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Fcfs-scheduling in a hard real-time environment under rush-hour conditions

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Abstract

We investigate some real-time behaviour of a (discrete time) single server system with FCFS (first come first serve) task scheduling under rush-hour conditions. The main result deals with the probability distribution of a random variable SRD(T), which describes the time the system operates without violating a fixed task service time deadlineT.

Relying on a simple general probability model, asymptotic formulas concerning the mean and the variance of SRD(T) are determined; for instance, if the average arrival rate is larger than the departure rate, the expectation of SRD(T) is proved to fulfilE[SRD(T)]=c 1+O(T −3) forT→∞, wherec 1 denotes some constant. If the arrival rate equals the departure rate, we findE[SRD(T)]∼c 2 T i for somei≥2.

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References

  1. E. A. Bender,Asymptotic methods in enumeration, SIAM Review 16 (1974), 485–515.

    Google Scholar 

  2. J. Blieberger and U. Schmid,Preemptive LCFS scheduling in hard real-time applications, Performance Evaluation (1991) (to appear).

  3. N. G. de Bruijn,Asymptotic Methods in Analysis, Dover Publications, Inc., New York, 1981.

    Google Scholar 

  4. M. Drmota and U. Schmid,Exponential limiting distributions in queueing systems with deadlines, (1991) SIAM J. Appl. Math. (to appear).

  5. P. Flajolet,Analyse d'algorithmes de manipulation d'arbes et de fichiers, Thèse Paris-Sud-Orsay, 1979; Cahiers de BURO 34–35 (1981), 1–209.

  6. P. Flajolet and A. Odlyzko,Singularity analysis of generating functions, SIAM J. Disc. Math. 3 (1990), 216–240.

    Google Scholar 

  7. P. Flajolet, J. C. Raoult and J. Vuillemin,The number of registers required to evaluate arithmetic expressions, Theoret. Comput. Sci. 9 (1979), 99–125.

    Google Scholar 

  8. P. Kirschenhofer and H. Prodinger,On the recursion depth of special tree traversal algorithms, Information and Computation 74, 15–32.

  9. L. Kleinrock,Queueing Systems, Vol. 1 and Vol. 2, John Wiley, New York, 1975.

    Google Scholar 

  10. D. E. Knuth,The Art of Computer Programing, Volume 1: Fundamental Algorithms. 2nd ed., Addison-Wesley, Reading, Mass., 1973.

    Google Scholar 

  11. D. E. Knuth,The Art of Computer Programming, Volume 3: Sorting and Searching., Addison-Wesley, Reading, Mass., 1973.

    Google Scholar 

  12. U. Schmid and J. Blieberger,Some investigations on FCFS scheduling in hard real-time applications, Journal of Computer and System Sciences (1991) (to appear).

  13. J. S. Vitter and P. Flajolet,Average-Case Analysis of Algorithms and Data Structures, Handbook of Theoretical Computer Science (J. van Leeuwen, ed.) (1990), North-Holland.

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Blieberger, J., Schmid, U. Fcfs-scheduling in a hard real-time environment under rush-hour conditions. BIT 32, 370–383 (1992). https://doi.org/10.1007/BF02074875

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  • DOI: https://doi.org/10.1007/BF02074875

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