Parameter variability and the existence of complex constraints between tasks are assured features of real-time scheduling. {\em Periodicity} of task sets is an additional feature that needs to be accomodated. Traditional scheduling models ignore the complexities involved in real-time scheduling by making simplistic assumptions about task interactions. In this paper, we present a model that captures the issues that we deem central to real-time scheduling in periodic task sets and demonstrate the existence of efficient and easily implementable algorithms for addressing schedulability queries in this model. Our model is very general and applicable to diverse areas ranging from real-time process scheduling in operating systems and avionics to manufacturing and traffic control. (Also cross-referenced as UMIACS-TR-2000-25)