CN112633589A - Probability model-based hybrid key task energy consumption optimization scheduling method - Google Patents
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Abstract
The invention relates to a probability model-based hybrid key task energy consumption optimization scheduling method, which comprises the following steps of establishing a probability-based hybrid key task scheduling model; calculating the execution time under the worst condition of the task in the low mode by using the probability of mode conversion; respectively calculating the low key level task speed S by using the worst execution time and the feasibility condition of system scheduling in the task low modeLOAnd high key level task speed SHI(ii) a Deducing a probability model of energy consumption by using the probability model of the execution time of the task; and finding out the execution probability of the high-key level task in a high mode, so that the average energy consumption of the system is the lowest. The method of the invention utilizes the probability of the taskAnd the model is used for minimizing the average energy consumption of the system.
Description
Technical Field
The invention relates to low-energy-consumption real-time scheduling of a hybrid key system, in particular to a probability model-based hybrid key task energy consumption optimization scheduling method.
Background
An embedded real-time system formed by integrating multiple applications with different key levels on the same platform becomes a hybrid key system. The hybrid key system has wide application in the aerospace field and the automotive electronics field. Such as aircraft flight control systems, automotive control systems, and cardiac pacemaker control systems. The operating environment of these systems is limited, and some of them operate even in extreme environments, and the energy for driving these systems usually adopts batteries, and because of the limited power supply capacity of the batteries, the energy consumption becomes an important factor that must be considered for designing these systems.
Existing energy consumption studies for hybrid critical systems assume that tasks are always executed at their worst case time, which is too pessimistic because the true execution time of a task tends to be lower than its worst case execution time; this results in wasted system resources. Therefore, the probability model-based hybrid key task energy consumption optimization scheduling method is provided, system resources can be utilized more effectively, and energy consumption is reduced.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a probabilistic model hybrid key task energy consumption optimization scheduling method.
In order to achieve the purpose, the technical scheme of the invention is as follows:
establishing a probability-based mixed key task scheduling model;
calculating the execution time under the worst condition of the task in the low mode by using the probability of mode conversion;
respectively calculating the low key level task speed S by using the worst execution time and the feasibility condition of system scheduling in the task low modeLOAnd high key level task speed SHI；
Deducing a probability model of energy consumption by using the probability model of the execution time of the task;
finding out the execution probability of the high key level task in a high mode to ensure that the average energy consumption of the system is the lowest;
the establishment of the probability-based hybrid key task scheduling model comprises the following steps:
consider a single processor system comprising n mutually independent hybrid key period task models Γ＝{τ1,τ2,…,τnMix the critical periodic tasks τi(1. ltoreq. i. ltoreq. n, i is an integer) from (T)i,Di,Li,Ci(LO),Ci(HI)，PETi) Is represented by the formula, wherein TiAnd DiAre each tauiThe period and relative deadline; l isiIs τiA key hierarchy of value LO (low key hierarchy task) or HI (high key hierarchy task); ci(LO) and Ci(HI) is each τiWorst case execution time in low mode and high mode. PETiIs task τiThe value of the historical execution time information of (2) is represented by a 3 × k matrix:
wherein, Cl(1. ltoreq. l. ltoreq.k) represents task τiExecution time at maximum processor speed; f. ofi(Cl) And Fi(Cl) Respectively represent execution time as ClA probability density function and an empirical distribution function; of particular note is task τiC of (A)i(LO) is not given in advance. There are three modes of the hybrid critical system, low mode, high mode, and transition mode. The low mode refers to all high key hierarchy mixed key period tasks tauiWhen the execution is finished, the execution time does not exceed Ci(LO); so-called high mode is to allow only high key hierarchy mixed key period tasks τiCompleting the execution; the conversion mode refers to a task period task tau with a high key leveliIts execution time exceeds Ci(LO) and the period of time it completes execution; if mixing the critical period task τiFor low key hierarchy tasks, then Ci(HI)＝Ci(LO); if mixing the critical period task τiFor high key level tasks, then Ci(HI)＞＝Ci(LO); the task set is scheduled by using a preemptive fixed priority strategy and is scheduled by using a monotone deadline strategy, and the period of the taskThe smaller, the greater its priority; the larger the period of a task, the smaller its priority.
Preferably, the calculating the worst execution time of the task in the low mode by using the probability of the mode conversion specifically includes:
mixed critical periodic tasks τiThe worst-case execution time in the low mode is calculated by:
wherein,
is that
Inverse function of empirical distribution function under distribution, PLO→HIIs the probability of a system mode transition,
represents the time distribution in different modes, W ∈ { LO, HI, TR } (LO, HI, TR represent low mode, high mode, and transition mode, respectively); task tauiExecution time distribution in low mode
Given by:
wherein [ ] denotes the Hadamard product of the matrix and x denotes Ci(LO) in PETiNumber of columns in (1), TxMeaning that the 3 xk matrix is truncated to a 3 x matrix, with the following extra columns removed, SLOIs the low key level task speed;
task tauiExecution time distribution in transition mode
Given by:
wherein K is Ci(LO)/SLO-Ci(LO)，T′xIndicating that the 3 xk matrix is truncated to a 3 x (k-x) matrix, with the previous extra columns removed, SHIIs the speed of high key level tasks.
Task tauiExecution time distribution in high mode
Given by:
wherein S isHIIs the speed of high key level tasks.
Preferably, the low key level task speed S is respectively calculated by using the worst execution time in the task low mode and the feasibility condition of system schedulingLOAnd high key level task speed SHI(ii) a The method specifically comprises the following steps:
mixed critical periodic tasks τiThe feasibility conditions in the low mode, the high mode and the transition mode are given by:
wherein, Ci(LO) and Ci(HI) is each τiWorst case execution times in low and high modes, hep (i) is the priority ratio of the mixed critical period task τiHigh set of tasks, MjIs mixing of critical period tasks taujThe number of task instances released within its response time; diIs mixing of critical period tasks tauiThe relative deadline of (c); low key hierarchy task speed SLOAnd high key level task speed SHICan be calculated by the above formula.
Preferably, a probability model of energy consumption is deduced by using a probability model of the execution time of the task; the method specifically comprises the following steps:
the energy consumption of the task is determined by power consumption, execution time and execution speed; the power consumption model of the system is given by:
wherein,
the maximum dynamic power consumption, the value of which can be normalized to 1; s is the normalized speed of the processor, theta is the ratio of the maximum static power consumption to the maximum dynamic power consumption, and the value of theta is generally 0.2; pindIs processor-independent power consumption, which takes on a value of 0.1;
therefore, the probability distribution of power consumption in the low mode
Calculated from the following formula:
probability distribution of energy consumption in high mode
Calculated from the following formula:
probability distribution of energy consumption in transition mode
Calculated from the following formula:
preferably, the execution probability of the high key level task in a high mode is found out, so that the average energy consumption of the system is the lowest; the method specifically comprises the following steps:
the average energy consumption of a task is equal to the probability product of the corresponding energy consumption and its corresponding mode, and the probability function f (E') characterizing each mode of the system is calculated by:
wherein
Is a high key hierarchy task τiProbability of execution in high mode, PLO→HIIs the probability of a system mode transition,
to represent
The probability density function in the distribution is,
to represent
The probability density function in the distribution is,
to represent
A probability density function in the distribution; the average energy consumption E for the task ensemble is therefore calculated by:
wherein,
to represent
The amount of energy consumed in the distribution,
to represent
The amount of energy consumed in the distribution,
to represent
Energy consumption values in the profile; to minimize the average energy consumption E, it is critical to find
Which in turn may pass PLO→HIAnd calculating the relation between the system and the state of the system, wherein the specific calculation method comprises the following steps:
wherein A represents τiThe previous task of (2) is run in high mode; b represents tauiThe execution time of the previous task exceeds the execution time of the worst case in the low mode; c represents tauiAfter the previous task is finished executing, the system is not in an idle state. Events A, B, C may be distributed by time in different patterns
To obtain the compound.
As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following advantages:
(1) the method comprises the steps of firstly, establishing a probability-based mixed key task scheduling model; calculating the execution time under the worst condition of the task in the low mode by using the probability of mode conversion; respectively calculating the low key level task speed S by using the worst execution time and the feasibility condition of system scheduling in the task low modeLOAnd high key level task speed SHI(ii) a Deducing a probability model of energy consumption by using the probability model of the execution time of the task; finding out the execution probability of the high key level task in a high mode; compared with the conventional method for scheduling the periodic tasks of the hybrid key system, the method disclosed by the invention has the advantages that the average energy consumption of the system is reduced by about 59.03% to the minimum; and can ensure that the periodic task is executed within the deadline of the periodic task; the energy consumption of the hybrid key system is reduced, the production cost of products is reduced, the service time of equipment is prolonged, and the replacement period of batteries is shortened.
The invention is further described in detail with reference to the drawings and the embodiments, but the method for optimally scheduling the energy consumption of the hybrid key tasks based on the probabilistic model is not limited to the embodiments.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
Detailed Description
The technical solutions in the embodiments of the present invention will be described and discussed in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1, the method for optimally scheduling energy consumption of mixed key tasks based on a probabilistic model according to the present invention includes the following steps:
step 101: and establishing a probability-based mixed key task scheduling model.
Consider a single-processor system containing n mutually independent mixed key period task models Γ ═ τ1,τ2,…,τnMix the critical periodic tasks τi(1. ltoreq. i. ltoreq. n, i is an integer) from (T)i,Di,Li,Ci(LO),Ci(HI)，PETi) Is represented by the formula, wherein TiAnd DiAre each tauiThe period and relative deadline; l isiIs τiA key hierarchy of value LO (low key hierarchy task) or HI (high key hierarchy task); ci(LO) and Ci(HI) is each τiWorst case execution time in low mode and high mode. PETiIs task τiThe value of the historical execution time information of (2) is represented by a 3 × k matrix:
wherein, Cl(1. ltoreq. l. ltoreq.k) represents task τiExecution time at maximum processor speed; f. ofi(Cl) And Fi(Cl) Respectively represent execution time as ClA probability density function and an empirical distribution function; of particular note is task τiC of (A)i(LO) is not given in advance. There are three modes of the hybrid critical system, low mode, high mode, and transition mode. The low mode refers to all high key hierarchy mixed key period tasks tauiWhen the execution is finished, the execution time does not exceed Ci(LO); so-called high mode is to allow only high key hierarchy mixed key period tasks τiCompleting the execution; the conversion mode refers to a task period task tau with a high key leveliIts execution time exceeds Ci(LO) and the period of time it completes execution; if mixing the critical period task τiFor low key hierarchy tasks, then Ci(HI)＝Ci(LO); if mixing the critical period task τiFor high key level tasks, then Ci(HI)＞＝Ci(LO); the task set is scheduled by using a preemptive fixed priority strategy and is scheduled by using a monotone deadline strategy, wherein the smaller the period of the task is, the larger the priority of the task is; the larger the period of a task, the smaller its priority.
Step 102: and calculating the worst-case execution time of the task in the low mode by using the probability of mode conversion.
Mixed critical periodic tasks τiThe worst-case execution time in the low mode is calculated by:
wherein,
is that
Inverse function of empirical distribution function under distribution, PLO→HIIs the probability of a system mode transition,
represents the time distribution in different modes, W ∈ { LO, HI, TR } (LO, HI, TR represent low mode, high mode, and transition mode, respectively); task tauiExecution time distribution in low mode
Given by:
wherein [ ] denotes the Hadamard product of the matrix and x denotes Ci(LO) in PETiNumber of columns in (1), TxMeaning that the 3 xk matrix is truncated to a 3 x matrix, with the following extra columns removed, SLOIs the low key level task speed;
task tauiExecution time distribution in transition mode
Given by:
wherein K is Ci(LO)/SLO-Ci(LO)，T′xIndicating that the 3 xk matrix is truncated to a 3 x (k-x) matrix, with the previous extra columns removed, SHIIs the speed of high key level tasks.
Task tauiExecution time distribution in high mode
Given by:
wherein S isHIIs the speed of high key level tasks.
Step 103: respectively calculating the low key level task speed S by using the worst execution time and the feasibility condition of system scheduling in the task low modeLOAnd high key level task speed SHI(ii) a The method specifically comprises the following steps:
mixed critical periodic tasks τiThe feasibility conditions in the low mode, the high mode and the transition mode are given by:
wherein, Ci(LO) and Ci(HI) is each τiWorst case execution times in low and high modes, hep (i) is the priority ratio of the mixed critical period task τiHigh set of tasks, MjIs mixing of critical period tasks taujThe number of task instances released within its response time; diIs mixing of critical period tasks tauiThe relative deadline of (c); low key hierarchy task speed SLOAnd high key level task speed SHICan be calculated by the above formula.
Step 104: deducing a probability model of energy consumption by using the probability model of the execution time of the task; the method specifically comprises the following steps:
the energy consumption of the task is determined by power consumption, execution time and execution speed; the power consumption model of the system is given by:
wherein,
the maximum dynamic power consumption, the value of which can be normalized to 1; s is the normalized speed of the processor, theta is the ratio of the maximum static power consumption to the maximum dynamic power consumption, and the value of theta is generally 0.2; pindIs processor-independent power consumption, which takes on a value of 0.1;
therefore, power consumption in the low modeProbability distribution
Calculated from the following formula:
probability distribution of energy consumption in high mode
Calculated from the following formula:
probability distribution of energy consumption in transition mode
Calculated from the following formula:
step 105: and finding out the execution probability of the high-key level task in a high mode, so that the average energy consumption of the system is the lowest.
The average energy consumption of a task is equal to the probability product of the corresponding energy consumption and its corresponding mode, and the probability function f (E') characterizing each mode of the system is calculated by:
wherein
Is a high key hierarchy task τiProbability of execution in high mode, PLO→HIIs the probability of a system mode transition,
to represent
The probability density function in the distribution is,
to represent
The probability density function in the distribution is,
to represent
A probability density function in the distribution; the average energy consumption E for the task ensemble is therefore calculated by:
wherein,
to represent
The amount of energy consumed in the distribution,
to represent
The amount of energy consumed in the distribution,
to represent
Energy consumption values in the profile; to minimize the average energy consumption E, it is critical to find
Which in turn may pass PLO→HIAnd calculating the relation between the system and the state of the system, wherein the specific calculation method comprises the following steps:
wherein A represents τiThe previous task of (2) is run in high mode; b represents tauiThe execution time of the previous task exceeds the execution time of the worst case in the low mode; c represents tauiAfter the previous task is finished executing, the system is not in an idle state. Events A, B, C may be distributed by time in different patterns
To obtain the compound.
In this embodiment, the mixed-cycle task set Γ ═ τ1,τ2Contains 2 periodic tasks τ1＝(30,30,HI,C1(LO),8,PET1)，τ2＝(30,30,LO,6,6,PET2) The history information of the execution time of the task is as follows:
get PLO→HI＝0.05，SHIWhen 1, it is known that1(LO) is 4, and S can be calculated from equations 6-8LO1/3. Therefore, the temperature of the molten metal is controlled,
due to tau2Is a low key hierarchy task and therefore does not have a high mode and a transition modeThe time profile of formula (la); the corresponding energy consumption distribution is as follows:
through calculation, the energy consumption is optimized to be rapid
Periodic task τ1The average energy consumption of (2) is 3.36; periodic task τ2The average energy consumption of (1.65); the total average energy consumption was 5.01; total energy consumption without using the probabilistic model system is 12.23; in the interval [0,30 ]]Scheduling the set of tasks internally saves energy consumption by about 59.03% compared to a method where the tasks are executed at their worst case execution time.
The above is only one preferred embodiment of the present invention. However, the present invention is not limited to the above embodiments, and any equivalent changes and modifications made according to the present invention, which do not bring out the functional effects beyond the scope of the present invention, belong to the protection scope of the present invention.
Claims (6)
1. A probability model-based hybrid key task energy consumption optimization scheduling method is characterized by comprising the following steps:
establishing a probability-based mixed key task scheduling model;
calculating the execution time under the worst condition of the task in the low mode by using the probability of mode conversion;
respectively calculating the low key level task speed S by using the worst execution time and the feasibility condition of system scheduling in the task low modeLOAnd high key level task speed SHI；
Deducing a probability model of energy consumption by using the probability model of the execution time of the task;
finding out the execution probability of the high key level task in a high mode to ensure that the average energy consumption of the system is the lowest;
2. the method according to claim 1, wherein the establishing of the probability-based hybrid mission critical energy consumption optimized scheduling model comprises:
consider a single-processor system containing n mutually independent mixed key period task models Γ ═ τ1,τ2,…,τnMix key periodic tasks, }, τiI is not less than 1 and not more than n, i is an integer, represented by (T)i,Di,Li,Ci(LO),Ci(HI)，PETi) Is represented by the formula, wherein TiAnd DiAre each tauiThe period and relative deadline; l isiIs τiThe value of the key hierarchy of (1) is LO low key hierarchy task or HI high key hierarchy task; ci(LO) and Ci(HI) is each τiWorst case execution time, PET, in low and high modesiIs task τiIs represented by a 3 × k matrix:
wherein, Cl(1. ltoreq. l. ltoreq.k) represents task τiExecution time at maximum processor speed; f. ofi(Cl) And Fi(Cl) Respectively represent execution time as ClA probability density function and an empirical distribution function; the hybrid key system has three modes, namely a low mode, a high mode and a conversion mode; the low mode refers to all high key hierarchy mixed key period tasks tauiWhen the execution is finished, the execution time does not exceed Ci(LO); so-called high mode is to allow only high key hierarchy mixed key period tasks τiCompleting the execution; the conversion mode refers to a task period task tau with a high key leveliIts execution time exceeds Ci(LO) and the period of time it completes execution; if mixing the critical period task τiFor low key hierarchy tasks, then Ci(HI)＝Ci(LO); if mixing the critical period task τiFor high key level tasks, then Ci(HI)＞＝Ci(LO); the task set is scheduled using a preemptive fixed priority policy.
3. The method for optimal scheduling of energy consumption of mixed critical tasks based on a probabilistic model according to claim 1, wherein the calculating of the worst case execution time of the task in the low mode using the probability of mode transformation specifically comprises:
mixed critical periodic tasks τiThe worst-case execution time in the low mode is calculated by:
wherein,
is that
Inverse function of empirical distribution function under distribution, PLO→HIIs the probability of a system mode transition,
represents the time distribution under different modes, W is belonged to { LO, HI, TR }; LO, HI, and TR represent low mode, high mode, and transition mode, respectively; task tauiExecution time distribution in low mode
Given by:
wherein [ ] denotes the Hadamard product of the matrix and x denotes Ci(LO) in PETiNumber of columns in (1), TxMeaning that the 3 xk matrix is truncated to a 3 x matrix, with the following extra columns removed, SLOIs the low key level task speed;
task tauiExecution time distribution in transition mode
Given by:
wherein K is Ci(LO)/SLO-Ci(LO)，T′xIndicating that the 3 x k matrix is truncated to a 3 x (k-x) matrix with the previous extra columns removed.
Task tauiExecution time distribution in high mode
Given by:
wherein S isHIIs the speed of high key level tasks.
4. The method for optimal scheduling of energy consumption of mixed key tasks based on probabilistic model according to claim 1, wherein the low key level task speed S is calculated by using the worst case execution time in task low mode and the feasibility condition of system schedulingLOAnd high key level task speed SHI(ii) a The method specifically comprises the following steps:
mixed critical periodic tasks τiThe feasibility conditions in the low mode, the high mode and the transition mode are given by:
wherein, Ci(LO) and Ci(HI) is each τiWorst case execution times in low and high modes, hep (i) is the priority ratio of the mixed critical period task τiHigh set of tasks, MjIs mixing of critical period tasks taujThe number of task instances released within its response time; diIs mixing of critical period tasks tauiThe relative deadline of (c); sLOLow key level task speed; sHIIs a high key level task speed.
5. The method for energy consumption optimized scheduling of hybrid critical tasks based on probabilistic models as defined in claim 1, wherein the probabilistic model of energy consumption is derived from a probabilistic model of the execution time of the tasks; the method specifically comprises the following steps:
the energy consumption of the task is determined by power consumption, execution time and execution speed; the power consumption model of the system is given by:
wherein,
is the maximum dynamic power consumption; s is the normalized speed of the processor, and theta is the ratio of the maximum static power consumption to the maximum dynamic power consumption; pindIs processor independent power consumption。
Probability distribution of energy consumption in low mode
Calculated from the following formula:
probability distribution of energy consumption in high mode
Calculated from the following formula:
probability distribution of energy consumption in transition mode
Calculated from the following formula:
6. the method for optimal scheduling of energy consumption of hybrid key tasks based on probabilistic models according to claim 1, wherein the execution probability of high key level tasks in a high mode is found to minimize the average energy consumption of the system; the method specifically comprises the following steps:
the average energy consumption of a task is equal to the probability product of the corresponding energy consumption and its corresponding mode, and the probability function f (E') characterizing each mode of the system is calculated by:
wherein P isi HIIs a high key hierarchy task τiProbability of execution in high mode, PLO→HIIs the probability of a system mode transition, fl LO(El LO) To represent
The probability density function in the distribution is,
to represent
The probability density function in the distribution is,
to represent
A probability density function in the distribution; the average energy consumption E for the task ensemble is therefore calculated by:
wherein,
to represent
The amount of energy consumed in the distribution,
to represent
The amount of energy consumed in the distribution,
to represent
Energy consumption values in the profile; to minimize the average energy consumption E, it is critical to find Pi HIWhich in turn may pass through PLO→HIAnd calculating the relation between the state of the system.
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