Academia.eduAcademia.edu

Outline

Title
Abstract
Introduction
References

Journal of Scheduling

Profile image of Michael PalisMichael Palis

2008

Abstract

Online real-time preemptive scheduling of jobs with deadlines on multiple machines †

Related papers

Special cases of online parallel job scheduling
Johann Hurink

In this paper we consider the online scheduling of jobs, which require processing on a number of machines simultaneously. These jobs are presented to a decision maker one by one, where the next job becomes known as soon as the current job is scheduled. The objective is to minimize the makespan. For the problem with three machines we give a

View PDFchevron_right
An O(n4) algorithm for preemptive scheduling of a single machine to minimize the number of late jobs
Claude M Le Pape

Operations Research Letters, 1999

Sevaux for many enlightening discussions on the topic of this paper. The author gratefully acknowledges the useful comments from the reviewer.

View PDFchevron_right
On-line scheduling on a single machine: maximizing the number of early jobs
Han Hoogeveen

Operations Research Letters, 2000

This note deals with the scheduling problem of maximizing the number of early jobs on a single machine. We investigate the on-line version of this problem in the Preemption-Restart model. This means that jobs may be preempted, but preempting results in all the work done on this job so far being lost. Thus, if the job is restarted, then it has to be done from scratch.

View PDFchevron_right
Online parallel machine scheduling to maximize the number of early jobs
Ming Liu

2012

We study a maximization problem: online scheduling on m identical machines to maximize the number of early jobs. The problem is online in the sense that all jobs arrive over time. Each job's characteristics, such as processing time and due date, become known at its arrival time. We consider the preemption-restart model, in which preemption is allowed, while once a job is restarted, it loses all the progress that has been made on this job so far. If in some schedule a job is completed before or at its due date, then it is called early or on time . The objective is to maximize the number of early jobs. For m identical machines, we prove an upper bound 1 − 1/2m of competitive ratio and show that ECT earliest completion time algorithm is 1/2-competitive.

View PDFchevron_right
The one-machine just-in-time scheduling problem with preemption
yann hendel

Discrete Optimization, 2009

This paper investigates the notion of preemption in scheduling, with earliness and tardiness penalties. Starting from the observation that the classical cost model where penalties only depend on completion times does not capture the just-in-time philosophy, we introduce a new model where the earliness costs depend on the start times of the jobs. To solve this problem, we propose an efficient representation of dominant schedules, and a polynomial algorithm to compute the best schedule for a given representation. Both a local search algorithm and a branch-and-bound procedure are then derived. Experiments finally show that the gap between our upper bound and the optimum is very small.

View PDFchevron_right
The single machine just-in-time scheduling problem with preemptions
yann hendel

2005

This paper deals with a variation of the single machine earliness/tardiness scheduling problem: preemption is allowed and, in order to penalize job interruptions, earliness costs depend on the starting time of the job while tardiness costs depend on the end times as in the usual models. We propose dominance properties and a polynomial time algorithm is given to solve the particular case where the sequence of the start and completion of the jobs is fixed.

View PDFchevron_right
Selective preemption strategies for parallel job scheduling
Rajkumar Kettimuthu

International Journal of High Performance Computing and Networking, 2005

Rajkumar Kettimuthu* Argonne National Laboratory, Argonne, IL 60439, USA The University of Chicago, Chicago, IL 60615, USA E-mail: kettimut@mcs.anl.gov *Corresponding author ... Vijay Subramani and Srividya Srinivasan Microsoft Corporation, Redmond, WA 98052, ...

View PDFchevron_right
Non-preemptive Scheduling on Machines with Setup Times
Friedhelm Meyer auf der Heide

Lecture Notes in Computer Science, 2015

Consider the problem in which n jobs that are classified into k types are to be scheduled on m identical machines without preemption. A machine requires a proper setup taking s time units before processing jobs of a given type. The objective is to minimize the makespan of the resulting schedule. We design and analyze an approximation algorithm that runs in time polynomial in n, m and k and computes a solution with an approximation factor that can be made arbitrarily close to 3 /2.

View PDFchevron_right
Preemptive scheduling with transportation delays between machines
Mourad Boudhar

Journal of Modelling in Management, 2020

PurposeThis paper studies the preemptive scheduling problem of independent jobs on identical machines. The purpose of this paper is to minimize the makespan under the imposed constraints, namely, the ones that relate the transportation delays which are required to transport a preempted job from one machine to another. This study considers the case when the transportation delays are variable.Design/methodology/approachThe contribution is twofold. First, this study proposes a new linear programming formulation in real and binary decision variables. Then, this study proposes and implements a solution strategy, which consists of two stages. The goal of the first stage is to obtain the best machines order using a local search strategy. For the second stage, the objective is to determine the best possible sequence of jobs. To solve the preemptive scheduling problem with transportation delays, this study proposes a heuristic and two metaheuristics (simulated annealing and variable neighbor...

View PDFchevron_right
A fast on-line algorithm for the preemptive scheduling of equal-length jobs on a single processor
Nodari Vakhania

2008

We propose a fast on-line algorithm for preemptive scheduling of equal-length jobs with due dates. The jobs are released on-line over time. We have a single processor that can handle at most one job simultaneously. Our objective is to minimize the number of late jobs, ones completed after their due dates.

View PDFchevron_right

References (28)

  1. Brandt S, Nutt G, Berk T, Humphrey M. Soft real-time application execution with dynamic quality of service assurance. 1998 International Workshop on Quality of Service, May 1998; 154-163.
  2. Compton C, Tennenhouse D. Collaborative load shedding. Proceedings of the Workshop on the role of real-time in multimedia=interactive computing systems, December 1993.
  3. Fan C. Realizing a soft real-time framework for supporting distributed multimedia applications. Proceedings of the 5th IEEE Workshop on the Future Trends of Distributed Computing Systems, August 1995; 128-134.
  4. Humphrey M, Berk T, Brandt S, Nutt G. Dynamic quality of service resource management for multimedia applications on general purpose operating systems. IEEE Workshop in Middleware for Distributed Real-Time Systems and Services, December 1997; 97-104.
  5. Jones M, Barbera III J, Forin A. An overview of the Rialto real-time architecture. Proceedings of the 7th ACM SIGOPS European Workshop, September 1996; 249-256.
  6. Jones M, Rosu D, Rosu M-C. CPU Reservations and time constraints: e cient, predictable scheduling of independent activities. Proceedings of the 16th ACM Symposium on Operating Systems Principles, October 1997.
  7. Liu H, Zarki ME. Adaptive source rate control for real-time wireless video transmission. Mobile Networks and Applications 1998; 3:49-60.
  8. Nieh J, Lam M. The design, implementation and evaluation of SMART: a scheduler for multimedia applications. Proceedings of the 16th ACM Symposium on Operating Systems Principles, October 1997.
  9. Nieh J, Lam M. Integrated processor scheduling for multimedia. Proceedings of the 5th International Workshop on Network and Operating System Support for Digital Audio and Video, April 1995.
  10. Rajugopal GR, Hafez RHM. Adaptive rate controlled, robust video communication over packet wireless networks. Mobile Networks and Applications 1998; 3:33-47.
  11. Yau DKY, Lam SS. Adaptive rate-controlled scheduling for multimedia applications. Proceedings of the IS&T=SPIE Multimedia Computing and Networking Conference, San Jose, CA, January 1996.
  12. Mok A. Fundamental design problems of distributed systems for the hard real-time environment. Doctoral Dissertation, M.I.T., 1983.
  13. Baruah S, Koren G, Mishra B, Ragunathan A, Rosier L, Sasha D. On-line scheduling in the presence of overload. Proceedings of the 32nd IEEE Symposium on Foundations of Computer Science, October 1991; 100-110. Copyright ? 2001 John Wiley & Sons, Ltd. J. Sched. 2001; 4:297-312
  14. Lipton RJ, Tomkins A. Online interval scheduling. Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms, 1994; 302-311.
  15. Becchetti L, Leonardi S, Muthukrishnan S. Scheduling to minimize average stretch without migration. Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms, 2000; 548-557.
  16. Bender M, Chakrabarti S, Muthukrishnan S. Flow and stretch metrics for scheduling continuous job streams. Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, 1999.
  17. Muthukrishnan S, Rajaraman R, Shaheen abd A, Gehrke JE. Online scheduling to minimize average stretch. Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science 1999; 433-443.
  18. Bar-Noy A, Guha S, Naor JS, Schieber B. Approximating the throughput of multiple machines in real-time scheduling. Proceedings of the 31st Annual ACM Symposium on Theory of Computing, 1999; 622-631.
  19. Sahni S. Algorithms for scheduling independent tasks. JACM 1976; 23:116 -127.
  20. Lawler EL. A dynamic programming approach for preemptive scheduling of a single machine to minimize the number of late jobs. Annals of Operations Research 1990; 26:125-133.
  21. Kise H, Ibaraki T, Mine H. A solvable case of one machine scheduling problems with ready and due date. Operations Research 1978; 26:121-126.
  22. Bar-Noy A, Bar-Yehuda R, Freund A, Naor JS, Schieber B. A uniÿed approach to approximating resource allocation and scheduling. Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, May 2000; 735-744.
  23. Berman P, DasGupta B. Improvements in throughput maximization for real-time scheduling. Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, May 2000; 680-687.
  24. Spieksma FCR. On the approximability of an interval scheduling problem. Journal of Scheduling 1999; 2:215-227. (preliminary version in the Proceedings of the APPROX'98 Conference. Lecture Notes in Computer Science, vol. 1444. Springer: Berlin, 1998; 169-180).
  25. Baruah S, Koren G, Mao D, Mishra B, Raghunathan A, Rosier L, Shasha D, Wang F. On the competitiveness of on-line real-time scheduling. Real-Time Systems 1992; 4:125-144.
  26. Koren G, Shasha D. An optimal on-line scheduling algorithm for overloaded real-time systems. SIAM Journal on Computing 1995; 24:318-339.
  27. Dertouzos M. Control robotics: the procedural control of physical processors. Proceedings of IFIP Congress, 1974; 807-813.
  28. Copyright ? 2001 John Wiley & Sons, Ltd. J. Sched. 2001; 4:297-312

Related papers

Online real‐time preemptive scheduling of jobs with deadlines on multiple machines
Michael Palis

Journal of Scheduling, 2001

In this paper, we derive bounds on performance guarantees of online algorithms for real-time preemptive scheduling of jobs with deadlines on K machines when jobs are characterized in terms of their minimum stretch factor α (or, equivalently, their maximum execution rate r = 1/α). We consider two well known preemptive models that are of interest from practical applications: the hard real-time scheduling model in which a job must be completed if it was admitted for execution by the online scheduler, and the firm real-time scheduling model in which the scheduler is allowed not to complete a job even if it was admitted for execution by the online scheduler. In both models, the objective is to maximize the sum of execution times of the jobs that were executed to completion, preemption is allowed, and the online scheduler must immediately decide, whenever a job arrives, whether to admit it for execution or reject it. We measure the competitive ratio of any online algorithm as the ratio of the value of the objective function obtained by this algorithm to that of the best possible offline algorithm. We show that no online algorithm can have a competitive ratio greater than 1 − (1/α) + ε for hard real-time scheduling with K ≥ 1 machines and greater than 1 − (3/(4 α)) + ε for firm real-time scheduling on a single machine, where ε > 0 may be arbitrarily small, even if the algorithm is allowed to know the value of α in advance. On the other hand, we exhibit a simple online scheduler that achieves a competitive ratio of at least 1 − (1/α) in either of these models with K machines. The performance guarantee of our simple scheduler shows that it is in fact an optimal scheduler for hard real-time scheduling with K machines. We also describe an alternative scheduler for firm real-time scheduling on a single machine in which the competitive ratio does not go to zero as α approaches 1. Both of our schedulers do not know the value of α in advance.

View PDFchevron_right
Online Real-Time Preemptive Scheduling of Jobs with Deadlines
Michael Palis

Lecture Notes in Computer Science, 2000

In this paper, we derive bounds on performance guarantees of online algorithms for real-time preemptive scheduling of jobs with deadlines on K machines when jobs are characterized in terms of their minimum stretch factor α (or, equivalently, their maximum execution rate r = 1/α). We consider two well known preemptive models that are of interest from practical applications: the hard real-time scheduling model in which a job must be completed if it was admitted for execution by the online scheduler, and the firm real-time scheduling model in which the scheduler is allowed not to complete a job even if it was admitted for execution by the online scheduler. In both models, the objective is to maximize the sum of execution times of the jobs that were executed to completion, preemption is allowed, and the online scheduler must immediately decide, whenever a job arrives, whether to admit it for execution or reject it. We measure the competitive ratio of any online algorithm as the ratio of the value of the objective function obtained by this algorithm to that of the best possible offline algorithm. We show that no online algorithm can have a competitive ratio greater than 1 − (1/α) + ε for hard real-time scheduling with K ≥ 1 machines and greater than 1 − (3/(4 α)) + ε for firm real-time scheduling on a single machine, where ε > 0 may be arbitrarily small, even if the algorithm is allowed to know the value of α in advance. On the other hand, we exhibit a simple online scheduler that achieves a competitive ratio of at least 1 − (1/α) in either of these models with K machines. The performance guarantee of our simple scheduler shows that it is in fact an optimal scheduler for hard real-time scheduling with K machines. We also describe an alternative scheduler for firm real-time scheduling on a single machine in which the competitive ratio does not go to zero as α approaches 1. Both of our schedulers do not know the value of α in advance.

View PDFchevron_right
Online Non-preemptive Scheduling on Unrelated Machines with Rejections
Abhinav Srivastav

Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures - SPAA '18, 2018

When a computer system schedules jobs there is typically a significant cost associated with preempting a job during execution. This cost can be from the expensive task of saving the memory's state and loading data into and out of memory. It is desirable to schedule jobs non-preemptively to avoid the costs of preemption. There is a need for non-preemptive system schedulers on desktops, servers and data centers. Despite this need, there is a gap between theory and practice. Indeed, few non-preemptive online schedulers are known to have strong foundational guarantees. This gap is likely due to strong lower bounds on any online algorithm for popular objectives. Indeed, typical worst case analysis approaches, and even resource augmented approaches such as speed augmentation, result in all algorithms having poor performance guarantees. This paper considers on-line non-preemptive scheduling problems in the worst-case rejection model where the algorithm is allowed to reject a small fraction of jobs. By rejecting only a few jobs, this paper shows that the strong lower bounds can be circumvented. This approach can be used to discover algorithmic scheduling policies with desirable worst-case guarantees. Specifically, the paper presents algorithms for the following two objectives: minimizing the total flow-time and minimizing the total weighted flow-time plus energy under the speed-scaling mechanism. The algorithms have a small constant competitive ratio while rejecting only a constant fraction of jobs. Beyond specific results, the paper asserts that alternative models beyond speed augmentation should be explored to aid in the discovery of good schedulers in the face of the requirement of being online and non-preemptive.

View PDFchevron_right
An Optimal Parallel Algorithm for Preemptive Job Scheduling that Minimizes Maximum Lateness
Susan Rodger

1988

ABSTRACT In this paper we present the Preemptive Minimize Maximum Lateness algorithm, an optimal parallel algorithm that schedules jobs for execution on a single processor machine with preemption. Each job is described by a release time, a deadline and a processing time. A job is considered late if it does not complete by its deadline and its lateness is defined as the difference between its completion time and deadline.

View PDFchevron_right
Semi-Online Preemptive Scheduling: One Algorithm for All Variants
Huy Anh Nguyen

Theory of Computing Systems, 2010

We present a unified optimal semi-online algorithm for preemptive scheduling on uniformly related machines with the objective to minimize the makespan. This algorithm works for all types of semi-online restrictions, including the ones studied before, like sorted (decreasing) jobs, known sum of processing times, known maximal processing time, their combinations, and so on. Based on the analysis of this algorithm, we derive some global relations between various semi-online restrictions and tight bounds on the approximation ratios for a small number of machines.

View PDFchevron_right
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved