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On the Problem of Finding Optimal Harmonic Periods

Mohaqeqi, Morteza; Nasri, Mitra; Xu, Yang LU ; Cervin, Anton LU and Årzén, Karl-Erik LU (2016) International Conference on Real-Time Networks and Systems In Proceedings of the 24rd International Conference on Real Time and Networks Systems p.171-180
Abstract
Harmonic periods have wide applicability in industrial real-time systems. Rate monotonic (RM) is able to schedule task sets with harmonic periods up to 100% utilization. Also, if there is no release jitter and execution time variation, RM and EDF generate the same schedule for each instance of a task. This property decreases the jitters which happen during sampling and actuation of the tasks, and hence, it increases the quality of service in control systems. In this paper, we consider the problem of optimal period assignment where the periods are constrained to be harmonic. First, we assume that an interval is determined a priori for each task from which its period can be selected. The goal is to assign a (harmonic) period to each task... (More)
Harmonic periods have wide applicability in industrial real-time systems. Rate monotonic (RM) is able to schedule task sets with harmonic periods up to 100% utilization. Also, if there is no release jitter and execution time variation, RM and EDF generate the same schedule for each instance of a task. This property decreases the jitters which happen during sampling and actuation of the tasks, and hence, it increases the quality of service in control systems. In this paper, we consider the problem of optimal period assignment where the periods are constrained to be harmonic. First, we assume that an interval is determined a priori for each task from which its period can be selected. The goal is to assign a (harmonic) period to each task such that the total system utilization is maximized while the task set remains feasible. We show that this problem is (at least) weakly NP-hard. This is shown by reducing the NP-complete number partitioning problem to the mentioned harmonic period assignment problem. Afterwards, we consider a variant of the problem in which the periods are not restricted to a special interval and the objective is to minimize the total weighted sum of the periods with the same feasibility constraint. We present two approximation algorithms for the second problem and show that the maximum error of these algorithms is bounded by a factor of 2. Our evaluations show that, on the average, results of the approximation algorithms are very close to an optimal solution. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Proceedings of the 24rd International Conference on Real Time and Networks Systems
pages
10 pages
publisher
ACM
conference name
International Conference on Real-Time Networks and Systems
external identifiers
  • scopus:84997079603
ISBN
978-1-4503-4787-7
DOI
10.1145/2997465.2997490
language
English
LU publication?
yes
id
f4647754-2da9-4925-9fdb-2ae90177f48a
date added to LUP
2016-10-24 12:01:40
date last changed
2017-04-10 11:23:57
@inproceedings{f4647754-2da9-4925-9fdb-2ae90177f48a,
  abstract     = {Harmonic periods have wide applicability in industrial real-time systems. Rate monotonic (RM) is able to schedule task sets with harmonic periods up to 100% utilization. Also, if there is no release jitter and execution time variation, RM and EDF generate the same schedule for each instance of a task. This property decreases the jitters which happen during sampling and actuation of the tasks, and hence, it increases the quality of service in control systems. In this paper, we consider the problem of optimal period assignment where the periods are constrained to be harmonic. First, we assume that an interval is determined a priori for each task from which its period can be selected. The goal is to assign a (harmonic) period to each task such that the total system utilization is maximized while the task set remains feasible. We show that this problem is (at least) weakly NP-hard. This is shown by reducing the NP-complete number partitioning problem to the mentioned harmonic period assignment problem. Afterwards, we consider a variant of the problem in which the periods are not restricted to a special interval and the objective is to minimize the total weighted sum of the periods with the same feasibility constraint. We present two approximation algorithms for the second problem and show that the maximum error of these algorithms is bounded by a factor of 2. Our evaluations show that, on the average, results of the approximation algorithms are very close to an optimal solution.},
  author       = {Mohaqeqi, Morteza and Nasri, Mitra and Xu, Yang and Cervin, Anton and Årzén, Karl-Erik},
  booktitle    = {Proceedings of the 24rd International Conference on Real Time and Networks Systems},
  isbn         = {978-1-4503-4787-7 },
  language     = {eng},
  month        = {10},
  pages        = {171--180},
  publisher    = {ACM},
  title        = {On the Problem of Finding Optimal Harmonic Periods},
  url          = {http://dx.doi.org/10.1145/2997465.2997490},
  year         = {2016},
}