Fcfs-scheduling in a hard real-time environment under rush-hour conditions
- 31 Downloads
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 Classification05A15 05C05 68C15 68E10
Keywordsreal-time behaviour FCFS scheduling trees probability generating functions singularity analysis asymptotics
Unable to display preview. Download preview PDF.
- 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).Google Scholar
- 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).Google Scholar
- 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.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.Google Scholar
- 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).Google Scholar
- 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