Advertisement

BIT Numerical Mathematics

, Volume 32, Issue 3, pp 370–383 | Cite as

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

  • J. Blieberger
  • U. Schmid
Part I Computer Science

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)]=c1+O(T−3) forT→∞, wherec1 denotes some constant. If the arrival rate equals the departure rate, we findE[SRD(T)]∼c2T i for somei≥2.

AMS Classification

05A15 05C05 68C15 68E10 

Keywords

real-time behaviour FCFS scheduling trees probability generating functions singularity analysis asymptotics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. A. Bender,Asymptotic methods in enumeration, SIAM Review 16 (1974), 485–515.Google Scholar
  2. 2.
    J. Blieberger and U. Schmid,Preemptive LCFS scheduling in hard real-time applications, Performance Evaluation (1991) (to appear).Google Scholar
  3. 3.
    N. G. de Bruijn,Asymptotic Methods in Analysis, Dover Publications, Inc., New York, 1981.Google Scholar
  4. 4.
    M. Drmota and U. Schmid,Exponential limiting distributions in queueing systems with deadlines, (1991) SIAM J. Appl. Math. (to appear).Google Scholar
  5. 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.Google Scholar
  6. 6.
    P. Flajolet and A. Odlyzko,Singularity analysis of generating functions, SIAM J. Disc. Math. 3 (1990), 216–240.Google Scholar
  7. 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. 8.
    P. Kirschenhofer and H. Prodinger,On the recursion depth of special tree traversal algorithms, Information and Computation 74, 15–32.Google Scholar
  9. 9.
    L. Kleinrock,Queueing Systems, Vol. 1 and Vol. 2, John Wiley, New York, 1975.Google Scholar
  10. 10.
    D. E. Knuth,The Art of Computer Programing, Volume 1: Fundamental Algorithms. 2nd ed., Addison-Wesley, Reading, Mass., 1973.Google Scholar
  11. 11.
    D. E. Knuth,The Art of Computer Programming, Volume 3: Sorting and Searching., Addison-Wesley, Reading, Mass., 1973.Google Scholar
  12. 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).Google Scholar
  13. 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.Google Scholar

Copyright information

© BIT Foundations 1992

Authors and Affiliations

  • J. Blieberger
    • 1
  • U. Schmid
    • 1
  1. 1.Department of Automation (183/1) Technical University of ViennaWienÖsterreich

Personalised recommendations