Periodic multiprocessor scheduling

Abstract

A number of scheduling and assignment problems are presented involving the execution of periodic operations in a multiprocessor environment. We consider the computational complexity of these problems and propose approximation algorithms for operations with identical periods as well as for operations with arbitrary integer periods.

Scheduling non-preemptive hard real-time tasks with strict periods

“….., n} be a set of tasks scheduled according to the condition (7), and τ c a candidate task which satisfies the condition (8). τ c can be scheduled N c times with the initial start times S 1 c given by…”

“…In order to schedule a set of non-preemptive tasks with strict periods, it is enough to study the behaviors of these tasks for a time interval equal to the LCM (Least Common Multiple), called the hyper-period [8].…”

Real-time Avionics Optimization

“…Instead, it seems much more reasonable to introduce one single variable for each task which represents its start offset. In order to be able to formulate with such variables that no two tasks on the same processor execute a job at the same time, we used a structural lemma [3]. The lemma proves an exact mathematical characterization on when two tasks on the same processor collide, depending on their offsets, their periods, and processing times.…”

Solving an Avionics Real-Time Scheduling Problem by Advanced IP-Methods

“…The periodic maintenance problem was introduced by Wei and Liu [WL83] in the context of single machine and unit execution times. Baruah et al [BRTV90] and independently Korst et al [KALW91,KAL96] show that the periodic maintenance problem is NP-hard. Moreover, minimizing the number of machines is hard to approximate within a factor of n 1−ε for any ε > 0 unless P = NP [EHN + 10,Bha98].…”