Task allocation, migration and scheduling for energy-efficient real-time multiprocessor architectures

2020

Background. In setting a problem of minimizing total tardiness by the heuristic based on remaining available and processing periods, there are two opposite ways to input the data: the job release dates are given in either ascending or descending order. It was recently ascertained that scheduling a few equal-length jobs is expectedly faster by ascending order, whereas scheduling 30 to 70 equal-length jobs is 1.5 % to 2.5 % faster by descending order. For the number of equal-length jobs between roughly 90 and 250, the ascending job order again results in shorter computation times. Objective. The goal is to ascertain whether the job order input is significant in scheduling by using the heuristic for the case when the jobs have different lengths. Job order efficiency will be studied on tight-tardy progressive idling-free 1machine preemptive scheduling. Methods. To achieve the said goal, a computational study is carried out with a purpose to estimate the averaged computation time for both ascending and descending orders of job release dates. Instances of the job scheduling problem are generated so that schedules which can be obtained trivially, without the heuristic, are excluded. Results. On average, the descending job order input gives a tiny advantage in computation time. This advantage decreases as the number of jobs increases. The decrement resembles a steep exponential decrease. The factual advantage is so insignificant that even after solving long series of job scheduling problems the saved computational time cannot be counted in minutes, not speaking about hours as it was for the case of equal-length jobs. Conclusions. The significance of the job order input is much lower than that for the case of equal-length jobs. Theoretically, the heuristic's efficient job order input does exist but its efficiency can be practically used only by working on extremely long series of scheduling problems where the number of jobs should not exceed 300.

Section: The Heuristic Based On Remaining Available and Processing Pementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tight-Tardy Progressive Idling-Free 1-Machine Preemptive Scheduling by Heuristic’s Efficient Job Order Input

2020

“…Heuristics are the only means which capable of scheduling hundreds and thousands of jobs, or more [2,3]. In some practical tasks, moreover, the entire schedule can be an extremely long sequence of jobs [4], whereas the heuristics allow online scheduling (once a job is scheduled at a time moment, it will not be changed and thus the jobs already scheduled can be executed straightforwardly without waiting for the entire schedule) [5].…”

Section: Introductionmentioning

confidence: 99%

Tight-Tardy Progressive Idling-Free 1-Machine Preemptive Scheduling With Job Priority Weights by Heuristic’s Efficient Job Order Input

2021

Background. In setting a problem of minimizing total weighted tardiness by the heuristic based on remaining available and processing periods, there are two opposite ways to input the data: the job release dates are given in either ascending or descending order. It was recently ascertained that scheduling a few equal-length jobs is expectedly faster by ascending order, whereas scheduling 30 to 70 equal-length jobs is 1.5 % to 2.5 % faster by descending order. For the number of equal-length jobs between roughly 90 and 250, the ascending job order again results in shorter computation times. In the case when the jobs have different lengths, the significance of the job order input is much lower. On average, the descending job order input gives a tiny advantage in computation time. This advantage decreases as the number of jobs increases. Objective. The goal is to ascertain whether the job order input is significant in scheduling by using the heuristic for the case when the jobs have different lengths with job priority weights. Job order efficiency will be studied on tight-tardy progressive idling-free 1-machine preemptive scheduling. Methods. To achieve the said goal, a computational study is carried out with a purpose to estimate the averaged computation time for both ascending and descending orders of job release dates. First, the computation time for the ascending job order input is estimated for a series of job scheduling problems. Then, in each instance of this series, job lengths, priority weights, release dates, and due dates are reversed making thus the respective instance for the descending job order input, for which computation time is estimated as well. Results. The significance of the job order input is much lower than that for the case of jobs without priorities. With assigning the job priority weights, the job order input becomes further “dithered”, adding randomly scattered priority weights to randomly scattered job lengths and partially randomized due dates. On average, the descending job order input is believed to give a tiny advantage in computation time in scheduling up to 100 jobs. However, this advantage, if any (being tinier than that in the case of random job lengths without priorities), quickly vanishes as the number of jobs increases. Conclusions. It is better to compose job scheduling problems which would be closer to the case with equal-length jobs without priorities, where the saved computational time can be counted in hours. Even if the job lengths and priority weights are scattered, it is recommended to artificially “flatten” them. When artificial manipulations over job processing periods and job priority weights are impossible, it is recommended to use the descending job order input in scheduling up to 100 jobs, and either job order input in scheduling more than 100 jobs, although substantial benefits are not expected in this case.

“…[1,2]. Besides, in computing, it is connected with optimizing parallelization of tasksets on multiprocessor systems [3,4].…”

Section: Introductionmentioning

confidence: 99%

“…So, the jobs already scheduled can be executed straightforwardly without waiting for the entire schedule. All the more so because the entire schedule can be an extremely long sequence of jobs [2,4,8,9].…”

Section: Introductionmentioning

confidence: 99%

Heuristic’s Job Order Efficiency in Tight-Tardy Progressive Idling-Free 1-Machine Preemptive Scheduling of Equal-Length Jobs

2020

Background. In setting a problem of minimizing total tardiness by the heuristic based on remaining available and processing periods, there are two opposite ways to input the data: the job release dates are given in either ascending or descending order. It was recently proved that an efficient job order can save significant computation time by using the Boolean linear programming model provided for finding schedules with the exactly minimal total tardiness. Objective. The goal is to ascertain whether the job order input is significant in scheduling by using the heuristic. Job order efficiency will be studied on tight-tardy progressive idling-free 1-machine preemptive scheduling of equal-length jobs. Methods. To achieve the said goal, a computational study is carried out with a purpose to estimate the averaged computation time for both ascending and descending orders of job release dates. Instances of the job scheduling problem are generated so that schedules which can be obtained trivially, without the heuristic, are excluded. Results. Scheduling a few jobs is expectedly faster by ascending order, but this part is full of computational artifacts. Scheduling 30 to 70 jobs is 1.5 % to 2.5 % faster by descending order. However, scheduling up to 90 jobs is expectedly still faster by descending order, although a risk of losing this advantage exists. For the number of jobs between roughly 90 and 250, the ascending job order again results in shorter computation times. Since the point of about 250 jobs, the advantage trend (of either ascending or descending order) appears more stable. Conclusions. In scheduling by using the heuristic, the job order input is indeed significant. The average relative difference does not exceed 1.5 % for 2 to 1000 jobs consisting up to 17 processing periods. For obtaining a statistically reliable computation speed advantage, it is better to consider no less than 250 jobs. As either the number of jobs or the number of job parts increases, the computation speed advantage may become unstable and eventually vanish. Nevertheless, the ascending job order can save a lot of computational time in the case of scheduling at least a few thousand jobs having just a few processing periods each. After solving thousands of such cases the saved time may be counted in hours.