Some Investigations on FCFS Scheduling in Hard Real Time Applications

We investigate some real time behaviour of a (discrete time) single server system with FCFS task scheduling. The main results deal with the probability distribution of a random variable SRD(T), which describes the time the system operates without violating a fixed task service time deadline T. The tree approach used for the derivation of our results is suitable for revisiting problems already solved by queueing theory, too. Relying on a simple general probability model, asymptotic formulas concerning all moments of SRD(T) are determined; for example, the expectation of SRD(T) is proved to grow exponentially in T, i.e., E[SRD(T)] ∼ C · κT for some κ > 1.

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