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

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.