LO-cri mode it is absolute it is dead in limited time between,
System is high safety critical level by two lifting process by lower security critical level, and the lifting process is to be first switch to HC/
LC cross-operation state, secondly each task is according to the η under HI-cri modeHIPriority is adjusted, after lifting process
The conversion moment is denoted as t*, the HC/LC cross-operation state, which is respectively as follows: HC cross-operation, indicates being discharged by HC for task, phase
When in wait state again be called when be restored to HC task status；LC cross-operation expression is discharged by LC
Task is equivalent in the state waited, is restored to LC task status when being called again；
The detailed step of the response time of two kinds of cross-operation under high safety critical mode are as follows:
1) the LC cross-operation response time of high safety critical level mode is analyzed；
If there isAndTask wjThe operation of release can be to task wiThe cross-operation of release is most
The difference execution time has an impact, which shows as safety-critical mode conversion moment t*And it is divided into before and later two parts, t*
Before and t*W laterjIn number of jobs be limited to respectivelyWithThen wjTo wiIntersection make
The worst response time of industryInfluence constraint condition it is as follows:
If there isAndwiCross-operation the worst response time only in t*Before by LC
Task wjInfluence, the constraint condition of the influence is formula (3):
IfAndLC task wjOnly in t*W is influenced lateriWhen the worst response of cross-operation
Between, the constraint condition of the influence is formula (4):
2) the HC cross-operation response time of high safety critical level mode is analyzed；
IfAndWhen, no matter it is in LO-cri mode or HI-cri mode, high priority
HC task wjT can be converted in mode*Front-to-back effect wiCross-operation worst-case response time calculate, the constraint condition of the influence
For formula (5):
IfAndWhen, wiThe cross-operation of release is only in t*Before by HC task wjShadow
Loud constraint condition are as follows:
IfAndWhen, HC task wjOnly in mode switch instant t*W is influenced lateriIntersect and makees
The response time of industry calculates, the constraint condition of influence are as follows:
Step 10: calculating task wiCross-operation the worst response time are as follows:
Step 11: t*The state after operation later is known as routine work state, and system is promoted to HI- by LO-cri mode
After cri mode, if there is no the operations for crossing HI-cri mode from LO-cri mode in system, i.e., there is no intersect to make
Industry, title system enter stable HI-cri operational mode, only exist the routine work of DM task in system at this time, are represented with N normal
Advise job state；
Task wiThe worst response time for discharging operation is only influenced by high-priority task, usesIt indicates, calculation formula
It is as follows:
Step 12: adding the routine work response time to obtain high safety critical mode lower by the cross-operation worst response time
Be engaged in wiThe worst response time:
Step 13: being respectively comparedWithAndWithIfAndSo task-set
Be it is schedulable, otherwise terminate immediately and execute current HI task.
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