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  • 1. Lennerstad, Håkan
    et al.
    Lundberg, Lars
    Guaranteeing Response Times for Aperiodic Tasks in Global Multiprocessor Scheduling2007In: Real-time systems, ISSN 0922-6443, E-ISSN 1573-1383, Vol. 35, no 2, p. 135-151Article in journal (Refereed)
    Abstract [en]

    We provide a constant time schedulability test for an on-line multiprocessor server handling aperiodic tasks. Dhall's effect is avoided by dividing the tasks in two priority classes based on task utilization: heavy and light. We prove that if the load on the multiprocessor server stays below U threshold = 3 - root 7 approximately equals 35.425%, the server can accept an incoming aperiodic task and guarantee that the deadlines of all accepted tasks will be met. The same number 35.425% is also a threshold for a task to be characterized as heavy. The bound U threshold = 3 - root 7 approximately equals 35.425% is easy-to-use, but not sharp if we know the number of processors in the multiprocessor system. Assuming the server to be equipped with m processors, we calculate a formula for the sharp bound U threshold (m), which converges to U threshold from above as m -> infinity . The results are based on a utilization function u(x) = 2(1 - x)/(2 + root 2+2x). By using this function, the performance of the multiprocessor server can in some cases be improved beyond U threshold(m) by paying the extra overhead of monitoring the individual utilization of the current tasks.

  • 2. Lundberg, Lars
    Slack-based multiprocessor scheduling of aperiodic real-time tasks2011In: Real-time systems, ISSN 0922-6443, E-ISSN 1573-1383, Vol. 47, no 6, p. 618-638Article in journal (Refereed)
    Abstract [en]

    We provide a constant time schedulability test and priority assignment algorithm for an on-line multiprocessor server handling aperiodic tasks. The so called Dhall's effect is avoided by dividing tasks in two priority classes based on their utilization: heavy and light. The improvement in this paper is due to assigning priority of light tasks based on slack-not on deadlines. We prove that if the load on the multiprocessor stays below (3 - √5)/2 ≈ 38.197%, the server can accept an incoming aperiodic task and guarantee that the deadlines of all accepted tasks will be met. This is better than the current state-of-the-art algorithm where the priorities of light tasks are based on deadlines (the corresponding bound is in that case 35.425%). The bound (3 - √5)/ 2 can be improved if the number of processors m is known. There is a formula for the sharp bound Uthreshold(m) = 3m - 2 - √5m 2 - 8m + 4/2(m - 1), which converges to (3 - √5)/2 from above as m→∞. For m≥3, the bound is higher (i.e., better) than the corresponding sharp bound for the state-of-the-art algorithm where the priorities of light tasks are based on deadlines. A simulation study also indicates that when m>3 the best effort behavior of the priority assignment scheme suggested here is better than that of the traditional scheme where priorities are based on deadlines.

  • 3. Lundberg, Lars
    Utilization based schedulability bounds for age constraint process sets in real-time systems2002In: Real-time systems, ISSN 0922-6443, E-ISSN 1573-1383, p. 273-295Article in journal (Refereed)
    Abstract [en]

    Some real-time systems consist of a number of processes that operate under age constraints. In such systems, the maximum time from the start of process L-i in cycle k to the end in cycle k+1 must not exceed the age constraint A(i) for that process. The age constraint can be met by using fixed priority scheduling and periods equal to A(i)/2. However, this approach restricts the number of process sets which are schedulable. In this paper, we define a method for obtaining process periods other than A(i)/2. The periods are calculated in such a way that the age constraints are met. Our approach is better in the sense that a larger number of process sets can be scheduled compared to using periods equal to A(i)/2. The main results in this paper are a number of performance bounds on age constraint processes. These bounds show that there is a significant gain in worst case as well as in best case behavior by using periods other than A(i)/2, particularly when there are a large number of processes in the system.

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