CN105893148A - Low-energy-consumption aporadic task scheduling method based on RM strategy - Google Patents

Abstract

The invention discloses a low-energy-consumption aporadic task scheduling method based on an RM strategy. The method comprises the steps that the initial priority and the execution priority of tasks are allocated before task set scheduling; the largest blocking time of the tasks and the processor demands under the worst condition are calculated; task sets are partitioned into the task set with the resource demands and the task set without the resource demands, the lowest running speed of the task set with the resource demands is calculated, and the lowest running speed of the task set without the resource demands is calculated; the running speed of the task sets in the off-line stage is calculated; an idle time management queue is built, the idle time of the tasks is calculated, the running speed of a processor is regulated through a DVS technique, and it is guaranteed that the final running speed is not lower than the key speed. According to the method, the condition that a universal power consumption model, the execution time of the tasks and the processor speed have the non-linear relationship and the processor speed switching expense are taken into account, the DVS technique and a DPM technique are combined, and therefore the energy consumption is greatly reduced.

Description

A kind of accidental task low energy consumption dispatching method based on RM strategy

Technical field

The present invention relates to the Real-Time Scheduling of the accidental task in embedded system field, particularly to a kind of idol based on RM strategy Send out task low energy consumption dispatching method.

Background technology

Embedded device application in life is more and more extensive, common embedded device such as mobile phone, MP3, IPAD, pen Remembering this computer etc., these equipment are all to use battery to power, and due to limited battery capacity, the energy consumption provided also is limited, right For these portable embedded devices, energy consumption problem highlights the most very much.Reduce energy consumption can not only the use of extension device time Between, reduce the caloric value of equipment；And the replacement cycle of battery can be reduced.Therefore, low energy consumption becomes setting of embedded device Meter target.Processor is the core of embedded device, and its power consumption overturns the dynamic power consumption and leakage current caused essentially from frequency The quiescent dissipation formed.Dynamic power management (DPM) technology and dynamic voltage regulation (DVS) technology are to reduce system energy consumption at present Common technology.DPM technology is mainly closed by the equipment that would sit idle for and is reduced system energy consumption.And DVS technology is mainly according to being The load of system dynamically regulates processor speed and reduces system energy consumption.

Many researchers is by classical Real-Time Scheduling is theoretical and Low-power Technology combines at present, solves the energy consumption of system Problem.But these researchs are primarily upon periodic task model and hybrid task model.At present accidental task model is ground Study carefully relatively fewer.Existing accidental task low energy consumption dispatching method, utilizes EDF strategy scheduler task, it is adaptable to dynamic priority System, ignores quiescent dissipation and the processor speed handover overhead of processor.Additionally, these methods assume the execution time of task Linear with processor speed.

Summary of the invention

It is an object of the invention to overcome the deficiencies in the prior art, propose a kind of accidental task low energy consumption based on RM strategy Dispatching method, RM (rate monotonic) strategy is Fixed-priority Scheduling Strategy strategy, and the priority of task by the cycle of task, (release by minimum Put interval) determine, the cycle (minimum release interval) is the least, and its priority is the highest, and the priority of task of high priority performs.The party Method is applicable to static priority tasks system, it is contemplated that general power consumption model, the execution time of task become with processor speed Non-linear relation situation, processor speed handover overhead, in combination with DVS technology and DPM technology.

The technical solution adopted for the present invention to solve the technical problems is:

A kind of accidental task low energy consumption dispatching method based on RM strategy, comprises the steps:

The initial priority of distribution task and execution priority；

Processor demand under the maximum obstruction time of calculating task and worst case；

Task-set being divided into the task-set of resource requirement and does not has the task-set of resource requirement, calculating respectively has resource Demand task-set and do not have the minimum operation speed of resource requirement task-set；

Calculate the speed of service of task-set off-line phase；

Set up free time management queue；Recovery task completes the free time produced ahead of time, will distribute to free time The task that current time queue medium priority is the highest, the computation processor current time speed of service；Processor current time is transported Line speed compares with the critical speed preset, and utilizes the DVS technology regulation processor speed of service to guarantee that it is not less than key Speed.

Initial priority and the execution priority of described distribution task include:

According to the initial priority of RM strategy distribution task, the minimum release interval of task is the least, and its initial priority is more High；

Task-set is divided into resource requirement and there is no the task subset of resource requirement；

Calculate the maximum in all initial priority sharing same resource tasks；

If task belongs to not having in resource requirement task subset of task, distribute its execution priority equal to initial priority Level；If task belongs to having in resource requirement task subset of task, distribute its execution priority all shared same equal to described Maximum in the initial priority of resource tasks.

In processor demand step under the maximum obstruction time of described calculating task and worst case, task T_iMaximum Blocking time B (T_i) it is expressed as:

$B\left(T_i\right)=\underset{\∀j,{\mathrm{EP}}_j\≥{\mathrm{IP}}_i>{\mathrm{IP}}_j}{\max }\left\{e_j\right|r_j=k\}$

Wherein, IP_iExpression task T_iInitial priority, EP_jAnd IP_jRepresent task T respectively_jExecution priority and initial Priority, e_jExpression task T_jThe execution time under worst case, r under maximum processor speed_jExpression task T_jResource need Asking, k is integer, and its span is 1≤k≤m, and m represents the number of task sharing resource；

Task T_iProcessor demand D under interval [0, L] worst case_0,LIt is expressed as:

Wherein, wherein e_iExpression task T_iThe execution time under worst case under maximum processor speed, L is more than 0 Real number, its value isRepresent and use resourceAll task minimums release interval, p_iExpression task T_i? Little release interval, r_iExpression task T_iResource requirement.

Described task-set it be divided into the task-set of resource requirement and there is no the task-set of resource requirement, and calculating respectively There is resource requirement task-set and do not have the minimum operation speed of resource requirement task-set to include:

Task-set is divided into the task-set of resource requirement and there is no the task-set of resource requirement；

There is minimum operation speed LS of resource requirement task-set_RTI () is according to the processor need under the worst case of task-set Ask calculating, represent by equation below:

${\mathrm{LS}}_{RT}\left(i\right)=\underset{P_{r_i}<L<p_i}{Max}\left(S_{RT}\right(i,L\left)\right)$

Wherein, S_RT(i, L) indicates that the task-set of resource requirement meets the minimum of its deadline in all tasks of moment L The speed of service, its value isExpression task T_jHolding under worst case The row time, p_jExpression task T_jMinimum release interval；

There is no minimum operation speed S of the task-set of resource requirement_NRTI () calculates according to the load of task-set, with following public Formula represents:

$S_{NRT}\left(i\right)=\underset{\underset{T_j\&NotElement;DTS}{j=i+1}}{\overset{n}{\&Sigma;}}\frac{e_j}{p_j\&CenterDot;F_c\left(n\right)}$

Wherein, DTS represents the task-set postponing release, and the interval of each task release time in DTS is both greater than it Little release interval, F_cN () represents the utilization rate upper bound that RM strategy scheduler task collection is feasible.

The speed of service equation below of described calculating task-set off-line phase represents:

Wherein, S_lubI () represents the accidental task-set minimum speed of service in interval [0, L], represent by equation below:

$S_{\mathrm{lub}}\left(i\right)={\mathrm{LS}}_{RT}\left(i\right)+S_{NRT}(i,L),P_{r_i}<L<p_i.$

Described free time represents by equation below:

$ST=\underset{i=1}{\overset{n}{\&Sigma;}}(W_i=0|U_i-{\mathrm{\&tau;}}_i)$

Wherein, W_iExpression task T_iResidue under worst case performs time, U_iExpression task T_iResidue perform the time, τ_i Represent processor speed handover overhead before this moment.

The described computation processor current time speed of service includes:

Computation processor current time speed of service S, wherein

By itself and speed S_sfpsasrCompare；If S > S_sfpsasr, S=S is set_sfpsasr；The most described S keeps constant.

Described speed S_sfpsasrComputational methods are as follows:

If during the processor free time, arranging S_sfpsasr=S_min, described S_minFor processor minimum operation speed；

When task T_iDischarge an example, and when it belongs to DTS, improve S_sfpsasr, the amount of raising is

When task T_iDo not discharge example, and time interval when it is not belonging to DTS and current exceedes between its minimum release Every time, reduce S_sfpsasr, the amount of reduction is

The initial priority equation below of described task represents:

IP_i=n-i+1

Wherein, n represents the number of accidental task in accidental task-set, and i is the integer more than or equal to 1 less than or equal to n.

Maximum equation below in described all initial priority sharing same resource tasks represents:

${\mathrm{\&pi;}}_i=\underset{1\&le;j\&le;n}{\max }\left\{{\mathrm{IP}}_j\right|r_j=i\}$

Wherein, 1≤i≤m, m represent the number of task sharing resource, r_jExpression task T_jResource requirement.

There is advantages that

(1) the accidental task low energy consumption dispatching method based on RM strategy that the present invention provides, not only allows for general merit Consumption model, the execution time of task become non-linear relation situation and processor speed handover overhead with processor speed, and The system of static priority tasks can be applicable to, utilize DVS technology and DPM technology simultaneously, thus than existing accidental task Low energy consumption dispatching method saves the energy consumption of about 79.37%～82.94%；

(2) it is able to ensure that accidental task completes to perform in its deadline, and is able to ensure that resource is by the use of mutual exclusion；

(3) reduction of system energy consumption, can reduce the production cost of product, the use time of delay apparatus, reduces battery Replacement cycle.

Below in conjunction with drawings and Examples, the present invention is described in further detail, but the one of the present invention is based on RM strategy Accidental task low energy consumption dispatching method be not limited to embodiment.

Accompanying drawing explanation

Fig. 1 is the flow chart schematic diagram of the inventive method；

Fig. 2 is the simulation experiment result figure of embodiments of the invention normalization energy consumption and system availability；

Fig. 3 is the simulation experiment result figure of embodiments of the invention normalization energy consumption and task real load.

Detailed description of the invention

Below in conjunction with the accompanying drawings and embodiment the present invention is described in further detail.

See Fig. 1, a kind of based on RM scheduling strategy the resource-constrained accidental task low energy consumption dispatching party that the present invention provides Method, comprises the steps:

Step 101: the initial priority of distribution task and execution priority；

Concrete, initial priority is allocated according to RM algorithm, and the minimum release interval of task is the least, and its priority is just The highest；Execution priority obtains distribution when the resources such as CPU start to perform in task, and its priority completes to perform it in task Before all keep constant；For not having the task of resource requirement, its initial priority is equal to its execution priority.

Further, task T_iInitial priority IP_iDistributing according to RM algorithm, its value is IP_i=n-i+1, i represent and appoint Business T_iSubscript, its value is integer between 1≤i≤n, wherein n number of accidental task in being accidental task-set；Task initial The numerical value of priority is the biggest, and its priority is the highest.

All use resources R_iThe limit priority π of task_iRepresenting, its value is calculated by following formula:

${\mathrm{\&pi;}}_i=\underset{1\&le;j\&le;n}{\max }\left\{{\mathrm{IP}}_j\right|r_j=i\}$

Wherein, 1≤i≤m, m represent the number of task sharing resource, and n represents the number of accidental task in accidental task-set, r_jIt it is task T_jResource requirement, IP_jRepresent task T respectively_jInitial priority.

The execution priority distribution method of task is as follows: task-set is divided into two disjoint subsets A and B.Set A In task there is no a resource requirement, the task in set B has resource requirement.The execution priority of the task in set A is equal to it Initial priority.The execution priority of the task in set B is equal in all initial priority sharing same resource tasks Maximum.For task T in set B_i, its execution priority EP_i=π_i。

Step 102: the processor demand under the maximum obstruction time of calculating task and worst case；

Concrete, task T_iMaximum obstruction time B (T_i) it is to be caused by the task that initial priority is lower than it, its Value isWherein e_jIt it is task T_jUnder maximum processor speed during the execution under worst case Between, r_jIt it is task T_jResource requirement, k is integer, and its span is 1≤k≤m, and m represents the number of task sharing resource, EP_jAnd IP_jIt is task T respectively_jExecution priority and initial priority.Task T_iProcess under interval [0, L] worst case Device demand D_0,L, its value isWherein e_iExpression task T_iWorst case under maximum processor speed Under the execution time, L is the real number more than 0, and its value isRepresent and use resourceAll tasks minimum Release interval, p_iExpression task T_iMinimum release interval, r_iExpression task T_iResource requirement.

Step 103: task-set be divided into the task-set of resource requirement and do not have the task-set of resource requirement, counting respectively Calculate and have resource requirement task-set and there is no the minimum operation speed of resource requirement task-set；

Concrete, task-set is divided into the task-set of resource requirement and there is no the task-set of resource requirement；There is resource Minimum operation speed LS of demand task-set_RTI () calculates according to the processor demand under the worst case of task-set, do not have resource to need Task minimum operation speed S of the task-set asked_NRTI () calculates according to the load of task-set, S_NRTI () is that set NRT (i) is in the momentAll tasks meet the minimum speed of service of its deadline, and its value is Wherein DTS is the task-set postponing release, and the interval of each task its release time in DTS is both greater than between its minimum release Every, e_jIt it is task T_jThe execution time under worst case, p_jIt it is task T_jMinimum release interval, F_cN () is that the scheduling of RM strategy is appointed The utilization rate upper bound that business collection is feasible, its value is

S_RT(i, L) is that the task-set having resource requirement is in the momentAll tasks meet its deadline The minimum speed of service, its value isAll shared resources R_iMinimum fortune Line speed S_RTMaximum LS of (i, L)_RTI () represents, its value is

Step 104: calculate the speed of service of task-set off-line phase；

Concrete, task T_iIn intervalBeing the only one task of having resource requirement, accidental task-set T is in interval Minimum speed of service S of [0, L]_lubI (), its value is S_lub(i)=LS_RT(i)+S_NRT(i,L),If accidental Business collection more than one task sharing resource, and its resource shared is different, speed of service L of task-set off-line phase_subMust expire The processor demand of all tasks of foot, its value is calculated by following formula:

Wherein r_iIt it is task T_iResource requirement, DTS be postpone release task-set,It is to use resourceAll Business minimum release interval, p_iIt it is task T_iMinimum release interval.

Step 105: set up free time management queue；Recovery task completes the free time produced ahead of time, during by the free time Between distribute to the task that current time queue medium priority is the highest, the computation processor current time speed of service；Processor is worked as The front moment speed of service compares with the critical speed preset, and utilizes the DVS technology regulation processor speed of service to guarantee that it is not Less than critical speed.

Concrete, the method setting up free time management queue α is: by setting up a chained list, task is excellent according to it First level order arrangement, is placed in this chained list, when the free time of task is equal to 0, it is removed from chained list, when task is complete When becoming to perform, it is inserted in chained list according to its priority orders.

Recovery task completes the free time ST of generation specifically ahead of time: free time Wherein W_iFor task T_iResidue under worst case performs time, U_iFor task T_iResidue perform the time, τ_iFor at this moment it Front processor speed handover overhead.Concrete, W_i, U_iE all it is arranged to during beginning_i, e_iWhen being the execution under task worst case Between, along with the execution of task, W_i, U_iAll reducing, if the time of t unit of tasks carrying, both reduces the unit of t accordingly, By W when task completes to perform_iIt is set to 0.τ_iIt is processor speed handover overhead, τ_i=K | S_i-S_j|, K is constant, S_i、S_jIt it is place The speed of reason device.

Further, is distributed to the task that now queue medium priority is the highest free time, calculate now processor fortune Line speed S, its value isBy itself and speed S_sfpsasrCompare, S_sfpsasrComputational methods as follows:

If during the processor free time, arranging S_sfpsasr=S_min, S_minFor processor minimum operation speed；

When task T_iDischarge an example, and when it belongs to DTS, improve S_sfpsasr, the amount of raising is

When task T_iDo not discharge example, and time interval when it is not belonging to DTS and current exceedes between its minimum release Every time, reduce S_sfpsasr, the amount of reduction is

When speed S > S_sfpsasrTime, S=S is set_sfpsasr；Otherwise speed S keeps constant.

Processor speed of service S is compared with the critical speed preset, utilizes DVS technology regulation processor to run speed Degree S guarantees that it is not less than critical speed.Described critical speed is the speed of service that system energy consumption is minimum, and different processors is crucial Speed is different.

Further, when processor is in idle condition, it is judged that whether idle interval now is more than processor state The expense of switching, if more, utilizes DPM technology, switches the processor into low power consumpting state；Otherwise, do not process.Tool Body, as long as idle interval is more than the expense of processor state switching, will automatically switch.

As in figure 2 it is shown, in the present embodiment, arrange under the execution time (WCET) under the worst case of task and best-case The ratio of execution time (BCET) be 5, system availability is 0.1 to 0.6, and step-length is 0.05, it is assumed that processor speed switches The constant of expense is 0.1.Comparing three kinds of methods, first, RM/DPP method in Fig. 2, the method task is all the time with maximum place Reason device speed performs；Second, SFPSASR method, assumes in the method that task performed with the execution time under its worst case, no Can reclaim the dynamic idle time, only utilize DVS technical energy saving；3rd, the method for the present invention, the method is in combination with DVS skill Art and DPM technology consider processor speed handover overhead, it is possible to utilize the dynamic idle time to reduce energy consumption；Exist with RM/DPP method System availability is to be normalized on the basis of energy consumption when 0.6.From figure 2 it can be seen that methodical energy consumption is all subject to The impact of system availability, system availability rises, and the methodical normalization energy consumption of institute rises；This is because system availability is more Height, the execution time increase of each task.The method of the present invention has obvious advantage compared with additive method, with RM/DPP method Compare the energy consumption saving 73.68%～85.22%, save the energy consumption of 49.08%～64.89% compared with SFPSASR.

As it is shown on figure 3, in the present embodiment, it is 0.31812 that Fig. 3 arranges system availability, investigate task real load to energy The impact of consumption, the ratio of WCET Yu BCET is from 1 to 10, and step-length is 1, it is assumed that the constant of processor speed handover overhead is 0.1, with RM/DPP algorithm is normalized on the basis of the energy consumption that ratio is 1 of WCET with BCET.The method compared in Fig. 3 and Fig. 2 Identical.From figure 3, it can be seen that the energy consumption of RM/DPP method is affected by the ratio of WCET with BCET；WCET and BCET Ratio rise, its normalization energy consumption decline；This is because the ratio of WCET with BCET is the highest, the true of task performs the time more Little.The change of the ratio of WCET Yu BCET, the impact on SFPSASR method and the method for the present invention is little.This is primarily due to The speed of service of both approaches task is limited by the speed of task-set off-line phase.The energy consumption of the method for the present invention is below The energy consumption of additive method, saves the energy consumption of 79.37%～82.94%, saving compared with SFPSASR compared with RM/DPP method 42.14%～51.73% energy consumption about.

The foregoing is only presently preferred embodiments of the present invention, not in order to limit the present invention, all spirit in the present invention and Within principle, any modification, equivalent substitution and improvement etc. made, should be included within the scope of the present invention.

Claims (10)

1. an accidental task low energy consumption dispatching method based on RM strategy, it is characterised in that including:

The initial priority of distribution task and execution priority；

Processor demand under the maximum obstruction time of calculating task and worst case；

Task-set being divided into the task-set of resource requirement and does not has the task-set of resource requirement, calculating respectively has resource requirement Task-set and do not have the minimum operation speed of resource requirement task-set；

Calculate the speed of service of task-set off-line phase；

Set up free time management queue；Recovery task completes the free time produced ahead of time, will distribute to currently free time The task that moment queue medium priority is the highest, the computation processor current time speed of service；Processor current time is run speed The critical speed spent and preset compares, and utilizes the DVS technology regulation processor speed of service to guarantee that it is not less than critical speed.

Accidental task low energy consumption dispatching method based on RM strategy the most according to claim 1, it is characterised in that described point Initial priority and the execution priority of joining task include:

According to the initial priority of RM strategy distribution task, the minimum release interval of task is the least, and its initial priority is the highest；

Task-set is divided into resource requirement and there is no the task subset of resource requirement；

Calculate the maximum in all initial priority sharing same resource tasks；

If task belongs to not having in resource requirement task subset of task, distribute its execution priority equal to initial priority；If Task belongs to having in resource requirement task subset of task, distributes its execution priority and appoints equal to described all shared same resources Maximum in the initial priority of business.

Accidental task low energy consumption dispatching method based on RM strategy the most according to claim 1, it is characterised in that described meter In processor demand step under the maximum obstruction time of calculation task and worst case, task T_iMaximum obstruction time B (T_i) table It is shown as:

$B\left(T_i\right)=\underset{\&ForAll;j,{\mathrm{EP}}_j\&GreaterEqual;{\mathrm{IP}}_i>{\mathrm{IP}}_j}{max}\left\{e_j\right|r_j=k\}$

Wherein, IP_iExpression task T_iInitial priority, EP_jAnd IP_jRepresent task T respectively_jExecution priority and initial priority Level, e_jExpression task T_jThe execution time under worst case, r under maximum processor speed_jExpression task T_jResource requirement, k For integer, its span is 1≤k≤m, and m represents the number of task sharing resource；

Task T_iProcessor demand D under interval [0, L] worst case_0,LIt is expressed as:

Wherein, wherein e_iExpression task T_iThe execution time under worst case under maximum processor speed, L is the reality more than 0 Number, its value is Represent and use resourceAll task minimums release interval, p_iExpression task T_iMinimum Release interval, r_iExpression task T_iResource requirement.

Accidental task low energy consumption dispatching method based on RM strategy the most according to claim 3, it is characterised in that described general Task-set is divided into the task-set of resource requirement and does not has the task-set of resource requirement, and calculating has resource requirement task respectively Collect and do not have the minimum operation speed of resource requirement task-set to include:

Task-set is divided into the task-set of resource requirement and there is no the task-set of resource requirement；

There is minimum operation speed LS of resource requirement task-set_RTI () is according to the processor demand meter under the worst case of task-set Calculate, represent by equation below:

${\mathrm{LS}}_{RT}\left(i\right)=\underset{P_{r_i}<L<p_i}{Max}\left(S_{RT}\right(i,L\left)\right)$

Wherein, S_RT(i, L) indicates that the task-set of resource requirement meets the minimum operation of its deadline in all tasks of moment L Speed, its value ise_jExpression task T_jDuring execution under worst case Between, p_jExpression task T_jMinimum release interval；

There is no minimum operation speed S of the task-set of resource requirement_NRTI () calculates according to the load of task-set, use equation below table Show:

$S_{NRT}\left(i\right)=\underset{T_j\&NotElement;DTS}{\overset{n}{\underset{j=i+1}{\mathrm{\&Sigma;}}}}\frac{e_j}{p_j\&CenterDot;F_c\left(n\right)}$

Wherein, DTS represents the task-set postponing release, and the interval of each task release time in DTS is both greater than its minimum and releases Put interval, F_cN () represents the utilization rate upper bound that RM strategy scheduler task collection is feasible.

Accidental task low energy consumption dispatching method based on RM strategy the most according to claim 4, it is characterised in that described meter The speed of service equation below calculating task-set off-line phase represents:

Wherein, S_lubI () represents the accidental task-set minimum speed of service in interval [0, L], represent by equation below:

$S_{lub}\left(i\right)={\mathrm{LS}}_{RT}\left(i\right)+S_{NRT}(i,L),P_{r_i}<L<p_i.$

Accidental task low energy consumption dispatching method based on RM strategy the most according to claim 1, it is characterised in that described sky Represent by equation below between idle:

$ST=\underset{i=1}{\overset{n}{\&Sigma;}}(W_i=0|U_i-{\mathrm{\&tau;}}_i)$

Wherein, W_iExpression task T_iResidue under worst case performs time, U_iExpression task T_iResidue perform the time, τ_iRepresent Processor speed handover overhead before this moment.

Accidental task low energy consumption dispatching method based on RM strategy the most according to claim 6, it is characterised in that described meter Calculate the processor current time speed of service to include:

Computation processor current time speed of service S, wherein

By itself and speed S_sfpsasrCompare；If S > S_sfpsasr, S=S is set_sfpsasr；The most described S keeps constant.

Accidental task low energy consumption dispatching method based on RM strategy the most according to claim 7, it is characterised in that described speed Degree S_sfpsasrComputational methods are as follows:

If during the processor free time, arranging S_sfpsasr=S_min, described S_minFor processor minimum operation speed；

When task T_iDischarge an example, and when it belongs to DTS, improve S_sfpsasr, the amount of raising is

When task T_iDo not discharge example, and when time interval when it is not belonging to DTS and current exceedes its minimum release interval, Reduce S_sfpsasr, the amount of reduction is

Accidental task low energy consumption dispatching method based on RM strategy the most according to claim 2, it is characterised in that described The initial priority equation below of business represents:

IP_i=n-i+1

Wherein, n represents the number of accidental task in accidental task-set, and i is the integer more than or equal to 1 less than or equal to n.

Accidental task low energy consumption dispatching method based on RM strategy the most according to claim 2, it is characterised in that described Maximum equation below in all initial priority sharing same resource tasks represents:

${\mathrm{\&pi;}}_i=\underset{1\&le;j\&le;n}{\max }\left\{{\mathrm{IP}}_j\right|r_j=i\}$

Wherein, 1≤i≤m, m represent the number of task sharing resource, r_jExpression task T_jResource requirement.