An Analysis of Zero-Clairvoyant Scheduling

Subramani, K.

doi:10.1007/3-540-46002-0_8

Cited by 11 publications

(7 citation statements)

References 19 publications

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“…There are a number of practical instances for which zero-clairvoyant scheduling is the only methodology available, since online computation is not permitted. For an overview of zero-clairvoyant scheduling in the presence of intra-period constraints only, see Subramani (2002a).…”

Section: Query Modelmentioning

confidence: 99%

“…Thus the entire procedure consists of (m + m ) convex minimisation calls, and hence the total time taken is O((m + m ) • C), where C is the fastest convex minimisation algorithm (Hiriart-urruty and Lemarechal 1993). Subramani (2002a) provides a detailed argument establishing that replacing each constraint by a number as specified by Algorithm 3 preserves the solution space. Thus, in the Order k restriction, the execution time variables can be eliminated through convex minimisation to get a simple linear program, which in turn can be solved using Bellman-Ford techniques.…”

Section: Algorithm 3 Transformation Proceduresmentioning

confidence: 99%

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Periodic Linear Programming with applications to real-time scheduling

Subramani¹

2005

Math. Struct. Comp. Sci.

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In this paper we introduce a new mathematical modelling technique called Periodic Linear Programming; the periodic properties of Periodic Linear Programs (PLPs) permit the specification of inter-period constraints in embedded systems, in a straightforward and natural manner. We analyse PLPs in which the relationship between program variables is restricted to the class of difference constraints. Our analysis establishes that such PLPs can be reduced to simple linear programs, and hence decided in polynomial time. The class of difference constraints is extremely important from the perspective of embedded systems design, in that it permits the specification of complex timing constraints in real-time specification languages. A PLP can be thought of as a finite-description tool that represents infinite-state systems; although we use this tool purely for the purpose of modelling real-time scheduling problems, PLPs also find applications in other areas, such as concurrency design. In studying this programming paradigm, we develop novel techniques that, to the best of our knowledge, are not part of the literature. We build on the PLP structure to introduce a generalisation called Periodic Quantified Linear Programming; this programming paradigm permits the specification and analysis of uncertainty in the parameters of a PLP. Consequently, a Periodic Quantified Linear Program (PQLP) is the natural modelling tool to capture the requirements of periodic, embedded systems that are characterised by uncertainty in the execution times of processes, periodicity and relative timing constraints. In this paper, we use the PQLP structure to model and solve the periodic version of the zero-clairvoyant scheduling problem. Modelling uncertainty in the problem description is a typical technique used to incorporate a measure of fault-tolerance in the specification.

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Section: Query Modelmentioning

confidence: 99%

Section: Algorithm 3 Transformation Proceduresmentioning

confidence: 99%

Periodic Linear Programming with applications to real-time scheduling

Subramani¹

2005

Math. Struct. Comp. Sci.

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“…The task of the dispatcher is to ensure that the schedulable jobs are commenced at the appropriate point on the time line. If the start times of jobs are constants, then the task of dispatching them is trivial [23]. However, in case of partially clairvoyant schedules, the start time of a job is a function of the execution times of jobs that are scheduled before it and hence dispatching is a non-trivial task.…”

Section: Introductionmentioning

confidence: 99%

On the Design and Implementation of a Shared Memory Dispatcher for Partially Clairvoyant Schedulers

Subramani

Yellajyosula

2007

Int J Parallel Prog

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With the onset of distributed computing in hard real-time applications, the problem of assigning to, scheduling in, and executing jobs on processors, has received a lot of attention. Usually, real-time systems are embedded in closed loop reactive environments with uncertain behaviors and such systems take varying times to respond to such stimuli. One of the fundamental features of such systems is the presence of complex timing constraints between pairs of jobs. A secondary feature is the non-constant nature of the execution times of jobs. Real-time operating systems such as MARUTI can measure the interval within which the execution time varies (Mosse et al. ) to schedule jobs with varying execution times and non-trivial timing constraints. The schedulability of the job set is determined offline and a set of dispatch functions are produced from the given set of constraints if the job set is schedulable. The dispatch functions bind the start time of a job J to an interval that depends on the start and execution times of jobs sequenced before J . The online dispatcher of the system reads these dispatch functions and computes the interval within which a job can start without violating the constraints imposed on the system. In certain situations, the dispatcher fails to dispatch a job as the time to compute the dispatch functions associated with a job is greater than the interval within which the job needs to be dispatched. This , we propose and implement a partially clairvoyant dispatching algorithm on a shared memory cluster with Concurrent Read Exclusive Write (CREW) architecture and contrast it with the sequential approach. For a preset number of processors, our approach has O(1) dispatch complexity while using a total of O(n 2 ) space, while the sequential approach requires (n) time. The detailed implementation profile obtained clearly demonstrates the superiority of the multiprocessor approach to dispatching. We also address the issue of scalability of the dispatcher for increasing number of processors and show that job sets of different sizes require different number of processors. Finally, we demonstrate the effect of execution time on the dispatchability of schedules.

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“…1 This research was fully supported by the Air-Force Office of Scientific Research under Contract FA9550-06-1-0550. Segmentation [5] and Real-Time scheduling [16]. Note that the NCCD problem is equivalent to checking whether a system of difference constraints is feasible [4].…”

Section: Introductionmentioning

confidence: 99%

A Zero-Space algorithm for Negative Cost Cycle Detection in networks

Subramani

2007

Journal of Discrete Algorithms

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This paper is concerned with the problem of checking whether a network with positive and negative costs on its arcs contains a negative cost cycle. The Negative Cost Cycle Detection (NCCD) problem is one of the more fundamental problems in network design and finds applications in a number of domains ranging from Network Optimization and Operations Research to Constraint Programming and System Verification. As per the literature, approaches to this problem have been either Relaxation-based or Contraction-based. We introduce a fundamentally new approach for negative cost cycle detection; our approach, which we term as the Stressing Algorithm, is based on exploiting the connections between the NCCD problem and the problem of checking whether a system of difference constraints is feasible. The Stressing Algorithm is an incremental, comparison-based procedure which is as efficient as the fastest known comparison-based algorithm for this problem. In particular, on a network with n vertices and m edges, the Stressing Algorithm takes O(m · n) time to detect the presence of a negative cost cycle or to report that none exists. A very important feature of the Stressing Algorithm is that it uses zero extra space; this is in marked contrast to all known algorithms that require (n) extra space. It is well known that the NCCD problem is closely related to the Single Source Shortest Paths (SSSP) problem, i.e., the problem of determining the shortest path distances of all the vertices in a network, from a specified source; indeed most algorithms in the literature for the NCCD problem are modifications of approaches to the SSSP problem. At this juncture, it is not clear whether the Stressing Algorithm could be extended to solve the SSSP problem, even if O(n) extra space is available.

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An Analysis of Zero-Clairvoyant Scheduling

Cited by 11 publications

References 19 publications

Periodic Linear Programming with applications to real-time scheduling

Periodic Linear Programming with applications to real-time scheduling

On the Design and Implementation of a Shared Memory Dispatcher for Partially Clairvoyant Schedulers

A Zero-Space algorithm for Negative Cost Cycle Detection in networks

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