Applications to the Liu—Layland Problem and Pinwheel Scheduling
This chapter presents a fresh approach to two hard real-time classical sequencing problems: the Liu—Layland periodic sequencing problem and the (generalized) pinwheel scheduling problem. We show that a number of important results obtained in the literature on either of these two problems follow quite easily from the properties of just-in-time sequences with small bottleneck deviations. We also present new solutions to the Liu—Layland problem based on the quota-divisor methods of apportionment. This fresh approach sheds a new light on the connections between the just-in-time optimization and the apportionment problem on one side and the hard two real-time scheduling problems on the other.
The Liu-Layland periodic sequencing problem  is one of the most fundamental problems studied in hard real-time computing systems. A system is said to be real-time if the correctness of its operation depends not only on the logical correctness of the tasks making it but also on the time at which the tasks are performed. In a hard real-time system, the completion of a task after its deadline is considered useless and may ultimately lead to a critical failure of the whole system. For instance, a task may calculate a current position of an aircraft in C seconds but the position must be updated every T seconds. Missing a deadline may prove fatal for the aircraft and generally for the system, thus deadlines must not be missed. More details about hard real-time systems can be found in Cheng , and Butazzo .
KeywordsSchedule Problem Time Slot Periodic Schedule Bottleneck Problem House Size
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