KR101065436B1 - Stochastic scheduling of a real-time parallel task with uncertain computation amount on mulit-core processors - Google Patents

Abstract

The present invention provides a probabilistic scheduling method and a low power multi-core processor using the same. The stochastic scheduling method represents an uncertainty calculation as a stochastic computational model when a plurality of processor cores executes an accurate computation of a given task and executes an unknown task before completion. Determine transition points of execution speed that minimize probabilistic expectations, calculate the expected value for the minimum energy consumption for each core number, and select the optimal number of cores with the stochastic minimum expected value based on the calculation results Characterized in that.

Description

Stochastic Scheduling of a Real-Time Parallel Task with Uncertain Computation Amount on Mulit-Core Processors}

The present invention relates to a probabilistic scheduling method of a multicore processor for real-time parallel tasks with an uncertain amount of computation.

BACKGROUND Recently, electronic devices such as computers, mobile communication terminals, and smart phones have been widely used due to technological developments in electric electronics, communication, and semiconductors. Such electronic devices may be equipped with a multicore processor to meet the high performance and multifunction needs of the user.

Multi-core processors are processors built with two or more cores. Multicore processors can solve some of the heat and power issues of a single processor and allow multiple tasks to be processed independently or in parallel on each core.

Moreover, with the evolution of server systems and high performance electronic devices, many device software or applications are increasingly demanding higher network bandwidth utilization or multitasking. In order to satisfy these demands, various methods for improving the throughput of a task or a network by efficiently utilizing multicores have been studied.

SUMMARY OF THE INVENTION An object of the present invention is to provide a probabilistic scheduling method capable of completing real-time parallel tasks with uncertain computations on a multicore processor before deadline with minimal energy consumption.

In addition, an object of the present invention is to provide a probabilistic scheduling method that can determine the execution speed according to the number of cores and the progress of calculation in order to stochastically minimize the estimated energy consumption.

According to an aspect of the present invention to solve the above technical problem, when a plurality of processor cores executes an unknown task before the completion of execution of a given task, a first calculation that represents the uncertain calculation amount as a stochastic calculation model step; Determining conversion points of execution speed for minimizing probabilistic expected values of energy consumption based on the stochastic computational model; Calculating an expected value for a minimum energy consumption for each core number of the plurality of processor cores; And a fourth step of selecting an optimal number of cores having a probabilistic minimum expected value based on the calculation result of the third step, and a probabilistic scheduling method of the multicore processor for a real-time parallel operation with an uncertain amount of computation is provided. .

According to the present invention, real-time parallel tasks with uncertain computations on a multicore processor can be completed before deadline with minimal energy consumption. In other words, minimizing energy consumption in multicore processors by expressing uncertain computation in a stochastic computational model and determining the execution speed and number of cores that minimize the probabilistic expectation of energy consumption based on the stochastic computational model. can do.

In addition, by applying a scheduling method that can minimize the energy consumption of the multi-core processor, it is possible to minimize the power consumption of the electronic device, increase the safety and integrity of the task execution, and increase the user convenience.

1 is a schematic flowchart of a probabilistic scheduling method (hereinafter, referred to simply as a probabilistic scheduling method) in a multicore processor for real-time parallel work with an uncertain calculation amount according to an embodiment of the present invention.
FIG. 2A is a diagram illustrating a probabilistic distribution of job end times of a general job employable in one embodiment of the present invention. FIG.
FIG. 2B illustrates a cumulative function of the probabilistic distribution of FIG. 2A.
2C is a diagram illustrating a difference function of the cumulative function of FIG. 2B.
3A and 3B are diagrams for describing a parallel processing-based stochastic computational model that can be employed in the stochastic scheduling method according to an embodiment of the present invention.
4A and 4B are diagrams for describing a method of using a stochastic calculation model that can be employed in the stochastic scheduling method according to an embodiment of the present invention.
5 is a diagram illustrating a process of removing an inefficient execution speed in a probabilistic scheduling method according to an embodiment of the present invention.
6A and 6B are diagrams for describing a method of finding a time of conversion of execution speed that can be employed in a probabilistic scheduling method according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

1 is a schematic flowchart of a probabilistic scheduling method (hereinafter, referred to simply as a probabilistic scheduling method) in a multicore processor for real-time parallel work with an uncertain calculation amount according to an embodiment of the present invention.

Referring to FIG. 1, in the probabilistic scheduling method, when a plurality of processor cores execute an unknown task before execution completion of an accurate computation of a given task, a first step of expressing an uncertain computation as a stochastic computational model (S110) ), A second step (S120) of determining execution points of execution speed for minimizing a probabilistic expected value of energy consumption based on a stochastic computational model, for a minimum energy consumption amount for each core number of a plurality of processor cores; A third step (S130) of calculating an expected value and a fourth step of selecting an optimal number of cores having a probabilistic minimum expected value based on the calculation result of the third step. Each step will be embodied by the following description.

The stochastic computational model can be expressed by representing the probabilistic distribution of task end times for a typical task as the difference function of the cumulative function. Here, the stochastic computational model refers to a function of the probability that a particular task is being performed at a particular time t.

Existing methods determine energy consumption based on the worst-case execution time, but if the average execution time is significantly shorter than the maximum execution time, the waste of available energy resources is large. Therefore, in the probabilistic scheduling method of the present embodiment, the cumulative function of the probabilistic distribution is expressed as a difference function and used as a stochastic computational model.

For example, in a single or multi-core processor, a typical task is in the form of a probabilistic distribution A _t as shown in FIG. Can be expressed. The best-case corresponds to the minimum execution time, and the worst-case corresponds to the maximum execution time.

Next, when the probability distribution function as shown in FIG. 2A is expressed as a cumulative probability as shown in FIG. 2B, the tail probability of the cumulative function may be represented as shown in FIG. 2C. have.

The cumulative function of FIG. 2B is surfaced as in Equation 1 below, and the difference function of FIG. 2C can be expressed as Equation 2.

[Equation 1]

[Equation 2]

Here, the difference function P _t represents the probability that a specific task is being performed at time t, and the difference function always decreases as the value of t increases. In the embodiment of the present invention, the difference function is used as a stochastic computational model.

Therefore, in the present embodiment, it is also preferable to accumulate data in advance so as to know the probabilistic distribution A _t as shown in Fig. 2A for a specific job.

Once the stochastic computational model is determined, it is possible to determine the probability that the task will be performed at a specific time (t) by the determined computational model, so that the operating mode can be determined (scheduled) based on this to optimize the utility of the task being performed. do.

Here, utility is a concept similar to the average expected value of the quality of service (QoS), and in the operation mode with high utility, the energy consumption is high and the operation efficiency is high, and in the operation mode with relatively low utility It can be defined as low consumption but low work performance. Task performance efficiency is, for example, the operating speed of the motor, the data transmission speed, the data throughput, the operating voltage of the central processing unit (CPU), the operating clock speed, etc., and the higher the utility, the higher the operating speed, but corresponding energy consumption. Will increase.

In an embodiment of the present invention, a low execution speed or a low utility may be applied in the first half of a high probability calculation process, and a high execution speed or high utility may be applied toward the second half of a low probability calculation progress. This configuration will be described in more detail below.

3A and 3B are diagrams for describing a parallel processing-based stochastic computational model that can be employed in the stochastic scheduling method according to an embodiment of the present invention.

Referring to FIG. 3A, applying the case in which two processor cores parallelize the same amount of computation for a particular task, the theoretically distributed maximum computation amount or task end time is cut in half. In FIG. 3A, P ¹ is # of Computation Cycles on a single core, and P ² is parallel throughput on a dual core.

In addition, according to the number of cores performing the task, the future calculation probability P _t may be expressed as a tail cumulative probability as illustrated in FIG. 3B. In FIG. 3B, P ¹ _t is a calculation probability in a single core, and P ² _t is a calculation probability in parallel processing of dual cores.

4A and 4B are diagrams for describing a method of using a stochastic calculation model that can be employed in the stochastic scheduling method according to an embodiment of the present invention.

It is assumed that the conventional method utilizes the worst-case calculation amount, that is, the maximum calculation amount to complete the deadline in determining the execution speed of the process core, for example, the clock frequency, as shown in FIG. 4A. In this embodiment, as shown in FIG. 4B, the first half of the calculation progress that is likely to be performed based on the future computation probability P _t is performed at a low execution speed, and the second half of the calculation progress that is unlikely to be performed is high execution. Run at speed.

In the foregoing case, since the actual calculation amount is less than the calculation amount of the maximum execution speed, the conventional method does not have an opportunity to reduce the energy consumption rate of the processor by applying a lower execution speed. However, in the present embodiment, the execution speed is adjusted according to the probability of the calculation amount so as to minimize the probabilistic expected value of the total energy consumption according to the probability P _t of the calculation amount. According to the present embodiment, the energy consumption can be minimized as compared with the conventional case when the calculation of the maximum execution speed is based, that is, when the task execution is completed at the same deadline.

A probabilistic scheduling method according to an embodiment of the present invention described above is represented as follows.

In the probabilistic scheduling method according to the present embodiment, the execution speed, for example, the operating frequency, is determined according to the number of cores performing a task and the progress of calculation so as to stochastically minimize the expected energy consumption for a given task.

To this end, the probabilistic scheduling method of this embodiment applies some basic operating principles. First, the latter part of the computation process with high probability applies a low execution rate, and the higher execution rate is applied toward the latter part of the computation process with a low probability. Second, c [m] is a time point when the execution speed f _m is applied and the next execution speed f _{(m + 1)} is applied. Where c [m] is less than or equal to c [m + 1]. Third, c [m] values are determined to minimize the probabilistic expectation value of the energy consumption, that is, the probabilistic expectation value, while completing the deadline.

In addition, in the probabilistic scheduling method according to the present embodiment, some system environment variables are applied. First, assuming a processor with N cores, the remaining cores are powered down when using n cores. Here, n is a natural number of 1 or more and N or less. Second, when using n cores, the probability probability distribution is expressed as P ⁿ , the worst-case computed amount is W ⁿ , and the deadline is expressed as D. Third, the M applicable execution speeds, e.g. clock frequencies, are respectively f ₁ , f ₂ ,... is represented by f _M. Here, M is a natural number larger than 2, and the relationship between each execution speed is f ₁ <f ₂ <. <f _M Fourth, the energy consumption needed to perform the calculation (a single cycle) for each step in the execution speed of f _m is expressed as e _m. Here, m is a natural number of 1 or more and M or less, and the relationship of energy consumption with respect to each execution speed is e ₁ <e ₂ <. <e _M

In order to determine an execution speed, for example, an operating frequency according to the number of cores performing the operation and the calculation progress, the probabilistic scheduling method of the present embodiment finds a solution according to Equation 3 for the fixed value of n.

&Quot; (3) &quot;

Here, Equation 3 has the condition of Equation 4 below.

&Quot; (4) &quot;

When N solutions are found by the above Equations 3 and 4, the optimal number of cores having the expected value of the minimum energy consumption is selected among the N solutions.

A process of determining an execution speed, for example, an operating frequency according to the number of cores performing the operation and the calculation progress amount will be described in more detail as follows.

5 is a diagram illustrating a process of removing an inefficient execution speed in a probabilistic scheduling method according to an embodiment of the present invention.

Referring to FIG. 5, in order to remove an inefficient execution speed for energy consumption, the method of the present embodiment removes a specific execution speed f _j having a relationship as in Equation 5 below.

[Equation 5]

Here, f _j satisfies the relationship f _i <f _j <f _k , and i, j, and k are natural numbers.

In the above process, the M execution speeds remaining after removing the specific execution speed having the relation of Equation 5 satisfy the following Equation 6 as shown in FIG. 5.

&Quot; (6) &quot;

Here, the predetermined execution speeds f _m and f _M satisfy the relationship f1 <f _m <f _M , and m and M are natural numbers.

Next, a conversion time point of the remaining M execution speeds is determined based on Equation 7 or Equation 8 below.

[Equation 7]

[Equation 8]

In equations (7) and (8), c [m] represents a conversion time point, and m is a natural number of 1 or more and less than M.

6A and 6B are diagrams for describing a method of finding a time of conversion of execution speed that can be employed in a probabilistic scheduling method according to an embodiment of the present invention.

As shown in Fig. 6A, c [2], c [3],... Which satisfy the above equation (7) or (8) while fixing the reference value c [1] from 1 to W ^{n in order} . , find the values of c [M]. Here, fixing _{c [1]} corresponds to fixing the value of P _{c [1]} in equation (7) or (8).

Next, the execution completion time using the c [m] values found by the reference value c [1] = 1 is calculated using Equation 9 below.

[Equation 9]

As a result of the calculation of Equation 9, if the completion time is greater than the deadline, the reference value is replaced with c [2], and C [2] is fixed from 1 to W ⁿ while satisfying Equation 7 or Equation 8 above. c [3], c [4],... , find the values of c [M].

In other words, if the completion time using the c [m] values found with the reference value c [b] = 1 is greater than the deadline, the reference value is set to c [b + 1] until the completion time is less than or equal to the deadline. While changing, find the value of c [m] that satisfies Equation 7 or Equation 8 above. Here, the change to c [b + 1] corresponds to changing the starting execution speed to f _{b + 1} in equation (9).

The reference value c [b] described above may be selected by a bisection search method as illustrated in FIG. 6B. The available c [b] values are selected by selecting a median value of the width corresponding to the amount of calculation (W), so that the remaining c [b + 1],. , c [M] values can be found.

In addition, by calculating the completion time using the found c [m] values using Equation 10 below, by comparing the calculation result with the deadline (D) value, the width of the available c [b] value is reduced I can go.

[Equation 10]

In this embodiment, an optimal c [b + 1],... Where the completion time is equal to the deadline (D) value using the bisecting test method. , c [M] Find the values.

Then, finally found c [b + 1],... , c [M] values are used to calculate the expected energy consumption stochastic expectation as shown in Equation 11 below.

[Equation 11]

Where c [0] is zero.

Next, for each n, 'expected energy consumption probability value' is calculated using Equation 3 above. Here, n is a natural number of 1 or more and N or less. That is, in this step, the process is repeated as many as the number of process cores in one processor core to calculate an energy consumption probabilistic expected value, and then n is selected based on the calculation result.

Next, in the multi-core processor, the values of P ⁿ and W ⁿ also change in accordance with the value of ⁿ , and the power supply of the Nn cores not used is turned off.

On the other hand, the execution speed f _b ,... , f _M is c [b] found in n cores,. , c [M] can be applied gradually.

According to the above-described embodiment, the multicore processor can perform low power operation by scheduling the number of cores and the execution speed to minimize the probabilistic expected amount of energy consumption based on the stochastic computational model.

In the above, the present invention has been described with reference to preferred embodiments, but the present invention is not limited to the above embodiments, and those skilled in the art to which the present invention pertains have various modifications and variations from this description. It will be possible. Therefore, the present invention should be construed with reference to the overall description of the appended claims and drawings, and all equivalent or equivalent modifications thereof will belong to the scope of the present invention.

Claims (9)

When multiple processor cores execute a task with an uncertain amount of computation that is unknown before completion of execution, the exact amount of computation required to complete a given task before the deadline is required to complete the given task before the deadline. A first step of expressing a calculation amount as a stochastic calculation model which is a difference function of a cumulative function with respect to the probability distribution function of the calculation amount of the given task;
Determining conversion time points of execution speed for minimizing a probabilistic expected value of energy consumption based on the stochastic calculation model;
Calculating an expected value for a minimum energy consumption amount for each core number of the plurality of processor cores; And
A fourth step of selecting an optimal number of cores having a probabilistic minimum expected value based on the calculation result of the third step
Stochastic scheduling method of a multicore processor for real-time parallel operation with an uncertain amount of computation comprising a.
delete The method of claim 1,
The third step includes a step of finding a solution according to Equation 3 below with respect to a fixed value of n in order to determine the execution speed according to the number of cores performing the operation and the calculation progress amount.
[Equation 3]

Here, Equation 3 has the condition of Equation 4 below,
[Equation 4]

Here, when the execution speed f _m is applied and the next execution speed f _{(m + 1)} is applied, it is called c [m], and c [m] is less than or equal to c [m + 1], The c [m] values are determined to minimize the probabilistic expected value of energy consumption while completing the run,
For a processor with N cores, where n cores are used, where n is a natural number greater than or equal to 1 and less than or equal to N, the remaining Nn cores are powered down, and the probability probability distribution is P ⁿ , a worst-case Computation is expressed by W ⁿ and deadline by D,
The M applicable execution speeds are f ₁ , f ₂ ,... , f _M , where M is a natural number greater than 2, and the relationship between each execution speed is f ₁ <f ₂ <. <f _M ,
The energy consumption required to perform a single cycle at the running speed of f _m is expressed as e _m , where m is a natural number greater than or equal to 1 and less than or equal to M, and the energy consumption for each running speed is The relationship is e ₁ <e ₂ <. <e _M ,
When N solutions are found by Equation 3, the fourth step is to perform a real-time parallel operation with an uncertain calculation amount, wherein the optimal number of cores having the expected value of the minimum energy consumption is selected among the N solutions. Probabilistic Scheduling Method of a Multicore Processor.
delete The method of claim 3,
The second step may include removing a specific execution speed having a relationship of Equation 5 below: Probabilistic scheduling method of a multicore processor for a real-time parallel operation with an uncertain amount of computation:
&Quot; (5) &quot;

Here, f _j represents the specific execution speed, satisfies the relationship f _i <f _j <f _k , and i, j, and k are natural numbers.
The method of claim 5,
The second step may include determining a conversion time point of the M execution speeds remaining after removing the specific execution speed having the relation of Equation 5 based on Equation 8 below. Probabilistic Scheduling of Multicore Processors for Parallel Jobs:
&Quot; (8) &quot;

Here, c [m] or c [y] represents the conversion point, and m or y is a natural number of 1 or more and less than M.
The method of claim 6,
In the second step, c [2], c [3],... Which satisfy Equation 8 while fixing the reference value c [1] from 1 to W ^{n in order} . , find the values of c [M],
The execution completion time using the c [m] values found by the reference value c [1] = 1 is calculated using Equation 9 below.
[Equation 9]

As a result of the calculation of Equation 9, if the execution completion time is greater than the deadline, c [3] satisfying Equation 8 while replacing C [2] from 1 to W ⁿ after replacing the reference value with c [2]. , c [4],... and a method of probabilistic scheduling of a multicore processor for real-time parallel work with an uncertain amount of computation, comprising steps of finding values of c [M].
The method of claim 7, wherein
In the second step, the execution completion time using the c [m] values found by the calculation of Equation 9 is calculated using Equation 10 below.
[Equation 10]

Comparing the result of the calculation according to Equation 10 with the deadline (D) value, the probability of the multi-core processor for real-time parallel operation with an uncertain amount of computation comprising reducing the width of the available c [b] value Scheduling Method.
The method of claim 8,
C [b + 1],... , Stochastic scheduling method of a multicore processor for real-time parallel operation with an uncertain amount of calculation, comprising calculating the expected energy consumption stochastic expectation using Equation 11 below using c [M] values:
[Equation 11]

Where c [0] is zero.

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