On Modeling Real-Time Task Systems

1 I n t r o d u c t i o n One of the fundamental problems in real-t ime research is to devise accurate yet tractable mathemat ica l models for real-t ime tasks. Liu & Layland introduced the basic periodic model in 1973 [13]. Since then, there have been many variations of it. Mok relaxed it with the sporadic model [14]. Leung ~ Whitehead considered the periodic model with start ing t ime [12]. Mok &= Chen later considered the variation of execution t ime and proposed a mul t i f rame model [15]. Baruah et. al. further introduced generalized mult i f rame model [1]. The scheduling of different models has also been extensively analyzed in other li teratures [4, 6, 10, 11, 17, 18]. In this paper, we take a look at the modeling itself and try to organize different models and their feasibility difficulties into a uniformed structure. Some of the work in above li terature are recited or reproduced to make this chapter a selfcontained unit. There is yet another type of models in which the parameters of each task depend on how they are scheduled. Harbour et. al. introduced a two-level(tasksubtask) model [9] where the real-time requirement of a subtask depends on how the previous subtask is scheduled; Han at. al. introduced the distance constrained real-t ime task where the finishing t imes of consecutive jobs must not be separated larger than a min imum t ime [8]. In this work we will concentrate on independent task models where the parameters of a task does not depend on how it is scheduled.