Preemptive LCFS Scheduling in Hard Real-Time Applications

Abstract We investigate the real-time behaviour of a (discrete time) single server system with preemptive LCFS task scheduling. 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 deadline T. The tree approach, used for the derivation of our results, is also suitable for revisiting problems in queueing theory. Relying on a simple general probability model, asymptotic formulas concerning all moments of SRD(T) are determined; for instance, the expectation of SRD(T) is proved to grow exponentially in T, i.e., E[SRD (T)]∼Cϱ T T 3 2 for some ϱ > 1.