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 deadline T 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 fulfil E[SRD(T)] = c, + O(T ') for T -+ m, where c, denotes some constant .If the arrival rate equals the departure rate, we find E[SRD(T)] c 2 T' for some i>2 . AMS Classification : OSA15, 05CO5, 68C15, 68E10 .