Scheduling Periodic Tasks in a Hard Real-Time Environment

Abstract

Abstract. We give a rigorous account on the complexity landscape of an important real-time scheduling problem that occurs in the design of software-based aircraft control. The goal is to distribute tasks τ i = (c i , p i ) on a minimum number of identical machines and to compute offsets a i for the tasks such that no collision occurs. A task τ i releases a job of running time c i at each time a i + k · p i , k ∈ N 0 and a collision occurs if two jobs are simultaneously active on the same machine. Our main results are as follows: (i) We show that the minimization problem cannot be approximated within a factor of n 1−ε for any ε > 0. (ii) If the periods are harmonic (for each i, j one has p i | p j or p j | p i ), then there exists a 2-approximation for the minimization problem and this result is tight, even asymptotically. (iii) We provide asymptotic approximation schemes in the harmonic case if the number of different periods is constant.

On the Complexity of Worst-Case Blocking Analysis of Nested Critical Sections

“…The intersection of the fields of real-time systems and computational complexity has received substantial attention in the past decades (e.g., see [26] for a survey of classic results), and intractability results for a variety of feasibility problems (e.g., [5,11,17,20,24]) and commonly used schedulability analysis methods have been established (e.g., [5,9,10]). 2 For instance, it is well known that the feasibility problem for periodic task sets is intractable [17].…”

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

“…However, as mentioned in [13], this later condition is very restrictive. In [14] Eisenbrand and al. proposed scheduling algorithms in the case of harmonic and non-harmonic tasks.…”

“…We can distinguish between the three following cases: The study of harmonic tasks is based on a bin tree [14], where each bin has a size equal to the smallest period T 1 . The initial bin contains a free slot of size equal to T 1 −C 1 .…”

“…As T 3 mod(T 2 ) = 6 = 0, then according to the condition (14) we have For τ c = τ 4 , the condition (8) is satisfied by τ 1 and τ c : C c = 1 and C 1 · δ (T c mod(T 1 )) = 2 · δ (27mod(9)) = 2. Thus, the task τ 4 is schedulable.…”

Schedulability analysis for independent partitions in integrated modular avionics systems

“…Faced with the significantly increasing number of partitions, the system designers gradually tend to rely on decision-making tools to produce valid scheduling tables for IMA systems. Meanwhile, for the avionics company, it is preferable to reallocate the start times and processors for all partitions only, rather than to redesign and rebuild the entire system [5]. Hence, it is desirable to develop an effective method, which determines whether all partitions in an IMA system are schedulable and provides valid allocations if they are schedulable.…”