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

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)]c₂Tⁱ for somei2.