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


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 


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


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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

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